Lecture 5 - The t-statistic, statistical hypothesis testing, one-sample and related-samples t-tests

Question 1

What are inferential statistics?

Answer 1

Statistics from a sample that we can uses to make inferences about parameters in a population.

Question 2

When we look at data from a sample and find the mean difference between a control group and an experimental group, we express it as______.

Answer 2

Cohen’s d

Question 3

To prove how significant the mean difference is, we use __________________.

Answer 3

Null hypothesis significance testing

Question 4

What are the 3 things that the t-value integrates?

Answer 4

1. How big the raw difference is between the means of two groups
2. The standard deviation - the mean difference relative to the variability in our data (Cohen’s d)
3. The sample size - standard error of the mean

Question 5

What does the distribution of the t-value allow us to do?

Answer 5

Make precise statements about the population in terms of probability.

Question 6

Why do we run a t-test?

Answer 6

To help us to determine whether a difference is “beyond reasonable doubt”.

It helps us to objectively decide whether or not the difference we observe could be due to sampling variability.

Question 7

What is Null Hypothesis Significance Testing?

Answer 7

A test which shows the likelihood of a set of sample data matching the null hypothesis. A t-test is a type of NHST.

Question 8

What is a Null Hypothesis?

Answer 8

The hypothesis (prediction) that there is no difference between the two sets of data that we are comparing.

Question 9

What is Standard Error of the Mean?

Answer 9

A measure of how accurately the sample mean represents the population mean.

Question 10

What is the formula to calculate Standard Error of the Mean?

Answer 10

SE = σ / √N

Standard error is σ divided by the square root of N

Key:
σ = standard deviation of the population
N = number of values in the sample

Question 11

Where does the Standard Error of the Mean come from?

Answer 11

The standard deviation of the sampling distribution of the means is the standard error of the mean.

Question 12

What is the sampling distribution of the means?

Answer 12

If we were to take the same sized sample from a population over and over again and plot the means of those samples on a histogram, this will give us an approximately normal distribution, similar to the distribution of the population but with a smaller standard deviation.

Question 13

Are the population mean and the mean of the sampling distribution the same?

Answer 13

Yes

Question 14

Are the population standard deviation and standard deviation of the sampling distribution (SE) the same?

Answer 14

No. The standard deviation of the sampling distribution is smaller.

Question 15

If the sample size is bigger, then the SE (the standard deviation of the sampling distribution) will be __________.

Answer 15

Smaller

Question 16

The smaller the SE, the more likely that the sample mean is ______________.

Answer 16

an accurate estimate of the population mean.

Question 17

The larger the sample size, the more accurately it will reflect __________.

Answer 17

the population.

Question 18

How can you reduce Standard Error when designing an experiment?

Answer 18

Use a bigger sample size

Question 19

The SE of the mean will be smaller when the sample size is _______.

Answer 19

larger.

Question 20

The SE of the mean will be smaller when the SD is _________.

Answer 20

smaller.

Question 21

Which one value tells us about the difference between the means of the samples, the variability of the scores in the samples, and the size of the samples.

Answer 21

The t-value / t-statistic

Question 22

In terms of SE, what does a t-value tell us?

Answer 22

How many Standard Errors separate the two means

Question 23

How should t-test results be reported?

Answer 23

example:

t(36) = 3.11, p = .004

The number in brackets is the degrees of freedom (N-1), the t-value is reported to 2dp and the p-value (probability) is reported to 3dp.

Question 24

What changes the shape of the t-distribution?

Answer 24

The sample size / degrees of freedom.

With a smaller sample size, the curve of the distribution is slightly flatter.

With infinite d.f the distribution would be exactly the same as the normal distribution. So, the bigger our sample size, the closer it will be to the shape of the normal distribution.

Question 25

How do you calculate the p-value?

Answer 25

The p-value is the probability that your t-value or a more extreme score exists in the null hypothesis distribution. Plot the t-value on the normal distribution curve and calculate the area under the curve for the smaller portion.

Question 26

What does a p-value of 0.05 or less mean?

Answer 26

It means that there is a significant difference between the means and therefore we reject the null hypothesis.

Question 27

What does “reject the null hypothesis” mean?

Answer 27

It means that we reject the idea that the two samples are the same. It means that we accept that there is a difference between the two samples that we are comparing, that an alternate hypothesis must be true.

Question 28

What does H₀ mean?

Answer 28

Null Hypothesis

Question 29

What does HA mean?

Answer 29

Alternate Hypothesis

Question 30

What is a p-value also known as?

Answer 30

Statistical significance

Question 31

If a t-value is large, it is likely that the p-value will be ________.

Answer 31

small.

Question 32

Conventionally, a p-value is deemed statistically significant if it is less than _____.

Answer 32

0.05

Question 33

What are the degrees of freedom for a one-sample t-test?

Answer 33

N-1

Because we only have one sample, one group of participants, we only take away 1.

Question 34

What are the degrees of freedom for an independent samples t-test?

Answer 34

N-2

Because we have two samples, two different groups of participants, we take away 2, one for each group.

Question 35

What are the degrees of freedom for a paired samples t-test?

Answer 35

N-1

Because although we have two samples, we only have one set of participants, so we only take away 1.

Question 36

If the degree of freedom is 30 or more we can assume that the t-distribution is ___________.

Answer 36

Normally distributed.