3 Hypothesis testing

Question 1

Describe the steps you would take to take a hypothesis test to decide if the difference between 2 means was statistically significant?

Answer 1

1. Assume H0
2. Predict SE
3. Observed difference
4. T and P value (obs/SE)
5. Reject or accept H0

Question 2

What do we assume when doing a hypothesis test?

Answer 2

Assume normal distribution

Question 3

How would p value be affected if standard deviation increases?

Answer 3

If SD is bigger, SE is bigger so t is smaller (t=obs/SE) so p gets bigger as SD increases.
This makes sense- if the variability increases, the chance of getting an extreme value is higher

Question 4

Calculate 95% CI for a mean difference of 4 points, where SE is 0.5

Answer 4

4+-(1.96x0.5) = 3.02, 4.98

Question 5

What does the confidence interval tell us?

Answer 5

If 0 falls within the interval, then there is a 95% probability that there is no difference between the 2 means, so accept H0

Question 6

Describe the 2 types of error

Answer 6

1. Alpha error- false positive - rejected H0, but there is no difference
2. Beta error - false negative - accepted H0, but there is a difference

Question 7

What is power and how do you calculate it?

Answer 7

Power = Correct rejection
Power = 1-B

Question 8

How does having fewer sample numbers affect the SE?

Answer 8

Less samples = higher SE (more variability)

Question 9

How does fewer samples affect the likelihood of rejecting H0?

Answer 9

Fewer samples = higher SE = lower z value = higher p value = more likely to accept H0

Makes sense - more variation in data so higher chance of observed value to be in the expected range

Question 10

What is statistical power?

Answer 10

The probability of finding an effect if it is there
The probability of not making a Type 2 error

Question 11

What statistical power do we typically aim for?

Answer 11

80%
20% chance of making Type II error (false negative)

Question 12

Describe what a Type I and Type II error is?

Answer 12

Type I - false positive (rejecting H0, though H0 is true- there is no actual effect)
Type 2 - false negative (accepting H0, though H0 is false- this is actually an effect)

Question 13

What is p value?

Answer 13

Chance of the observed value if H0 is true

Question 14

What are the 4 factors that affect power and how do they affect it?

Answer 14

Sample size - greater sample size = more power
Effect size - greater observed effect = greater power
SD - greater SD = less power
Significance level desired - 99% vs 95% –> more = less power

Question 15

What does sigma mean in statistics?

Answer 15

Standard deviation

Question 16

Sample size calculations are not idealised. What do they not account for/assume?

Answer 16

They don’t account for losses to follow up in prospective studies
They assume individuals are independent observations

Question 17

When you do an independent 2 sample t test for hypothesis testing, what is the first thing you need to do? And what will come up on SPSS?

Answer 17

Normality check first using Kolmogorov-Smirnov
It will show the Levene’s Test for Equality of variance which will give you the p value labelled as sig.
If sig<0.05 (thinking reject so use assume not equal row)
If sig>0.05 (thinking accept H0 so use assume equal row)

Question 18

What test do we use instead of t test for Proportions?

Answer 18

Z test / chi square test

Question 19

What is the Z test?

Answer 19

a statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution.