Lecture 3 and 4 - Hypothesis Testing - t-tests

Question 1

When do we use t-tests/t-statistic?

Answer 1

When we do not know the population standard deviation.

Question 2

What are the assumptions made about data when a t-test is used?

Answer 2

The assumptions made when doing a t-test with a set of data are:
That the data is distributed evenly.
That the samples/measures are independent.
That there is homogeneous variance between the samples.

Question 3

How do you determine the degrees of freedom when conducting a t-test?

Answer 3

Sample size - 1 or Sample size of both groups - 2.

It is a measure for how much data can vary freely.

Question 4

In regards to the distribution of data, a bigger sample size will have….?

Answer 4

A more normally distributed set of data.

Question 5

What are the three t-tests we discussed this semester?

Answer 5

Single-sample t-tests (comparing sample mean to a known value)

Paired-sample t-tests (comparing the mean of the same sample at different times. Looking for a difference across time/due to a certain treatment for example.

Independent-measures t-test (comparing the means of two different samples, such as comparing a control to a sample that received a treatment).

Question 6

What is the difference between standard deviation and standard error?

Answer 6

Stand deviation reflects the variance within a sample.
Standard error reflects/aims to reflect the variation of means of samples of a population.

Question 7

What does the standard error represent?

Answer 7

Standard error is an estimate of the standard deviation of a population. It is used when we do not know the population standard deviation.

Question 8

If t-empirical is greater than t-critical what does this mean?

Answer 8

It means that our data represents a statistically significant difference. And we can reject the Null Hypothesis.

Question 9

If we are just looking for whether there is a difference or not in our data compared to another set of data/value what kind of t-test would we use?

Answer 9

Two-tailed t-test.

Question 10

If we want to know whether our data is different in a particular direction, such as more than, what type of t-test do we use?

Answer 10

A one-tailed t-test.

Question 11

In regards to standard error, what does a smaller sample size do?

Answer 11

A smaller sample size results in a larger standard error which in turn results in a smaller t-value. This means that with a smaller sample it is less likely to get significant result.

Question 12

When doing an independent measures t-test we need to calculate the standard error of the mean difference.
In order to calculate the standard error of the mean difference we need to calculate the pooled variance.
What about the sample size comes into play here?

Answer 12

We can only calculate pooled variance if the sample sizes are the same (in the way we were shown in class, there are other ways to account for different sample sizes).

Question 13

When calculating the difference between two sample means using an independent measures t-test what are the two key things to remember?

Answer 13

We need to calculate pooled variance in order to determine the standard error of the mean difference.
Degrees of freedom is calculated by adding the sample sizes together and subtracting 2.

Question 14

When doing a paired-samples/repeated-measures t-test what are we measuring and how is it different to an independent-measures t-test?

Answer 14

In an independent measures t-test we are measuring the difference between two means and seeing if that difference is significant.
In a paired-samples t-test we are measuring whether the difference observed is significant. So we are looking at the mean difference and not the difference of means.

Question 15

What t-test looks at the mean difference and not the difference in means?

Answer 15

Paired-samples t-test.

Question 16

In paired-samples t-test what does the standard error used?

Answer 16

The standard error is the standard error of the differences in means and uses the standard deviation of the difference between means at two different times.

Question 17

What is one of the limitations of the t-statistic and how do we account for this?

Answer 17

One of the main limitations of the t-statistic is that whilst may be helpful in allowing us to determine whether a difference is significant or not it does not tell us how big the difference actually is.
This is because the t-statistic is very much influenced by the sample size. This means that if the sample size is big enough, enough then even a small difference will show up as significant.

Question 18

What is Cohen’s d and why do we use it?

Answer 18

Cohen’s d is a measure of effect size that is independent of sample size.
It is calculated by taking the mean difference and dividing it by the standard deviation of the difference (if doing a paired-samples t-test or independent-measures t-test) or just the standard deviation if doing a single sample t-test comparing with another known value.

Question 19

In 1988 Cohen suggested what different Cohen’s d values represented in terms of small, medium and large effect.
What are the values associated with these effect sizes?

Answer 19

Small effect is around d=0.2
Medium effect is around d=0.5
Large effect is around d=0.8