Question

T statistic

1. Why do we use the t statistic?
2. What is standard error?
3. What’s the difference between a one-sample t-test, an independent measures t test, and a repeated measures t-test?
4. Walk through the 5 steps of hypothesis testing using a one-sample t-test.
5. What are the assumptions of the t test?

One-way ANOVA

6. There are two sources of variation. What are they? Why do we care about them?
7. Why do we use ANOVA? In other words, why don’t we just use t-tests?
8. What are post hoc tests and why do we care about them?
9. What’s the distinction between a between subjects/groups ANOVA vs. within subjects/groups ANOVA?
10. What are the assumptions of ANOVA?

Answer 1

Why do we use the t statistic?

The t statistic is a measure of how extreme a statistical estimate is. You compute this statistic by subtracting the hypothesized value from the statistical estimate and then dividing by the estimated standard error. In many, but not all situation, the hypothesized value would be zero.

The t-statistic is sometimes also referred to as a t-test, t-ratio, or Wald statistic.

If the sample size is less than 30 and the population variance is not known then we use t-test otherwise we use z-test.

What is the standard error?

Standard error measures the statistical accuracy of an estimate. It's equal to the standard deviation/ root of n

What’s the difference between a one-sample t-test, an independent measures t-test, and a repeated measures t-test?

We use one-sample t-test in order to check for the difference between one sample and the population mean.

We use independent measures t-test to compare groups of participants that are not related in any way. So, we select the groups, which are independent of one another. So, subjects or individuals in one group have no relationship to participants in the second group. so, sometimes it is called as a between-subjects design.

We use repeated measures t-test to compare groups that are related in some way. There are many ways that participants in the two groups can be related. One way is that participants in the first group are the same as participants in the second group. This is sometimes called a repeated measures design. In this case, the same participants are measured at different points of time, to check if there difference in means of both measures.

Walkthrough the 5 steps of hypothesis testing using a one-sample t-test.

1)

Creating a null and alternate hypothesis.

2)

Creation of rejection region, based on the information the significance level α, and the critical value t_c

3)

Test statistic based on the given mean, standard deviation and n

4)

The decision about the null hypothesis.

Based on critical value and t-statistic we decide what will be the decision. We can use the p-value approach.

5)

Conclude the decision and find if the mean is different from the population mean.