Size 5
| Mean |
|---|
| 24.400 |
| 21.000 |
| 25.200 |
| 24.600 |
| 26.200 |
| 23.000 |
| 19.800 |
| 27.800 |
| 23.600 |
| 21.800 |
Ten independent samples of size 5; each row reports only the sample mean (x̄). Values are to three decimals.
| Number of Samples | Mean of Means |
|---|---|
| 1 | 26.600 |
| 2 | 27.500 |
| 3 | 26.867 |
| 4 | 26.150 |
| 5 | 26.040 |
| 6 | 26.033 |
| 7 | 26.600 |
| 8 | 25.625 |
| 9 | 25.778 |
| 10 | 25.460 |
| 20 | 24.730 |
| 30 | 24.347 |
| 40 | 24.190 |
| 50 | 24.084 |
| 60 | 24.210 |
| 70 | 24.154 |
| 80 | 24.097 |
| 90 | 24.044 |
| 100 | 24.000 |
| 200 | 24.238 |
| 300 | 24.177 |
| 400 | 24.044 |
| 500 | 23.989 |
| 600 | 24.010 |
| 700 | 23.979 |
| 800 | 23.987 |
| 900 | 23.998 |
| 1,000 | 23.988 |
Cumulative reporting: after each of the first 10 samples, then every 10 through 100, and every 100 through 1,000.
Size 25
| Mean |
|---|
| 24.400 |
| 23.480 |
| 23.960 |
| 24.400 |
| 23.120 |
| 23.440 |
| 23.840 |
| 24.840 |
| 25.360 |
| 23.040 |
Ten independent samples of size 25; each row reports only the sample mean (x̄). Values are to three decimals.
| Number of Samples | Mean of Means |
|---|---|
| 1 | 25.440 |
| 2 | 24.940 |
| 3 | 23.440 |
| 4 | 23.140 |
| 5 | 23.512 |
| 6 | 23.913 |
| 7 | 24.046 |
| 8 | 24.265 |
| 9 | 24.267 |
| 10 | 24.392 |
| 20 | 24.344 |
| 30 | 24.377 |
| 40 | 24.365 |
| 50 | 24.274 |
| 60 | 24.317 |
| 70 | 24.216 |
| 80 | 24.204 |
| 90 | 24.209 |
| 100 | 24.192 |
| 200 | 24.062 |
| 300 | 24.098 |
| 400 | 24.040 |
| 500 | 24.043 |
| 600 | 24.041 |
| 700 | 24.015 |
| 800 | 23.991 |
| 900 | 24.001 |
| 1,000 | 23.989 |
Cumulative reporting: after each of the first 10 samples, then every 10 through 100, and every 100 through 1,000.
Size 100
| Mean |
|---|
| 23.190 |
| 22.560 |
| 24.160 |
| 23.730 |
| 24.300 |
| 24.650 |
| 22.240 |
| 24.800 |
| 24.100 |
| 23.570 |
Ten independent samples of size 100; each row reports only the sample mean (x̄). Values are to three decimals.
| Number of Samples | Mean of Means |
|---|---|
| 1 | 23.380 |
| 2 | 23.785 |
| 3 | 23.837 |
| 4 | 23.918 |
| 5 | 23.858 |
| 6 | 23.845 |
| 7 | 23.910 |
| 8 | 24.059 |
| 9 | 24.028 |
| 10 | 23.932 |
| 20 | 23.871 |
| 30 | 23.864 |
| 40 | 23.967 |
| 50 | 23.991 |
| 60 | 24.051 |
| 70 | 24.106 |
| 80 | 24.093 |
| 90 | 24.079 |
| 100 | 24.069 |
| 200 | 24.054 |
| 300 | 24.032 |
| 400 | 24.046 |
| 500 | 24.025 |
| 600 | 24.025 |
| 700 | 24.029 |
| 800 | 24.022 |
| 900 | 24.009 |
| 1,000 | 24.016 |
Cumulative reporting: after each of the first 10 samples, then every 10 through 100, and every 100 through 1,000.
Size 1000
| Mean |
|---|
| 23.682 |
| 23.735 |
| 23.971 |
| 23.936 |
| 23.796 |
| 23.683 |
| 24.001 |
| 23.728 |
| 24.039 |
| 23.629 |
Ten independent samples of size 1,000; each row reports only the sample mean (x̄). Values are to three decimals.
| Number of Samples | Mean of Means |
|---|---|
| 1 | 23.761 |
| 2 | 23.901 |
| 3 | 24.021 |
| 4 | 24.054 |
| 5 | 24.084 |
| 6 | 24.027 |
| 7 | 24.044 |
| 8 | 24.033 |
| 9 | 24.030 |
| 10 | 23.995 |
| 20 | 23.936 |
| 30 | 23.952 |
| 40 | 23.945 |
| 50 | 23.963 |
| 60 | 23.995 |
| 70 | 23.991 |
| 80 | 23.987 |
| 90 | 23.994 |
| 100 | 23.999 |
| 200 | 24.001 |
| 300 | 23.999 |
| 400 | 24.004 |
| 500 | 24.009 |
| 600 | 24.005 |
| 700 | 24.002 |
| 800 | 24.003 |
| 900 | 24.000 |
| 1,000 | 24.001 |
Cumulative reporting: after each of the first 10 samples, then every 10 through 100, and every 100 through 1,000.
Methodology for Generating Values
Population. SWLS scores are integers from 5 to 35. We simulate a truncated normal so the truncated population has mean μ = 24 and SD = 6. We solve for parameters (μsim, σsim) of an underlying normal and truncate to [5,35].
Sampling. Each sample of size n is drawn independently with the same truncation and integer rounding used in the app. For each sample we compute only the mean x̄. For the cumulative table we report only the number of samples drawn and the mean of the accumulated sample means.