T-test

Question 1

What is a z-score?

Answer 1

A z-score quantifies how many standard deviations an observation or data point is away from the mean

z = (x - μ) / σ

x = data point, u = mean, o = sd

Question 2

What is the mean and the sd of a z-score?

Answer 2

The mean will always be 0, and the sd 1

Question 3

What is one benifit of calculating a z-score?

Answer 3

It allows us to compare values on different scales.

Question 4

What is the equation for a one-sample t-test?

Answer 4

t = sampMean – popMean / estimatedpop(sd) / √n]

Question 5

What happens to our t-statistic if our mean and pop mean are close together? (one-sample)

Answer 5

One has a lower t-score as these numbers represent the numerator in the equation.

Question 6

What will happen to our t-statistic if n increases?

Answer 6

Our t-statistic is likely to increase as well.

Question 7

How is a t-distribution calculated, and how does it differ from a normal distribution?

Answer 7

This is obtained by averaging lots of possible choices for pop(sd). It is different from a normal distribution in that it has heavier tails.

Question 8

Why does the size of the rejection region change as n increases?

Answer 8

Becasue the t-distribution depends on the sample size. If sample size goes down, the distriubtion looks more wide. Up, and it becomes more tall and narrow.

Question 9

Why aren’t one-sided tests recomended?

Answer 9

Because they could be doubling your chance of a type I error.

Question 10

Why aren’t one-sided tests recomended?

Answer 10

Because they could be doubling your chance of a type I error.

Question 11

What is the same and what is different about a Welsh and Student t-test?

Answer 11

They both assume the population is normal, and that observations are independently sampled. Student population has equal variance, Welsh does not

Welsh is a safer test to run. Student estimates a pooled ‘sd’.

Question 12

Why is there a debate around checking for normality?

Answer 12

Tests are fairly robust to small violations of normality. Because it is always likely to show something is not normal with large enough samples sizes.

Question 13

When using a QQ-plot to asses normality, what should it look like and what is it using?

Answer 13

Should look like a scatter-plot where the value points represent percentiles. Normality is represented with a straight line.

limitation: have to eyeball a graph.

Question 14

What is one problem with a Shapio-Wilk test?

Answer 14

Often significant if sample size is too large (>50).

Question 15

What does a Shapiro-Wilk test print?

Answer 15

A W-score and a p-value.

a significant p = means not normal

Question 16

When testing normality assumption, what do you have to rememeber?

Answer 16

That this assumption is that each group is normally distributed. Not just one, or both groups combined.

Test has to be run on each group individually.

Question 17

What are non-paramatic tests? Give example + limitation.

Answer 17

These are tests that don’t make assumptions about the shape (normality) of a distribution. Not as powerful, can increase rate of Type II error. eg, Wilcoxon test

Question 18

What does a Wilcoxon test do?

Answer 18

Rather than testing the residuels it looks at each data point of two groups and counts how many times the value of one group is higher than the other. W-score output.

Null: you should expect W = approx. half the possible combinations.

Question 19

How should a t-statistic stat block look?

Answer 19

t(df) = t_sat, p-value

Question 20

How do you caluclate a cohen’s d?

Answer 20

d = mean1 - mean2 / sd

Question 21

Approx. reading of cohen’s d?

Answer 21

0.2 (small)
0.5 (med)
0.8 (large)

Question 22

What code do you need to include to run a student test?

Answer 22

var.equal=TRUE

Question 23

What code to run a one-sided test?

Answer 23

add alternative=“less” or
alternative=“greater” for t.test()