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übersteigt (für ",[569,1874,1876,1901],{"className":1875},[572],[569,1877,1879],{"className":1878},[576],[578,1880,1881],{"xmlns":580},[582,1882,1883,1898],{},[585,1884,1885,1887,1889,1892,1894],{},[588,1886,1755],{},[723,1888,725],{},[1343,1890,1891],{},"5",[1746,1893,1748],{},[588,1895,1897],{"mathvariant":1896},"normal","%",[592,1899,1900],{"encoding":594},"\\alpha = 5\\,\\%",[569,1902,1904,1922],{"className":1903,"ariaHidden":599},[598],[569,1905,1907,1910,1913,1916,1919],{"className":1906},[603],[569,1908],{"className":1909,"style":608},[607],[569,1911,1755],{"className":1912,"style":1848},[612,613],[569,1914],{"className":1915,"style":872},[871],[569,1917,725],{"className":1918},[876],[569,1920],{"className":1921,"style":872},[871],[569,1923,1925,1929,1932,1936],{"className":1924},[603],[569,1926],{"className":1927,"style":1928},[607],"height:0.8056em;vertical-align:-0.0556em;",[569,1930,1891],{"className":1931},[612],[569,1933],{"className":1934,"style":1935},[871],"margin-right:0.1667em;",[569,1937,1897],{"className":1938},[612],": ",[569,1941,1943,1958],{"className":1942},[572],[569,1944,1946],{"className":1945},[576],[578,1947,1948],{"xmlns":580},[582,1949,1950,1955],{},[585,1951,1952],{},[1343,1953,1954],{},"3,841",[592,1956,1957],{"encoding":594},"3{,}841",[569,1959,1961],{"className":1960,"ariaHidden":599},[598],[569,1962,1964,1968,1972,1979],{"className":1963},[603],[569,1965],{"className":1966,"style":1967},[607],"height:0.8389em;vertical-align:-0.1944em;",[569,1969,1971],{"className":1970},[612],"3",[569,1973,1975],{"className":1974},[612],[569,1976,1978],{"className":1977},[1834],",",[569,1980,1982],{"className":1981},[612],"841"," bei einem, ",[569,1985,1987,2002],{"className":1986},[572],[569,1988,1990],{"className":1989},[576],[578,1991,1992],{"xmlns":580},[582,1993,1994,1999],{},[585,1995,1996],{},[1343,1997,1998],{},"5,991",[592,2000,2001],{"encoding":594},"5{,}991",[569,2003,2005],{"className":2004,"ariaHidden":599},[598],[569,2006,2008,2011,2014,2020],{"className":2007},[603],[569,2009],{"className":2010,"style":1967},[607],[569,2012,1891],{"className":2013},[612],[569,2015,2017],{"className":2016},[612],[569,2018,1978],{"className":2019},[1834],[569,2021,2023],{"className":2022},[612],"991"," bei zwei Freiheitsgraden).",[565,2026,2027,2028,2031,2032,2077,2078,2121],{},"Für eine ",[616,2029,2030],{},"Vierfeldertafel"," mit den Zellen ",[569,2033,2035,2055],{"className":2034},[572],[569,2036,2038],{"className":2037},[576],[578,2039,2040],{"xmlns":580},[582,2041,2042,2052],{},[585,2043,2044,2047,2049],{},[588,2045,2046],{},"a",[723,2048,1978],{"separator":599},[588,2050,2051],{},"b",[592,2053,2054],{"encoding":594},"a, b",[569,2056,2058],{"className":2057,"ariaHidden":599},[598],[569,2059,2061,2065,2068,2071,2074],{"className":2060},[603],[569,2062],{"className":2063,"style":2064},[607],"height:0.8889em;vertical-align:-0.1944em;",[569,2066,2046],{"className":2067},[612,613],[569,2069,1978],{"className":2070},[1834],[569,2072],{"className":2073,"style":1935},[871],[569,2075,2051],{"className":2076},[612,613]," (erste Zeile) und ",[569,2079,2081,2100],{"className":2080},[572],[569,2082,2084],{"className":2083},[576],[578,2085,2086],{"xmlns":580},[582,2087,2088,2097],{},[585,2089,2090,2092,2094],{},[588,2091,665],{},[723,2093,1978],{"separator":599},[588,2095,2096],{},"d",[592,2098,2099],{"encoding":594},"c, d",[569,2101,2103],{"className":2102,"ariaHidden":599},[598],[569,2104,2106,2109,2112,2115,2118],{"className":2105},[603],[569,2107],{"className":2108,"style":2064},[607],[569,2110,665],{"className":2111},[612,613],[569,2113,1978],{"className":2114},[1834],[569,2116],{"className":2117,"style":1935},[871],[569,2119,2096],{"className":2120},[612,613]," (zweite Zeile) gibt es eine Kurzformel:",[569,2123,2125],{"className":2124},[694],[569,2126,2128,2217],{"className":2127},[572],[569,2129,2131],{"className":2130},[576],[578,2132,2133],{"xmlns":580,"display":703},[582,2134,2135,2214],{},[585,2136,2137,2143,2145],{},[1416,2138,2139,2141],{},[588,2140,1420],{},[1343,2142,1423],{},[723,2144,725],{},[732,2146,2147,2171],{},[585,2148,2149,2151,2153,2155,2157,2159,2161,2163,2165],{},[588,2150,590],{},[1746,2152,1748],{},[723,2154,1484],{"stretchy":1483},[588,2156,2046],{},[588,2158,2096],{},[723,2160,1489],{},[588,2162,2051],{},[588,2164,665],{},[1416,2166,2167,2169],{},[723,2168,1495],{"stretchy":1483},[1343,2170,1423],{},[585,2172,2173,2175,2177,2180,2182,2184,2186,2188,2190,2192,2194,2196,2198,2200,2202,2204,2206,2208,2210,2212],{},[723,2174,1484],{"stretchy":1483},[588,2176,2046],{},[723,2178,2179],{},"+",[588,2181,2051],{},[723,2183,1495],{"stretchy":1483},[723,2185,1484],{"stretchy":1483},[588,2187,665],{},[723,2189,2179],{},[588,2191,2096],{},[723,2193,1495],{"stretchy":1483},[723,2195,1484],{"stretchy":1483},[588,2197,2046],{},[723,2199,2179],{},[588,2201,665],{},[723,2203,1495],{"stretchy":1483},[723,2205,1484],{"stretchy":1483},[588,2207,2051],{},[723,2209,2179],{},[588,2211,2096],{},[723,2213,1495],{"stretchy":1483},[592,2215,2216],{"encoding":594},"\\chi^2 = \\frac{n\\,(ad - bc)^2}{(a+b)(c+d)(a+c)(b+d)}",[569,2218,2220,2267],{"className":2219,"ariaHidden":599},[598],[569,2221,2223,2227,2258,2261,2264],{"className":2222},[603],[569,2224],{"className":2225,"style":2226},[607],"height:1.0585em;vertical-align:-0.1944em;",[569,2228,2230,2233],{"className":2229},[612],[569,2231,1420],{"className":2232},[612,613],[569,2234,2236],{"className":2235},[816],[569,2237,2239],{"className":2238},[820],[569,2240,2242],{"className":2241},[825],[569,2243,2246],{"className":2244,"style":2245},[829],"height:0.8641em;",[569,2247,2249,2252],{"style":2248},"top:-3.113em;margin-right:0.05em;",[569,2250],{"className":2251,"style":838},[837],[569,2253,2255],{"className":2254},[842,843,844,845],[569,2256,1423],{"className":2257},[612,845],[569,2259],{"className":2260,"style":872},[871],[569,2262,725],{"className":2263},[876],[569,2265],{"className":2266,"style":872},[871],[569,2268,2270,2274],{"className":2269},[603],[569,2271],{"className":2272,"style":2273},[607],"height:2.4271em;vertical-align:-0.936em;",[569,2275,2277,2280,2472],{"className":2276},[612],[569,2278],{"className":2279},[914,915],[569,2281,2283],{"className":2282},[732],[569,2284,2286,2463],{"className":2285},[820,821],[569,2287,2289,2460],{"className":2288},[825],[569,2290,2293,2385,2393],{"className":2291,"style":2292},[829],"height:1.4911em;",[569,2294,2295,2298],{"style":931},[569,2296],{"className":2297,"style":935},[837],[569,2299,2301,2304,2307,2310,2313,2316,2319,2322,2325,2328,2331,2334,2337,2340,2343,2346,2349,2352,2355,2358,2361,2364,2367,2370,2373,2376,2379,2382],{"className":2300},[612],[569,2302,1484],{"className":2303},[914],[569,2305,2046],{"className":2306},[612,613],[569,2308],{"className":2309,"style":893},[871],[569,2311,2179],{"className":2312},[897],[569,2314],{"className":2315,"style":893},[871],[569,2317,2051],{"className":2318},[612,613],[569,2320,1495],{"className":2321},[1026],[569,2323,1484],{"className":2324},[914],[569,2326,665],{"className":2327},[612,613],[569,2329],{"className":2330,"style":893},[871],[569,2332,2179],{"className":2333},[897],[569,2335],{"className":2336,"style":893},[871],[569,2338,2096],{"className":2339},[612,613],[569,2341,1495],{"className":2342},[1026],[569,2344,1484],{"className":2345},[914],[569,2347,2046],{"className":2348},[612,613],[569,2350],{"className":2351,"style":893},[871],[569,2353,2179],{"className":2354},[897],[569,2356],{"className":2357,"style":893},[871],[569,2359,665],{"className":2360},[612,613],[569,2362,1495],{"className":2363},[1026],[569,2365,1484],{"className":2366},[914],[569,2368,2051],{"className":2369},[612,613],[569,2371],{"className":2372,"style":893},[871],[569,2374,2179],{"className":2375},[897],[569,2377],{"className":2378,"style":893},[871],[569,2380,2096],{"className":2381},[612,613],[569,2383,1495],{"className":2384},[1026],[569,2386,2387,2390],{"style":944},[569,2388],{"className":2389,"style":935},[837],[569,2391],{"className":2392,"style":952},[951],[569,2394,2395,2398],{"style":955},[569,2396],{"className":2397,"style":935},[837],[569,2399,2401,2404,2407,2410,2413,2416,2419,2422,2425,2428,2431],{"className":2400},[612],[569,2402,590],{"className":2403},[612,613],[569,2405],{"className":2406,"style":1935},[871],[569,2408,1484],{"className":2409},[914],[569,2411,2046],{"className":2412},[612,613],[569,2414,2096],{"className":2415},[612,613],[569,2417],{"className":2418,"style":893},[871],[569,2420,1489],{"className":2421},[897],[569,2423],{"className":2424,"style":893},[871],[569,2426,2051],{"className":2427},[612,613],[569,2429,665],{"className":2430},[612,613],[569,2432,2434,2437],{"className":2433},[1026],[569,2435,1495],{"className":2436},[1026],[569,2438,2440],{"className":2439},[816],[569,2441,2443],{"className":2442},[820],[569,2444,2446],{"className":2445},[825],[569,2447,2449],{"className":2448,"style":1455},[829],[569,2450,2451,2454],{"style":1458},[569,2452],{"className":2453,"style":838},[837],[569,2455,2457],{"className":2456},[842,843,844,845],[569,2458,1423],{"className":2459},[612,845],[569,2461,858],{"className":2462},[857],[569,2464,2466],{"className":2465},[825],[569,2467,2470],{"className":2468,"style":2469},[829],"height:0.936em;",[569,2471],{},[569,2473],{"className":2474},[1026,915],[560,2476,2478],{"id":2477},"beispiele","Beispiele",[565,2480,2481,2482,2512],{},"Je ",[569,2483,2485,2499],{"className":2484},[572],[569,2486,2488],{"className":2487},[576],[578,2489,2490],{"xmlns":580},[582,2491,2492,2497],{},[585,2493,2494],{},[1343,2495,2496],{},"100",[592,2498,2496],{"encoding":594},[569,2500,2502],{"className":2501,"ariaHidden":599},[598],[569,2503,2505,2509],{"className":2504},[603],[569,2506],{"className":2507,"style":2508},[607],"height:0.6444em;",[569,2510,2496],{"className":2511},[612]," Personen aus Gruppe A und Gruppe B werden gefragt, ob sie ein Produkt kaufen würden:",[2514,2515,2516,2534],"table",{},[2517,2518,2519],"thead",{},[2520,2521,2522,2525,2528,2531],"tr",{},[2523,2524],"th",{},[2523,2526,2527],{},"ja",[2523,2529,2530],{},"nein",[2523,2532,2533],{},"Summe",[2535,2536,2537,2551,2564],"tbody",{},[2520,2538,2539,2543,2546,2549],{},[2540,2541,2542],"td",{},"Gruppe A",[2540,2544,2545],{},"60",[2540,2547,2548],{},"40",[2540,2550,2496],{},[2520,2552,2553,2556,2559,2562],{},[2540,2554,2555],{},"Gruppe B",[2540,2557,2558],{},"45",[2540,2560,2561],{},"55",[2540,2563,2496],{},[2520,2565,2566,2568,2571,2574],{},[2540,2567,2533],{},[2540,2569,2570],{},"105",[2540,2572,2573],{},"95",[2540,2575,2576],{},"200",[565,2578,2579,2580,2795,2796,3006,3007,3047],{},"Erwartete Häufigkeiten: ",[569,2581,2583,2621],{"className":2582},[572],[569,2584,2586],{"className":2585},[576],[578,2587,2588],{"xmlns":580},[582,2589,2590,2618],{},[585,2591,2592,2599,2601,2613,2615],{},[709,2593,2594,2596],{},[588,2595,713],{},[1343,2597,2598],{},"11",[723,2600,725],{},[732,2602,2603,2611],{},[585,2604,2605,2607,2609],{},[1343,2606,2496],{},[723,2608,730],{},[1343,2610,2570],{},[1343,2612,2576],{},[723,2614,725],{},[1343,2616,2617],{},"52,5",[592,2619,2620],{"encoding":594},"E_{11} = \\frac{100 \\cdot 105}{200} = 52{,}5",[569,2622,2624,2682,2776],{"className":2623,"ariaHidden":599},[598],[569,2625,2627,2630,2673,2676,2679],{"className":2626},[603],[569,2628],{"className":2629,"style":1358},[607],[569,2631,2633,2636],{"className":2632},[612],[569,2634,713],{"className":2635,"style":812},[612,613],[569,2637,2639],{"className":2638},[816],[569,2640,2642,2665],{"className":2641},[820,821],[569,2643,2645,2662],{"className":2644},[825],[569,2646,2648],{"className":2647,"style":1378},[829],[569,2649,2650,2653],{"style":833},[569,2651],{"className":2652,"style":838},[837],[569,2654,2656],{"className":2655},[842,843,844,845],[569,2657,2659],{"className":2658},[612,845],[569,2660,2598],{"className":2661},[612,845],[569,2663,858],{"className":2664},[857],[569,2666,2668],{"className":2667},[825],[569,2669,2671],{"className":2670,"style":1008},[829],[569,2672],{},[569,2674],{"className":2675,"style":872},[871],[569,2677,725],{"className":2678},[876],[569,2680],{"className":2681,"style":872},[871],[569,2683,2685,2689,2767,2770,2773],{"className":2684},[603],[569,2686],{"className":2687,"style":2688},[607],"height:1.1901em;vertical-align:-0.345em;",[569,2690,2692,2695,2764],{"className":2691},[612],[569,2693],{"className":2694},[914,915],[569,2696,2698],{"className":2697},[732],[569,2699,2701,2755],{"className":2700},[820,821],[569,2702,2704,2752],{"className":2703},[825],[569,2705,2708,2723,2731],{"className":2706,"style":2707},[829],"height:0.8451em;",[569,2709,2711,2714],{"style":2710},"top:-2.655em;",[569,2712],{"className":2713,"style":935},[837],[569,2715,2717],{"className":2716},[842,843,844,845],[569,2718,2720],{"className":2719},[612,845],[569,2721,2576],{"className":2722},[612,845],[569,2724,2725,2728],{"style":944},[569,2726],{"className":2727,"style":935},[837],[569,2729],{"className":2730,"style":952},[951],[569,2732,2734,2737],{"style":2733},"top:-3.394em;",[569,2735],{"className":2736,"style":935},[837],[569,2738,2740],{"className":2739},[842,843,844,845],[569,2741,2743,2746,2749],{"className":2742},[612,845],[569,2744,2496],{"className":2745},[612,845],[569,2747,730],{"className":2748},[897,845],[569,2750,2570],{"className":2751},[612,845],[569,2753,858],{"className":2754},[857],[569,2756,2758],{"className":2757},[825],[569,2759,2762],{"className":2760,"style":2761},[829],"height:0.345em;",[569,2763],{},[569,2765],{"className":2766},[1026,915],[569,2768],{"className":2769,"style":872},[871],[569,2771,725],{"className":2772},[876],[569,2774],{"className":2775,"style":872},[871],[569,2777,2779,2782,2786,2792],{"className":2778},[603],[569,2780],{"className":2781,"style":1967},[607],[569,2783,2785],{"className":2784},[612],"52",[569,2787,2789],{"className":2788},[612],[569,2790,1978],{"className":2791},[1834],[569,2793,1891],{"className":2794},[612]," und ",[569,2797,2799,2837],{"className":2798},[572],[569,2800,2802],{"className":2801},[576],[578,2803,2804],{"xmlns":580},[582,2805,2806,2834],{},[585,2807,2808,2815,2817,2829,2831],{},[709,2809,2810,2812],{},[588,2811,713],{},[1343,2813,2814],{},"12",[723,2816,725],{},[732,2818,2819,2827],{},[585,2820,2821,2823,2825],{},[1343,2822,2496],{},[723,2824,730],{},[1343,2826,2573],{},[1343,2828,2576],{},[723,2830,725],{},[1343,2832,2833],{},"47,5",[592,2835,2836],{"encoding":594},"E_{12} = \\frac{100 \\cdot 95}{200} = 47{,}5",[569,2838,2840,2898,2987],{"className":2839,"ariaHidden":599},[598],[569,2841,2843,2846,2889,2892,2895],{"className":2842},[603],[569,2844],{"className":2845,"style":1358},[607],[569,2847,2849,2852],{"className":2848},[612],[569,2850,713],{"className":2851,"style":812},[612,613],[569,2853,2855],{"className":2854},[816],[569,2856,2858,2881],{"className":2857},[820,821],[569,2859,2861,2878],{"className":2860},[825],[569,2862,2864],{"className":2863,"style":1378},[829],[569,2865,2866,2869],{"style":833},[569,2867],{"className":2868,"style":838},[837],[569,2870,2872],{"className":2871},[842,843,844,845],[569,2873,2875],{"className":2874},[612,845],[569,2876,2814],{"className":2877},[612,845],[569,2879,858],{"className":2880},[857],[569,2882,2884],{"className":2883},[825],[569,2885,2887],{"className":2886,"style":1008},[829],[569,2888],{},[569,2890],{"className":2891,"style":872},[871],[569,2893,725],{"className":2894},[876],[569,2896],{"className":2897,"style":872},[871],[569,2899,2901,2904,2978,2981,2984],{"className":2900},[603],[569,2902],{"className":2903,"style":2688},[607],[569,2905,2907,2910,2975],{"className":2906},[612],[569,2908],{"className":2909},[914,915],[569,2911,2913],{"className":2912},[732],[569,2914,2916,2967],{"className":2915},[820,821],[569,2917,2919,2964],{"className":2918},[825],[569,2920,2922,2936,2944],{"className":2921,"style":2707},[829],[569,2923,2924,2927],{"style":2710},[569,2925],{"className":2926,"style":935},[837],[569,2928,2930],{"className":2929},[842,843,844,845],[569,2931,2933],{"className":2932},[612,845],[569,2934,2576],{"className":2935},[612,845],[569,2937,2938,2941],{"style":944},[569,2939],{"className":2940,"style":935},[837],[569,2942],{"className":2943,"style":952},[951],[569,2945,2946,2949],{"style":2733},[569,2947],{"className":2948,"style":935},[837],[569,2950,2952],{"className":2951},[842,843,844,845],[569,2953,2955,2958,2961],{"className":2954},[612,845],[569,2956,2496],{"className":2957},[612,845],[569,2959,730],{"className":2960},[897,845],[569,2962,2573],{"className":2963},[612,845],[569,2965,858],{"className":2966},[857],[569,2968,2970],{"className":2969},[825],[569,2971,2973],{"className":2972,"style":2761},[829],[569,2974],{},[569,2976],{"className":2977},[1026,915],[569,2979],{"className":2980,"style":872},[871],[569,2982,725],{"className":2983},[876],[569,2985],{"className":2986,"style":872},[871],[569,2988,2990,2993,2997,3003],{"className":2989},[603],[569,2991],{"className":2992,"style":1967},[607],[569,2994,2996],{"className":2995},[612],"47",[569,2998,3000],{"className":2999},[612],[569,3001,1978],{"className":3002},[1834],[569,3004,1891],{"className":3005},[612],", in der zweiten Zeile ebenso. Jede Zelle weicht um ",[569,3008,3010,3025],{"className":3009},[572],[569,3011,3013],{"className":3012},[576],[578,3014,3015],{"xmlns":580},[582,3016,3017,3022],{},[585,3018,3019],{},[1343,3020,3021],{},"7,5",[592,3023,3024],{"encoding":594},"7{,}5",[569,3026,3028],{"className":3027,"ariaHidden":599},[598],[569,3029,3031,3034,3038,3044],{"className":3030},[603],[569,3032],{"className":3033,"style":1967},[607],[569,3035,3037],{"className":3036},[612],"7",[569,3039,3041],{"className":3040},[612],[569,3042,1978],{"className":3043},[1834],[569,3045,1891],{"className":3046},[612]," ab:",[569,3049,3051],{"className":3050},[694],[569,3052,3054,3108],{"className":3053},[572],[569,3055,3057],{"className":3056},[576],[578,3058,3059],{"xmlns":580,"display":703},[582,3060,3061,3105],{},[585,3062,3063,3069,3071,3077,3079,3099,3102],{},[1416,3064,3065,3067],{},[588,3066,1420],{},[1343,3068,1423],{},[723,3070,725],{},[1416,3072,3073,3075],{},[1343,3074,3021],{},[1343,3076,1423],{},[723,3078,730],{},[585,3080,3081,3083,3089,3091,3097],{},[723,3082,1484],{"fence":599},[732,3084,3085,3087],{},[1343,3086,1423],{},[1343,3088,2617],{},[723,3090,2179],{},[732,3092,3093,3095],{},[1343,3094,1423],{},[1343,3096,2833],{},[723,3098,1495],{"fence":599},[723,3100,3101],{},"≈",[1343,3103,3104],{},"4,51",[592,3106,3107],{"encoding":594},"\\chi^2 = 7{,}5^2 \\cdot \\left(\\frac{2}{52{,}5} + \\frac{2}{47{,}5}\\right) \\approx 4{,}51",[569,3109,3111,3155,3208,3396],{"className":3110,"ariaHidden":599},[598],[569,3112,3114,3117,3146,3149,3152],{"className":3113},[603],[569,3115],{"className":3116,"style":2226},[607],[569,3118,3120,3123],{"className":3119},[612],[569,3121,1420],{"className":3122},[612,613],[569,3124,3126],{"className":3125},[816],[569,3127,3129],{"className":3128},[820],[569,3130,3132],{"className":3131},[825],[569,3133,3135],{"className":3134,"style":2245},[829],[569,3136,3137,3140],{"style":2248},[569,3138],{"className":3139,"style":838},[837],[569,3141,3143],{"className":3142},[842,843,844,845],[569,3144,1423],{"className":3145},[612,845],[569,3147],{"className":3148,"style":872},[871],[569,3150,725],{"className":3151},[876],[569,3153],{"className":3154,"style":872},[871],[569,3156,3158,3161,3164,3170,3199,3202,3205],{"className":3157},[603],[569,3159],{"className":3160,"style":2226},[607],[569,3162,3037],{"className":3163},[612],[569,3165,3167],{"className":3166},[612],[569,3168,1978],{"className":3169},[1834],[569,3171,3173,3176],{"className":3172},[612],[569,3174,1891],{"className":3175},[612],[569,3177,3179],{"className":3178},[816],[569,3180,3182],{"className":3181},[820],[569,3183,3185],{"className":3184},[825],[569,3186,3188],{"className":3187,"style":2245},[829],[569,3189,3190,3193],{"style":2248},[569,3191],{"className":3192,"style":838},[837],[569,3194,3196],{"className":3195},[842,843,844,845],[569,3197,1423],{"className":3198},[612,845],[569,3200],{"className":3201,"style":893},[871],[569,3203,730],{"className":3204},[897],[569,3206],{"className":3207,"style":893},[871],[569,3209,3211,3215,3387,3390,3393],{"className":3210},[603],[569,3212],{"className":3213,"style":3214},[607],"height:2.4em;vertical-align:-0.95em;",[569,3216,3219,3228,3301,3304,3307,3310,3381],{"className":3217},[3218],"minner",[569,3220,3224],{"className":3221,"style":3223},[914,3222],"delimcenter","top:0em;",[569,3225,1484],{"className":3226},[3227,844],"delimsizing",[569,3229,3231,3234,3298],{"className":3230},[612],[569,3232],{"className":3233},[914,915],[569,3235,3237],{"className":3236},[732],[569,3238,3240,3289],{"className":3239},[820,821],[569,3241,3243,3286],{"className":3242},[825],[569,3244,3247,3267,3275],{"className":3245,"style":3246},[829],"height:1.3214em;",[569,3248,3249,3252],{"style":931},[569,3250],{"className":3251,"style":935},[837],[569,3253,3255,3258,3264],{"className":3254},[612],[569,3256,2785],{"className":3257},[612],[569,3259,3261],{"className":3260},[612],[569,3262,1978],{"className":3263},[1834],[569,3265,1891],{"className":3266},[612],[569,3268,3269,3272],{"style":944},[569,3270],{"className":3271,"style":935},[837],[569,3273],{"className":3274,"style":952},[951],[569,3276,3277,3280],{"style":955},[569,3278],{"className":3279,"style":935},[837],[569,3281,3283],{"className":3282},[612],[569,3284,1423],{"className":3285},[612],[569,3287,858],{"className":3288},[857],[569,3290,3292],{"className":3291},[825],[569,3293,3296],{"className":3294,"style":3295},[829],"height:0.8804em;",[569,3297],{},[569,3299],{"className":3300},[1026,915],[569,3302],{"className":3303,"style":893},[871],[569,3305,2179],{"className":3306},[897],[569,3308],{"className":3309,"style":893},[871],[569,3311,3313,3316,3378],{"className":3312},[612],[569,3314],{"className":3315},[914,915],[569,3317,3319],{"className":3318},[732],[569,3320,3322,3370],{"className":3321},[820,821],[569,3323,3325,3367],{"className":3324},[825],[569,3326,3328,3348,3356],{"className":3327,"style":3246},[829],[569,3329,3330,3333],{"style":931},[569,3331],{"className":3332,"style":935},[837],[569,3334,3336,3339,3345],{"className":3335},[612],[569,3337,2996],{"className":3338},[612],[569,3340,3342],{"className":3341},[612],[569,3343,1978],{"className":3344},[1834],[569,3346,1891],{"className":3347},[612],[569,3349,3350,3353],{"style":944},[569,3351],{"className":3352,"style":935},[837],[569,3354],{"className":3355,"style":952},[951],[569,3357,3358,3361],{"style":955},[569,3359],{"className":3360,"style":935},[837],[569,3362,3364],{"className":3363},[612],[569,3365,1423],{"className":3366},[612],[569,3368,858],{"className":3369},[857],[569,3371,3373],{"className":3372},[825],[569,3374,3376],{"className":3375,"style":3295},[829],[569,3377],{},[569,3379],{"className":3380},[1026,915],[569,3382,3384],{"className":3383,"style":3223},[1026,3222],[569,3385,1495],{"className":3386},[3227,844],[569,3388],{"className":3389,"style":872},[871],[569,3391,3101],{"className":3392},[876],[569,3394],{"className":3395,"style":872},[871],[569,3397,3399,3402,3406,3412],{"className":3398},[603],[569,3400],{"className":3401,"style":1967},[607],[569,3403,3405],{"className":3404},[612],"4",[569,3407,3409],{"className":3408},[612],[569,3410,1978],{"className":3411},[1834],[569,3413,3415],{"className":3414},[612],"51",[565,3417,3418,3419,684],{},"Die Kurzformel liefert denselben Wert: ",[569,3420,3422,3484],{"className":3421},[572],[569,3423,3425],{"className":3424},[576],[578,3426,3427],{"xmlns":580},[582,3428,3429,3481],{},[585,3430,3431,3477,3479],{},[732,3432,3433,3461],{},[585,3434,3435,3437,3439,3441,3443,3445,3447,3449,3451,3453,3455],{},[1343,3436,2576],{},[723,3438,730],{},[723,3440,1484],{"stretchy":1483},[1343,3442,2545],{},[723,3444,730],{},[1343,3446,2561],{},[723,3448,1489],{},[1343,3450,2548],{},[723,3452,730],{},[1343,3454,2558],{},[1416,3456,3457,3459],{},[723,3458,1495],{"stretchy":1483},[1343,3460,1423],{},[585,3462,3463,3465,3467,3469,3471,3473,3475],{},[1343,3464,2496],{},[723,3466,730],{},[1343,3468,2496],{},[723,3470,730],{},[1343,3472,2570],{},[723,3474,730],{},[1343,3476,2573],{},[723,3478,3101],{},[1343,3480,3104],{},[592,3482,3483],{"encoding":594},"\\frac{200 \\cdot (60 \\cdot 55 - 40 \\cdot 45)^2}{100 \\cdot 100 \\cdot 105 \\cdot 95} \\approx 4{,}51",[569,3485,3487,3652],{"className":3486,"ariaHidden":599},[598],[569,3488,3490,3494,3643,3646,3649],{"className":3489},[603],[569,3491],{"className":3492,"style":3493},[607],"height:1.4539em;vertical-align:-0.345em;",[569,3495,3497,3500,3640],{"className":3496},[612],[569,3498],{"className":3499},[914,915],[569,3501,3503],{"className":3502},[732],[569,3504,3506,3632],{"className":3505},[820,821],[569,3507,3509,3629],{"className":3508},[825],[569,3510,3513,3545,3553],{"className":3511,"style":3512},[829],"height:1.1089em;",[569,3514,3515,3518],{"style":2710},[569,3516],{"className":3517,"style":935},[837],[569,3519,3521],{"className":3520},[842,843,844,845],[569,3522,3524,3527,3530,3533,3536,3539,3542],{"className":3523},[612,845],[569,3525,2496],{"className":3526},[612,845],[569,3528,730],{"className":3529},[897,845],[569,3531,2496],{"className":3532},[612,845],[569,3534,730],{"className":3535},[897,845],[569,3537,2570],{"className":3538},[612,845],[569,3540,730],{"className":3541},[897,845],[569,3543,2573],{"className":3544},[612,845],[569,3546,3547,3550],{"style":944},[569,3548],{"className":3549,"style":935},[837],[569,3551],{"className":3552,"style":952},[951],[569,3554,3556,3559],{"style":3555},"top:-3.485em;",[569,3557],{"className":3558,"style":935},[837],[569,3560,3562],{"className":3561},[842,843,844,845],[569,3563,3565,3568,3571,3574,3577,3580,3583,3586,3589,3592,3595],{"className":3564},[612,845],[569,3566,2576],{"className":3567},[612,845],[569,3569,730],{"className":3570},[897,845],[569,3572,1484],{"className":3573},[914,845],[569,3575,2545],{"className":3576},[612,845],[569,3578,730],{"className":3579},[897,845],[569,3581,2561],{"className":3582},[612,845],[569,3584,1489],{"className":3585},[897,845],[569,3587,2548],{"className":3588},[612,845],[569,3590,730],{"className":3591},[897,845],[569,3593,2558],{"className":3594},[612,845],[569,3596,3598,3601],{"className":3597},[1026,845],[569,3599,1495],{"className":3600},[1026,845],[569,3602,3604],{"className":3603},[816],[569,3605,3607],{"className":3606},[820],[569,3608,3610],{"className":3609},[825],[569,3611,3614],{"className":3612,"style":3613},[829],"height:0.8913em;",[569,3615,3617,3621],{"style":3616},"top:-2.931em;margin-right:0.0714em;",[569,3618],{"className":3619,"style":3620},[837],"height:2.5em;",[569,3622,3626],{"className":3623},[842,3624,3625,845],"reset-size3","size1",[569,3627,1423],{"className":3628},[612,845],[569,3630,858],{"className":3631},[857],[569,3633,3635],{"className":3634},[825],[569,3636,3638],{"className":3637,"style":2761},[829],[569,3639],{},[569,3641],{"className":3642},[1026,915],[569,3644],{"className":3645,"style":872},[871],[569,3647,3101],{"className":3648},[876],[569,3650],{"className":3651,"style":872},[871],[569,3653,3655,3658,3661,3667],{"className":3654},[603],[569,3656],{"className":3657,"style":1967},[607],[569,3659,3405],{"className":3660},[612],[569,3662,3664],{"className":3663},[612],[569,3665,1978],{"className":3666},[1834],[569,3668,3415],{"className":3669},[612],[565,3671,3672,3673,3793,3794,3831,3832,3902,3903,3942],{},"Mit ",[569,3674,3676,3712],{"className":3675},[572],[569,3677,3679],{"className":3678},[576],[578,3680,3681],{"xmlns":580},[582,3682,3683,3709],{},[585,3684,3685,3687,3689,3691,3693,3695,3697,3699,3701,3703,3705,3707],{},[723,3686,1484],{"stretchy":1483},[1343,3688,1423],{},[723,3690,1489],{},[1343,3692,1492],{},[723,3694,1495],{"stretchy":1483},[723,3696,1484],{"stretchy":1483},[1343,3698,1423],{},[723,3700,1489],{},[1343,3702,1492],{},[723,3704,1495],{"stretchy":1483},[723,3706,725],{},[1343,3708,1492],{},[592,3710,3711],{"encoding":594},"(2-1)(2-1) = 1",[569,3713,3715,3736,3763,3784],{"className":3714,"ariaHidden":599},[598],[569,3716,3718,3721,3724,3727,3730,3733],{"className":3717},[603],[569,3719],{"className":3720,"style":1518},[607],[569,3722,1484],{"className":3723},[914],[569,3725,1423],{"className":3726},[612],[569,3728],{"className":3729,"style":893},[871],[569,3731,1489],{"className":3732},[897],[569,3734],{"className":3735,"style":893},[871],[569,3737,3739,3742,3745,3748,3751,3754,3757,3760],{"className":3738},[603],[569,3740],{"className":3741,"style":1518},[607],[569,3743,1492],{"className":3744},[612],[569,3746,1495],{"className":3747},[1026],[569,3749,1484],{"className":3750},[914],[569,3752,1423],{"className":3753},[612],[569,3755],{"className":3756,"style":893},[871],[569,3758,1489],{"className":3759},[897],[569,3761],{"className":3762,"style":893},[871],[569,3764,3766,3769,3772,3775,3778,3781],{"className":3765},[603],[569,3767],{"className":3768,"style":1518},[607],[569,3770,1492],{"className":3771},[612],[569,3773,1495],{"className":3774},[1026],[569,3776],{"className":3777,"style":872},[871],[569,3779,725],{"className":3780},[876],[569,3782],{"className":3783,"style":872},[871],[569,3785,3787,3790],{"className":3786},[603],[569,3788],{"className":3789,"style":2508},[607],[569,3791,1492],{"className":3792},[612]," Freiheitsgrad ist der kritische Wert ",[569,3795,3797,3810],{"className":3796},[572],[569,3798,3800],{"className":3799},[576],[578,3801,3802],{"xmlns":580},[582,3803,3804,3808],{},[585,3805,3806],{},[1343,3807,1954],{},[592,3809,1957],{"encoding":594},[569,3811,3813],{"className":3812,"ariaHidden":599},[598],[569,3814,3816,3819,3822,3828],{"className":3815},[603],[569,3817],{"className":3818,"style":1967},[607],[569,3820,1971],{"className":3821},[612],[569,3823,3825],{"className":3824},[612],[569,3826,1978],{"className":3827},[1834],[569,3829,1982],{"className":3830},[612],". Wegen ",[569,3833,3835,3854],{"className":3834},[572],[569,3836,3838],{"className":3837},[576],[578,3839,3840],{"xmlns":580},[582,3841,3842,3851],{},[585,3843,3844,3846,3849],{},[1343,3845,3104],{},[723,3847,3848],{},">",[1343,3850,1954],{},[592,3852,3853],{"encoding":594},"4{,}51 > 3{,}841",[569,3855,3857,3884],{"className":3856,"ariaHidden":599},[598],[569,3858,3860,3863,3866,3872,3875,3878,3881],{"className":3859},[603],[569,3861],{"className":3862,"style":1967},[607],[569,3864,3405],{"className":3865},[612],[569,3867,3869],{"className":3868},[612],[569,3870,1978],{"className":3871},[1834],[569,3873,3415],{"className":3874},[612],[569,3876],{"className":3877,"style":872},[871],[569,3879,3848],{"className":3880},[876],[569,3882],{"className":3883,"style":872},[871],[569,3885,3887,3890,3893,3899],{"className":3886},[603],[569,3888],{"className":3889,"style":1967},[607],[569,3891,1971],{"className":3892},[612],[569,3894,3896],{"className":3895},[612],[569,3897,1978],{"className":3898},[1834],[569,3900,1982],{"className":3901},[612]," wird die Unabhängigkeit auf dem ",[569,3904,3906,3924],{"className":3905},[572],[569,3907,3909],{"className":3908},[576],[578,3910,3911],{"xmlns":580},[582,3912,3913,3921],{},[585,3914,3915,3917,3919],{},[1343,3916,1891],{},[1746,3918,1748],{},[588,3920,1897],{"mathvariant":1896},[592,3922,3923],{"encoding":594},"5\\,\\%",[569,3925,3927],{"className":3926,"ariaHidden":599},[598],[569,3928,3930,3933,3936,3939],{"className":3929},[603],[569,3931],{"className":3932,"style":1928},[607],[569,3934,1891],{"className":3935},[612],[569,3937],{"className":3938,"style":1935},[871],[569,3940,1897],{"className":3941},[612],"-Niveau verworfen: Die Kaufbereitschaft hängt von der Gruppe ab.",[560,3944,3946],{"id":3945},"typische-fehler","Typische Fehler",[3948,3949,3950,3954,4129,4132],"ul",{},[3951,3952,3953],"li",{},"Die erwarteten Häufigkeiten als Gesamtzahl geteilt durch die Zellenzahl berechnen. Sie hängen von den Randsummen ab.",[3951,3955,3956,3957,4031,4032,684],{},"Die Freiheitsgrade als ",[569,3958,3960,3982],{"className":3959},[572],[569,3961,3963],{"className":3962},[576],[578,3964,3965],{"xmlns":580},[582,3966,3967,3979],{},[585,3968,3969,3971,3973,3975,3977],{},[588,3970,634],{},[723,3972,730],{},[588,3974,665],{},[723,3976,1489],{},[1343,3978,1492],{},[592,3980,3981],{"encoding":594},"r \\cdot c - 1",[569,3983,3985,4003,4022],{"className":3984,"ariaHidden":599},[598],[569,3986,3988,3991,3994,3997,4000],{"className":3987},[603],[569,3989],{"className":3990,"style":886},[607],[569,3992,634],{"className":3993,"style":649},[612,613],[569,3995],{"className":3996,"style":893},[871],[569,3998,730],{"className":3999},[897],[569,4001],{"className":4002,"style":893},[871],[569,4004,4006,4010,4013,4016,4019],{"className":4005},[603],[569,4007],{"className":4008,"style":4009},[607],"height:0.6667em;vertical-align:-0.0833em;",[569,4011,665],{"className":4012},[612,613],[569,4014],{"className":4015,"style":893},[871],[569,4017,1489],{"className":4018},[897],[569,4020],{"className":4021,"style":893},[871],[569,4023,4025,4028],{"className":4024},[603],[569,4026],{"className":4027,"style":2508},[607],[569,4029,1492],{"className":4030},[612]," zählen. Richtig ist ",[569,4033,4035,4066],{"className":4034},[572],[569,4036,4038],{"className":4037},[576],[578,4039,4040],{"xmlns":580},[582,4041,4042,4064],{},[585,4043,4044,4046,4048,4050,4052,4054,4056,4058,4060,4062],{},[723,4045,1484],{"stretchy":1483},[588,4047,634],{},[723,4049,1489],{},[1343,4051,1492],{},[723,4053,1495],{"stretchy":1483},[723,4055,1484],{"stretchy":1483},[588,4057,665],{},[723,4059,1489],{},[1343,4061,1492],{},[723,4063,1495],{"stretchy":1483},[592,4065,1508],{"encoding":594},[569,4067,4069,4090,4117],{"className":4068,"ariaHidden":599},[598],[569,4070,4072,4075,4078,4081,4084,4087],{"className":4071},[603],[569,4073],{"className":4074,"style":1518},[607],[569,4076,1484],{"className":4077},[914],[569,4079,634],{"className":4080,"style":649},[612,613],[569,4082],{"className":4083,"style":893},[871],[569,4085,1489],{"className":4086},[897],[569,4088],{"className":4089,"style":893},[871],[569,4091,4093,4096,4099,4102,4105,4108,4111,4114],{"className":4092},[603],[569,4094],{"className":4095,"style":1518},[607],[569,4097,1492],{"className":4098},[612],[569,4100,1495],{"className":4101},[1026],[569,4103,1484],{"className":4104},[914],[569,4106,665],{"className":4107},[612,613],[569,4109],{"className":4110,"style":893},[871],[569,4112,1489],{"className":4113},[897],[569,4115],{"className":4116,"style":893},[871],[569,4118,4120,4123,4126],{"className":4119},[603],[569,4121],{"className":4122,"style":1518},[607],[569,4124,1492],{"className":4125},[612],[569,4127,1495],{"className":4128},[1026],[3951,4130,4131],{},"Mit Prozentwerten statt absoluten Häufigkeiten rechnen.",[3951,4133,4134],{},"Ein signifikantes Ergebnis als Nachweis einer Ursache deuten. Der Test zeigt nur einen Zusammenhang.",{"title":4136,"searchDepth":4137,"depth":4137,"links":4138},"",2,[4139,4140,4141],{"id":562,"depth":4137,"text":563},{"id":2477,"depth":4137,"text":2478},{"id":3945,"depth":4137,"text":3946},[4143,4146,4149,4152,4155,4157,4160],{"lhs":4144,"rhs":4145},"100 * 105 \u002F 200","52.5",{"lhs":4147,"rhs":4148},"100 * 95 \u002F 200","47.5",{"lhs":4150,"rhs":4151},"(60 - 52.5)^2\u002F52.5 + (40 - 47.5)^2\u002F47.5 + (45 - 52.5)^2\u002F52.5 + (55 - 47.5)^2\u002F47.5","56.25 * (2\u002F52.5 + 2\u002F47.5)",{"lhs":4153,"rhs":4154},"round(56.25 * (2\u002F52.5 + 2\u002F47.5), 2)","4.51",{"lhs":4156,"rhs":4151},"200 * (60*55 - 40*45)^2 \u002F (100 * 100 * 105 * 95)",{"lhs":4158,"rhs":4159},"round(2 * (1 - 0.5 * (1 + erf(sqrt(3.841) \u002F sqrt(2)))), 3)","0.05",{"lhs":4161,"rhs":4162},"(a+b+c+d)*(a*d - b*c)^2 \u002F ((a+b)*(c+d)*(a+c)*(b+d))","(a - (a+b)*(a+c)\u002F(a+b+c+d))^2 \u002F ((a+b)*(a+c)\u002F(a+b+c+d)) + (b - (a+b)*(b+d)\u002F(a+b+c+d))^2 \u002F ((a+b)*(b+d)\u002F(a+b+c+d)) + (c - (c+d)*(a+c)\u002F(a+b+c+d))^2 \u002F ((c+d)*(a+c)\u002F(a+b+c+d)) + (d - (c+d)*(b+d)\u002F(a+b+c+d))^2 \u002F ((c+d)*(b+d)\u002F(a+b+c+d))","E_{ij} \\geq 5 \\text{ für alle Zellen (Faustregel)}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>5\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E_{ij} \\geq 5\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9694em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">5\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">für alle Zellen (Faustregel)\u003C\u002Fspan>",null,"md","chi-square-independence","\\chi^2 = \\sum_{i=1}^{r} \\sum_{j=1}^{c} \\frac{(N_{ij} - E_{ij})^2}{E_{ij}}, \\quad E_{ij} = \\frac{N_{i\\cdot} \\cdot N_{\\cdot j}}{n}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>χ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmfrac>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmrow>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\chi^2 = \\sum_{i=1}^{r} \\sum_{j=1}^{c} \\frac{(N_{ij} - E_{ij})^2}{E_{ij}}, \\quad E_{ij} = \\frac{N_{i\\cdot} \\cdot N_{\\cdot j}}{n}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0585em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">χ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:3.0652em;vertical-align:-1.4138em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2777em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4138em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9721em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0463em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3603em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">⋅\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">⋅\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fchi-quadrat-unabhaengigkeitstest",[],[4176,4177,4178,4179],"chi-square-test","contingency-table","independent-events","hypothesis-test",{"title":548,"description":4136},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fchi-quadrat-unabhaengigkeitstest","Der Chi-Quadrat-Unabhängigkeitstest prüft anhand einer Kreuztabelle, ob zwei Merkmale unabhängig sind.",[4184,4185,4186,4187,4188],"hypothesentest","kontingenztafel","unabhängigkeit","chi-quadrat-verteilung","kreuztabelle",[4190,4193,4196,4199,4203,4207,4211,4215],{"symbol":1426,"meaning":4191,"symbolHtml":4192},"Wert der Testgröße","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>χ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\chi^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0085em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">χ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":634,"meaning":4194,"symbolHtml":4195},"Anzahl der Zeilen (Ausprägungen des ersten Merkmals)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":665,"meaning":4197,"symbolHtml":4198},"Anzahl der Spalten (Ausprägungen des zweiten Merkmals)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4200,"meaning":4201,"symbolHtml":4202},"N_{ij}","beobachtete Häufigkeit in Zeile i und Spalte j","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">N_{ij}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9694em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4204,"meaning":4205,"symbolHtml":4206},"E_{ij}","erwartete Häufigkeit bei Unabhängigkeit","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E_{ij}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9694em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4208,"meaning":4209,"symbolHtml":4210},"N_{i\\cdot}","Summe der Zeile i","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation 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mtight\">⋅\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4212,"meaning":4213,"symbolHtml":4214},"N_{\\cdot j}","Summe der Spalte j","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>N\u003C\u002Fmi>\u003Cmrow>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">N_{\\cdot j}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9694em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">⋅\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":590,"meaning":4216,"symbolHtml":4217},"Gesamtzahl der Beobachtungen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","cEJRWc6xZJDCksHZHnvFmzADrEXT0LNkfenycwLPnmw",[4220,4223,4226,4229],{"stem":4221,"title":4222,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fchi-quadrat-anpassungstest","Chi-Quadrat-Anpassungstest",{"stem":4224,"title":4225,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fhypothesentest","Hypothesentest",{"stem":4227,"title":4228,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Funabhaengige-ereignisse","Stochastische Unabhängigkeit",{"stem":4230,"title":2030,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvierfeldertafel",1793824284913]