## How to Determine a p-Value When Testing a Null Hypothesis

in close agreement with the exact results. From this approximation we can see that the basic structure of a statistical test of hypothesis consists of the ratio of signal to noise. In our case, the signal is (pπ), the observed deviation from the null hypothesis, while the noise is the standard deviation of P:

Photo provided by Flickr

The test statistic for a linear regression is ts=/. It gets larger as the degrees of freedom (n−2) get larger or the r2 gets larger. Under the null hypothesis, the test statistic is t-distributed with n−2 degrees of freedom. When reporting the results of a linear regression, most people just give the r2 and degrees of freedom, not the ts value. Anyone who really needs the ts value can calculate it from the r2 and degrees of freedom.

## I’m stuck on how to value the null or alternative hypotheses

Photo provided by Flickr

Null hypothesis- SCL approach will have no effect on how primary school students learn English skills compared to when they’re taught using a teacher-centered approach

## Do not reject the null hypothesis C) ..

To illustrate how easy it is to fool yourself with time-series data, I tested the correlation between the number of moose on Isle Royale in the winter and the number of strikeouts thrown by major league baseball teams the following season, using data for 2004–2013. I did this separately for each baseball team, so there were 30 statistical tests. I'm pretty sure the null hypothesis is true (I can't think of anything that would affect both moose abundance in the winter and strikeouts the following summer), so with 30 baseball teams, you'd expect the P value to be less than 0.05 for 5% of the teams, or about one or two. Instead, the P value is significant for 7 teams, which means that if you were stupid enough to test the correlation of moose numbers and strikeouts by your favorite team, you'd have almost a 1-in-4 chance of convincing yourself there was a relationship between the two. Some of the correlations look pretty good: strikeout numbers by the Cleveland team and moose numbers have an r2 of 0.70 and a P value of 0.002:

## do not reject the null hypothesis ..

Fortunately, numerous simulation studies have shown that regression and correlation are quite robust to deviations from normality; this means that even if one or both of the variables are non-normal, the P value will be less than 0.05 about 5% of the time if the null hypothesis is true (Edgell and Noon 1984, and references therein). So in general, you can use linear regression/correlation without worrying about non-normality.

## interval and p-values to reject the null hypothesis

Regardless of the outcome of the chi-square test of independence, we would nothave been allowed to reject the hypothesis of independent assortment if we had observed more recombinant than parental offspring.

One final note on this last test.