Week 7 day 2

Question 1

When do we use independent samples t-test?

Answer 1

When we have data from two independent samples and we want to know whether they are from the same population or not.

Question 2

What is the difference between a Student t-test and a Welch t-test?

Answer 2

The student t-test is dependent on homoscedasity between the two samples, i.e. they have the same variance/sd.

The Welch test can account for difference variance.

Question 3

What influences the size of the t-statistic?

Answer 3

1. How different the means are (obviously).
2. The degrees of freedom/ sample size.
3. The variance of the two sample. Increased variance decreases t.

Question 4

Should you always say that you use a Welch independent samples t-test?

Answer 4

Yes.

Question 5

What type of t-test do we use if the data of each sample is not independent?

Answer 5

A paired-samples t-test.

Question 6

Are paired-samples t-tests always repeated-measures tests?

Answer 6

No.
A paired samples t-test would also be used if there were multiple responses from an individual/s in different contexts.
In other words, for every row there are two data points.

Question 7

Is a repeated measures paired samples t-test essentially just a one sample t-test done on the mean difference in response at each time point?

Answer 7

Yes.

Question 8

What is the null hypothesis for a paired-sample t-test?

Answer 8

That the difference is 0.

Question 9

What are the assumptions required for doing t-tests?

Answer 9

1. That the distribution of the each population is normal.
2. The data are independent, unless you are doing a paired-samples t-test that allows for specific dependence.
3. For Student tests, the assumption is that the two groups being tested have the same variance.

Question 10

How do we test for normality of data?

Answer 10

One way is to use a quantile-quantile plot. This graphs the theoretical quantiles against the observed quantiles. If there is a straight line then we can assume normality.

Another way is to look at a histogram.

Both these require a qualitative judgement.

For a quantitative check, you can do a Shapiro-Wilk test.

Question 11

What are some of the reasons why checking for normality is not necessary?

Answer 11

1. Most statistical tests are quite robust against violations of normality.
2. Tests for normality will say any set of data is not normal if the sample size is large enough.

Question 12

What is the Shapiro-Wilk test?

Answer 12

It is a test for normality of data.

In R shapiro.test() generates a W stat and a p-value. A W less than 1 indicates data not normal.

The null for a shapiro-wilk test is that the data IS normally distributed. Therefore, a p value < .05 is saying that the data is NOT normally distributed.

Question 13

If you are testing for normality, do you need to test normality for the distribution of each sample/group?

Answer 13

Yes.

Question 14

When checking the normality of data in a paired-samples t-test, do we need to test normality of the difference or the two data sets?

Answer 14

A paired-samples t-test is a one-sample t-test on the difference between groups. This means that we need to check the normality of the difference variable, and not the distribution of each group.

Question 15

What are non-parametric tests?

Answer 15

These tests do not make assumptions about the shape of the distribution of the data, i.e. does not require that they are normally distributed.

Question 16

What are some short-comings with non-parametric tests?

Answer 16

They are not as powerful. There is a higher type II error rate.

Question 17

What is the non-parametric test equivalent to a t-test?

Answer 17

The Wilcoxon.

Question 18

Can we use Cohen’s D as an effect size for a Wilcoxon test?

Answer 18

No. This is because Cohen’s D assumes normality of data.

Question 19

Why would it be very bad if you accidentally used a paired-samples t-test instead of an independent-samples t-test (if you had independent samples, that is)?

Answer 19

Paired-samples t-tests have much greater likelihood of generating significant results, that is, they have a higher type I error rate when used on independent samples, because the null is 0.