Basic Statistical Testing

To understand the results of any survey, two calculations are necessary: the margin of error and the statistical significance of any differences found. Click here for a basic explanation of the relevant statistic procedures. To conduct the calculations yourself, or to view the actual formulas, click on the appropriate link in the box at right.

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Basic Statistical Testing Options

Calculate the margin of error for ...

Proportions/Percentages Means

Test whether a difference is significant between two ...

Proportions/Percentages Means

Other analyses...

Chi-Square Calculation Formula

chi-sq = sum[(E_i,j - A_i,j) / E_i,j ]

where E_i,j represents the expected value for cell i, j

E_i,j = (T_i x T_j) / N T_i = sum of values in column i, T_j = sum of values in row j, N = total of values in table

A_i,j represents the actual value for cell i, j

For significance, test chi-sq against critical values for the Chi Square Distribution

df = (columns-1) x (rows-1)

                        Significance Level
        df       90%       95%       99%
         1    2.7055    3.8415    6.6349
         2    4.6052    5.9915    9.2104
         3    6.2514    7.8147   11.3449
         4    7.7794    9.4877   13.2767
         5    9.2363   11.0705   15.0863
         6   10.6446   12.5916   16.8119
         7    12.017   14.0671   18.4753
         8   13.3616   15.5073   20.0902
         9   14.6837    16.919    21.666
        10   15.9872    18.307   23.2093
        11    17.275   19.6752    24.725
        12   18.5493   21.0261    26.217
        13   19.8119    22.362   27.6882
        14   21.0641   23.6848   29.1412
        15   22.3071   24.9958    30.578
        16   23.5418   26.2962   31.9999
        17    24.769   27.5871   33.4087
        18   25.9894   28.8693   34.8052
        19   27.2036   30.1435   36.1908
        20    28.412   31.4104   37.5663
        21   29.6151   32.6706   38.9322
        22   30.8133   33.9245   40.2894
        23   32.0069   35.1725   41.6383
        24   33.1962    36.415   42.9798
        25   34.3816   37.6525    44.314
        26   35.5632   38.8851   45.6416
        27   36.7412   40.1133   46.9628
        28   37.9159   41.3372   48.2782
        29   39.0875   42.5569   49.5878
        30    40.256    43.773   50.8922
        31   41.4217   44.9853   52.1914
        32   42.5847   46.1942   53.4857
        33   43.7452   47.3999   54.7754
        34   44.9032   48.6024   56.0609
        35   46.0588   49.8018    57.342
        36   47.2122   50.9985   58.6192
        37   48.3634   52.1923   59.8926
        38   49.5126   53.3835    61.162
        39   50.6598   54.5722   62.4281
        40    51.805   55.7585   63.6908
        41   52.9485   56.9424     64.95
        42   54.0902    58.124   66.2063
        43   55.2302   59.3035   67.4593
        44   56.3685   60.4809   68.7096
        45   57.5053   61.6562   69.9569
        46   58.6405   62.8296   71.2015
        47   59.7743   64.0011   72.4432
        48   60.9066   65.1708   73.6826
        49   62.0375   66.3387   74.9194
        50   63.1671   67.5048   76.1538
        51   64.2954   68.6693    77.386
        52   65.4224   69.8322   78.6156
        53   66.5482   70.9934   79.8434
        54   67.6728   72.1532   81.0688
        55   68.7962   73.3115    82.292
        56   69.9185   74.4683   83.5136
        57   71.0397   75.6237   84.7327
        58   72.1598   76.7778   85.9501
        59   73.2789   77.9305   87.1658
        60    74.397    79.082   88.3794
        61   75.5141   80.2321   89.5912
        62   76.6302    81.381   90.8015
        63   77.7454   82.5287   92.0099
        64   78.8597   83.6752   93.2167
        65    79.973   84.8206    94.422
        66   81.0855   85.9649   95.6256
        67   82.1971    87.108   96.8277
        68   83.3079   88.2502   98.0283
        69   84.4179   89.3912   99.2274
        70    85.527   90.5313  100.4251
        71   86.6354   91.6703  101.6214
        72   87.7431   92.8083  102.8163
        73   88.8499   93.9453  104.0098
        74   89.9561   95.0815  105.2019
        75   91.0615   96.2167  106.3929
        76   92.1662    97.351  107.5824
        77   93.2702   98.4844  108.7709
        78   94.3735    99.617  109.9582
        79   95.4762  100.7486   111.144
        80   96.5782  101.8795  112.3288
        81   97.6796  103.0095  113.5123
        82   98.7803  104.1387  114.6948
        83   99.8805  105.2672  115.8762
        84    100.98  106.3949  117.0566
        85  102.0789  107.5217  118.2356
        86  103.1773  108.6479  119.4137
        87   104.275  109.7733  120.5909
        88  105.3723   110.898  121.7672
        89  106.4689   112.022  122.9422
        90   107.565  113.1452  124.1162
        91  108.6606  114.2679  125.2893
        92  109.7556  115.3898  126.4616
        93  110.8501   116.511   127.633
        94  111.9442  117.6317  128.8032
        95  113.0377  118.7516  129.9725
        96  114.1307  119.8709  131.1411
        97  115.2232  120.9897  132.3089
        98  116.3153  122.1077  133.4756
        99  117.4069  123.2252  134.6415
       100   118.498  124.3421  135.8069