5

The correlation coefficient in the qqplot can be used as a test for normality (in the case of a normal qqplot, or for some other null distribution model). See for instance this paper Developing a Test of Normality in the Classroom. But if the correlation in the plot is useful as an effect size, is another matter ... test statistics by themselves are not ...


3

Your setting describes a pretest-posttest-control group design, hence you should not use a (standardized) mean difference measure but a (standardized) measure of mean change. You can read a broad overview in Chapter 6 of the Cochrane Handbook and in Viechtbauer's documentation on conducting meta-analysis in R with the metafor package. What is mean change? ...


2

The exact conversion of a point-biserial correlation coefficient (i.e., the correlation between a binary and a numeric/quantitative variable) to a Cohen's d value is: $$d = \frac{r \sqrt{h}}{\sqrt{1-r^2}},$$ where $h = m/n_0 + m/n_1$, $m = n_0 + n_1 - 2$, and $n_0$ and $n_1$ are the number of 0's and 1's respectively. Here is some R code to demonstrate that ...


1

My guess is that your expectation is that the regression coefficients will be estimates of the contrasts you have coded. However, that is not the case. Let's look at just one three-level factor. Your coding is $$ \begin{align*} \mu_1 &= \beta_0 -2\beta_1 + 0\beta_2\\ \mu_2 &= \beta_0 +\beta_1 -\beta_2\\ \mu_3 &= \beta_0 + \beta_1 + \beta_2 \end{...


1

Regarding question 1, the use of the phrase "significantly increases" is a but dubious. You can reject the null and have the promotion increase sign up rate by a negligible amount (say half a percent). Under some circumstances, that is not a significant increase in the sign up, and yet the null is rejected. Its hard to put it in a phrase, but I ...


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