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Calculating the sample size properly is crucial when using a matched pairs design. In matched pairs, each member of one group is paired with a member of another group based on specific criteria, like parent-child relationships in our case.
When determining the sample size from a t-test, you should look at the degrees of freedom (df). This is usually listed in scientific results in parentheses, right next to the t-score. Here, it was noted as 29, which means there are 29 degrees of freedom in this study.
This often suggests a straightforward calculation: the number of observations (i.e., pairs of participants) minus one gives you the df. Therefore, with 29 degrees of freedom, the total sample size is actually 30 parent-child pairs. This calculation is essential to ensure that the data interpreted covers all required comparative participants, which in this study, helps confirm the reliability of the results.

Understanding statistical significance is key in interpreting results, especially in psychological or social studies. In the given exercise, the findings indicated that parents spent significantly less time on social networking sites than their children, with a reported statistic of \( t(29) = 4.021 \), and a \( p \)-value of less than 0.05.
The \( p \)-value is a metric that helps researchers determine the probability that the observed results could happen by random chance. A \( p \)-value lower than 0.05 is typically considered statistically significant, like we observe here.
This implies there is strong evidence to suggest a real generational difference in behavior, in terms of social networking usage. It means the observed difference in time is likely not just by chance, hence the null hypothesis (which would state there is no difference) is rejected. Therefore, these results are significant enough to conclude the substantial difference between parents and their children in this context.

Effect size is a crucial part of understanding the magnitude or strength of a finding, beyond its statistical significance. In our exercise, the effect size is represented by Cohen's \( d \) value, which is given as 0.49.
Cohen's \( d \) provides a standardized means of measuring the difference between two means, which, in the context of matched pairs, helps understand how prominent the difference is in practical terms.

• Cohen suggested that a \( d \) value around 0.2 indicates a small effect,
• 0.5 indicates a medium effect,
• and a 0.8 indicates a large effect.

With a Cohen's \( d \) of 0.49, this study's effect size is on the border of small to medium. This suggests a moderate difference in the amount of time spent on social networking between parents and their children.
Even with statistical significance, the effect size provides insights into the real-world impact of the findings, marking this difference as meaningful but not vastly different across the generational line.