Null Hypothesis(H 0): The data are normally distributed.The normality test results would appear in the new windows.Select the “State” as the “By variables (optional).”.Click in the blank box right below “By variables (optional)” and “State” appears in the list box on the left.Select “Retail Price” as the “Variables.”.A window named “Graphical Summary” pops up.Click Stat → Basic Statistics → Graphical Summary.Step 1: Test the normality of the retail price for both state A and B. The null hypothesis is that the price in state A is equal to the price in state B. In this example we will be comparing the average price of a product in two different states. Alternative Hypothesis(H a) : μ 1 ≠ μ 2.Use Minitab to Run a Two-Sample T TestĬase study: We are trying to compare the average retail price of a product in state A and state B.ĭata File: “Two-Sample T Test” tab in “Sample Data.xlsx” If |t calc| < t crit, we fail to reject the null and claim there is not any statistically significant difference between the means of the two populations. Two sample t-test is more robust than a z-test when the sample size is small ( t crit, we reject the null and claim there is a statistically significant difference between the means of the two populations.The variances of both populations are unknown.

The data of both populations are normally distributed.

The data of both populations are continuous.

The sample data drawn from both populations are unbiased and representative.

Where: μ 1 is the mean of one population and μ 2 is the mean of the other population of our interest.

Alternative Hypothesis H a) : μ 1 ≠ μ 2.

This doesn't require you to make assumptions that you can't really be sure of, and it almost never makes much of a change in your results.Two sample t test is a hypothesis test to study whether there is a statistically significant difference between the means of two populations. The conservative choice is to use the 'Unequal Variances' column, meaning that the data sets are not pooled. For these reasons, the whole idea of pooling is controversial, and some textbooks don't even mention it as a possibility.įinally, even after you go through all that, pooling or not ('Equal Variances' column or 'Unequal Variances' column in StatTools results) usually makes only a minor difference. Also, an F test requires that both populations be normally distributed, not just approximately normal as with a t test, and you virtually never know for sure that the populations are normal. You can perform an F test, but even if you get a large p-value in the F test you have only failed to reject the hypothesis that the population variances are equal you haven't proved it. Some books and calculators use the term 'pooling'-if the variances are equal then you can 'pool the data sets', treating them as coming from one population.īut how can you know if the population variances are equal? Well, there's the rub: in the vast majority of cases you can't know. In turn that means your confidence interval is usually a bit narrower and you are more likely to be able to reject the null hypothesis. Higher degrees of freedom translate to a higher critical t and lower p-value. (Note: population variances, not sample variances.) Tha is usually (not always) a bit higher than the degrees of freedom computed by the general formula. However, if you know that the population variances are equal, you can use df = n 1 + n 2 − 2. For two-sample inferences, the general formula for degrees of freedom is shown at right. As you know, there are an infinite number of t distributions, each one determined by its degrees of freedom. The sampling distribution of the difference of sample means follows a Student's t distribution.

Unless you want more details, you can stop reading now. Here's the short answer: just use the Unequal Variances column. StatTools gives two columns of results, headed 'Equal Variances' and 'Unequal Variances'. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. 'Equal Variances' and 'Unequal Variances' in Two-Sample Inferences 'Equal Variances' and 'Unequal Variances' in Two-Sample Inferencesġ7.11.

Two sample unequal variance t test