Question

2. Look at the table for the Paired samples test to find your t calculated, df, and significance. Remember that significance level will appear in the Sig (2-tailed) column. Any value that is smaller than .05 will be significant at the .05 level or higher. In a sentence describe the results and report them in APA style, including r² and evaluation (you will need to calculate r² by hand).

3. What type of error in hypothesis testing is possible given the above result? How likely is this error given r²?

4. Briefly describe why a paired samples t-test was calculated for the school IQ data, but an independent samples t-test was calculated for the depression and sleep data.

Paired Samples Statistics N Std. Deviation Std. Eror Mean Mean 115.1667 113.2500 Pair 1 10 for twin at school 12 6.67197 1.92603 1Q for twin at home 12 6.89038 1.98908 Paired Samples Correlations N CorelationSig | IQ fortuin at school & 10/ for twin at home Pair 1 12 893 Paired Samples Test Paired Differences 95 % Confidence Mean Std. Deviation Std. Bror Mean Lower 1.91667 1Q for twin at school - 10 for twin at home Pair 1 3.14667 .90836 -08263 Paired Samples Test Paired 95% Confidence Interval of the Upper 3.91596 dt Sig. (2-tailed) Pair 1 IQ for twin at school 10 for twin at home 2.110 .059

Answer 1

From the Paired samples test output,

t calculated = 2.110

df = 11

Significance = 0.059

$r^2$ = 0.893² = 0.797

Since the p-value (significance) is less than the 0.05 significance level, we reject the null hypothesis and conclude that there is significant evidence that the mean difference in IQ for twin at school and home is not zero.

3.

Since, we have rejected the null hypothesis, there may be chance that the null hypothesis is true. In this case, we are committing Type I error. So, Type I error is possible given the above result.

For a large $r^2$, the probability of committing Type I error is low.

4.

Paired samples t-test was calculated for the school IQ data because of the dependent samples in both groups (home and school). The IQ at school and at home were measured for the same twins.

Independent samples t-test was calculated for the depression and sleep data because the samples in two groups used were independent. That is, same people were not used in both the groups.