prac que's 1 Flashcards
assuming equal population variances required for ANOVA
levene’s test = null hypothesis is that the variables is equal
can assume equal when
The largest standard deviation (Stim1) was not more than double the smallest one (Stim2) – there is an old rule of thumb that uses this as a check for equality of variances.
Provide an interpretation for each of the follow-up comparisons made, within the context of the study.
want to look at multiple comparisons table and sig. colum to see differences btwn 3 groups
numbers are p values so if below 0.05, it is significant
what is the purpose of having a controlled group
We have evidence that Stim2 gives higher scores than Stim1 for the exercise task and could have seen this without the control group. However, without the control group we would not have been able to see that Stim1 itself was not effective.
Non-parametric statistical approaches require fewer assumptions than parametric analyses. Explain then why we should not simply use a non-parametric approach for all studies?
If assumptions are satisfied then parametric tests are more powerful than their nonparametric counterparts (although the difference can be minor). Parametric tests also provide direct estimates for effects, including confidence intervals. Nonparametric tests come with their own assumptions too.
Explain briefly what the Central Limit Theorem tells us and the role it plays in statistical inference.
The Central Limit Theorem says that the distribution of the sample mean is approximately Normal for sufficiently large samples. Since t tests and ANOVA are based on assuming the sample means have Normal distributions, this means that we can use these methods even if the data seem slightly skewed, particularly if the sample sizes are large.
The Pearson correlation coefficient was computed to be 0.59. How would you interpret this in the context of the study described?
There is a moderate positive association meaning that patients who had been in the program for more weeks tend to have higher functioning scores.
Based on your impressions of the scatterplot and the Pearson correlation coefficient would you consider it worthwhile to perform further analysis of this dataset? If so, what type of analysis would you perform?
The association seems to be stronger than what is reflected in a correlation of 0.59. This is likely due to a few large deviations from the overall pattern affecting the Pearson value. It may be worth using a non-parametric alternative here, such as Spearman’s rho. [Indeed, Spearman’s rho is 0.71 for this data.
Do you think this study was designed effectively in order to find a cause-and-effect relationship between number of weeks in the program and self-perceived daily functioning? Please explain your answer.
It is difficult to established cause and effect with an observational study. Even if it turns out to be a good predictor of daily functioning, it is not necessarily the case that the program participation has caused the improvement.
Would you feel confident about making a decision on the difference in effectiveness of the two programs based on this study? Briefly explain your answer.
Although there is very strong evidence of a difference, since the study is observational it is difficult to determine whether the Centre 1 program is less effective because of the program itself or because of some other factor (such as children with severe difficulties presenting more often at Centre 1 than at Centre 2).
