T-tests

Question 1

What is Standard Error of the mean and what is its importance?

Answer 1

Standard Error of the Mean (SEm ) is the measure used to reflect sampling error

SEM is the standard deviation of the sample means

SEM is an acknowledgment that our prediction of the population parameter is an educated guess

• Therefore, it is tied to a statement of the probability that the guess is right/wrong

SEm = SD / Sqr(N)

Question 2

How does Standard Error of the Mean change when Standard Deviation increases? Why?

Answer 2

Sem would increase, numerator gets bigger but why?

If our sample has a tight cluster of data, then probably we have a lot of people around the population mean,

Question 3

Why does the Standard Error of the Mean increase as sample size decreases?

Answer 3

If you increase your sample size, your data becomes more reflective of the true population = more confidence

Question 4

How do we interpret SeM

Answer 4

The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean.

Question 5

What happens to the probability of an error (α) as we increase our estimate of the range that we expect to contain the population mean (i.e. going from the 68% to 95% CI)?

Answer 5

It will decrease as we increase confidence

Question 6

What is hypothesis testing for a two-tailed test?

Answer 6

An objective method of establishing whether something is NOT true

Null Hypothesis (𝐻𝑜) – Any difference between our samples occurred due to chance (i.e. sampling error)

Alternate Hypothesis (𝐻𝐴) – Difference observed between our samples did not occur due to chance

Question 7

What is the use of an independent samples t- test? And 3 assumptions made when using it?

Answer 7

Establish the difference between two independent samples drawn from population

 Population, and therefore, samples are normally distributed
 Groups are mutually exclusive
 Homogeneity of variances (e.g. both groups have similar standard deviations)

Question 8

What is the degrees of freedom for s Independent samples t-test

Answer 8

𝑑f= (𝑁control −1) + (𝑁experimental −1)

Question 9

What are the problems with a independent t-test?

Answer 9

Assumes no relationship between groups

If there is, then variance gets double-counted.

An effect that may be present in a population may be missed when comparing our two samples

Run paired t-test to combat this

Question 10

What are the uses from a paired t-test and 3 assumptions?

Answer 10

Establish the difference between two means collected at different time points from the same sample
Assumptions:

 Population, and therefore, sample is normally distributed

 Same individuals are in both samples

 Homogeneity of variances (e.g. both time points have similar standard deviations)

𝑑f = 𝑁 − 1

Question 11

Why are the df for a paired samples t-test smaller than an independent samples t-test?

Answer 11

You are collecting from the same group in paired as opposed to two in a independent

Question 12

What are the 3 steps in interpreting a T test

Answer 12

Statement of what type of test was conducted, what the independent and

dependent variables were (typically done in methods section of a paper)

Describe whether the results are significant or not significant, provide relevant statistical information (t, df, p)

Interpret the statistical results relating back to the question of interest (e.g. if significant, go back and look at means to provide specific direction of difference)

Question 13

If you run a paired samples t-test when you have mutually exclusive groups are you more likely to get a Type I or Type II error? Why?

Answer 13

Think of answer

Question 14

What is cohens d?

Answer 14

The mean of the control + the mean of the experimental/ SD of control (measured in SD)

Used to measure effect size (How many standard deviations is the experimental group mean from the control group?)

Size

> 0.8 ~0.5 ~0.2

Interpretation

Large effect Moderate effect Small effect