Example: Calculating the p-value from a t-test by hand

Set the significance level, , the probability of making a Type I error to be small — 0.01, 0.05, or 0.10. Compare the P-value to . If the P-value is less than (or equal to) , reject the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than , do not reject the null hypothesis.

A p-value higher than 0.05 (> 0.05) is not statistically significant and indicates strong evidence for the null hypothesis. This means we retain the null hypothesis and reject the alternative hypothesis. You should note that you cannot accept the null hypothesis, we can only reject the null or fail to reject it.

1. Step 1: State the null and alternative hypotheses.
2. Step 2: Find the test statistic.
3. Step 3: Find the p-value for the test statistic. To find the p-value by hand, we need to use the t-Distribution table with n-1 degrees of freedom.
4. Step 4: Draw a conclusion.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 19.58. We use the Chi-Square Distribution Calculator to find P(Χ2 > 19.58) = 0.0001.

Interpret the key results for Chi-Square Test for Association

1. Step 1: Determine whether the association between the variables is statistically significant.
2. Step 2: Examine the differences between expected counts and observed counts to determine which variable levels may have the most impact on association.

A chi-square (χ2) statistic is a test that measures how a model compares to actual observed data. The chi-square statistic compares the size any discrepancies between the expected results and the actual results, given the size of the sample and the number of variables in the relationship.

Formulate an Analysis Plan Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used.

The null hypothesis of the Chi-Square test is that no relationship exists on the categorical variables in the population; they are independent.