Scheffe's Test Demo

Scheffe's test is a parametric multi-comparison procedure which tests the hypotheses that the means of each pair of waves are equal. In this example we consider the following six waves:

data1data2data3data4data5data6
36.34 58.55 50.42 41.41 47.81 38.17
52.08 57 40.04 64.21 46.28 36.96
50.09 44.9 41.77 58.33 59 38.28
37.81 52.66 42.61 60.37 55.73 33.13
58.98 67.99 37.75 55.32 54.58 39.97
63.93 52.98 41.42 55.75 43.74 47.99
37.55 51.1 39.48 63.74 59.02 49.66
40.64 47.96 43.79 67.86 46.75 42.51

1. Basic Scheffe's test.

To run the test execute the command:

StatsScheffeTest/T=1/Q data1,data2,data3,data4,data5,data6

The results are displayed in the Scheffe Test table:

PairDiffSESSaConclusion
data6_vs_data1 -6.34375 3.61625 1.75424 3.4912 1
data6_vs_data2 -13.3087 3.61625 3.68027 3.4912 0
data6_vs_data3 -1.32625 3.61625 0.366748 3.4912 1
data6_vs_data4 -17.54 3.61625 4.85033 3.4912 0
data6_vs_data5 -10.78 3.61625 2.98099 3.4912 1
data5_vs_data1 4.43625 3.61625 1.22676 3.4912 1
data5_vs_data2 -2.52875 3.61625 0.699275 3.4912 1
data5_vs_data3 9.45375 3.61625 2.61424 3.4912 1
data5_vs_data4 -6.76 3.61625 1.86934 3.4912 1
data4_vs_data1 11.1962 3.61625 3.0961 3.4912 1
data4_vs_data2 4.23125 3.61625 1.17007 3.4912 1
data4_vs_data3 16.2138 3.61625 4.48359 3.4912 0
data3_vs_data1 -5.0175 3.61625 1.38749 3.4912 1
data3_vs_data2 -11.9825 3.61625 3.31352 3.4912 1
data2_vs_data1 6.965 3.61625 1.92603 3.4912 1

The table indicates that hypotheses μ62, μ64 and μ43 must be rejected while the remaining hypotheses for the equality of the means are accepted.

2. Testing multiple contrasts.

The contrast hypothesis is defined by a contrast wave. For example, if

Picture0

denotes the mean of the wave datai then to test the hypothesis

Picture1

We start by creating the contrast wave:

Make/N=6/O cWave={1,2,1,2,2,1}

Next we execute the test:

StatsScheffeTest/T=1/Q/CONW=cWave data1,data2,data3,data4,data5,data6

The results are displayed in the Scheffe test table (shown here transposed):

Difference 11.3196
SE 2.08784
S 5.42167
Salpha 3.4912
Conclusion 0

As the statistic S exceeds the critical value Salpha we reject the contrast H0.