Hypothesis Testing

Question 1

What is a hypothesis?

Answer 1

A testable statement which entrails our beliefs about our observations

Question 2

What is the null hypothesis (H0)?

Answer 2

That there will be no finding (no effect, association, relationship etc)

Question 3

What is the alternative hypothesis (H1)?

Answer 3

The characteristic being studied is different from zero

Question 4

What can you conclude with a two sided test?

Answer 4

The characteristic is different from zero but could be anything in either directiom

Question 5

What can you conclude with a one sided test?

Answer 5

The characteristic is EITHER larger than zero OR smaller than zero

Question 6

You can ________ or ___________ the null hypothesis but you cannot & _________ or _____________ it.

Answer 6

You reject or not reject the null hypothesis but you cannot accept or not accept it.

(Just because you did not find the treasure does not mean you can say for certain it isn’t there)

Question 7

You can ________ or ___________ the alternative hypothesis but you cannot _________ or _____________ it.

Answer 7

You can accept or not accept the alternative hypothesis but you cannot reject or not reject it.

(again, if you can’t find the treasure you can’t claim for certain that it is or isn’t there)

Question 8

What is a type I error?

Answer 8

A false positive (probability α) - the probability of rejecting the null hypothesis when actually it was true

e.g. positive covid test but you don’t have covid

Question 9

What is a type II error?

Answer 9

A false negative (probability β) - the nl hypothesis was not rejected but was false

e.g. negative covid test but you do have covid

Question 10

What is α significance level?

Answer 10

Usually set α < 0.05

If we find a difference, we are at least 95% confident that there is a difference (1-α)

(NOT rejecting the H0, and the H0 is true)

Question 11

What is Power?

Answer 11

Usually set at 0.80

If there is a difference, we are at least 80% confidence that we’d be able to find it.

(H0 is rejected and is false)

Question 12

What increases our ability to detect a difference and the power of our study?

Answer 12

▪️Increased sample size
▪️Increased effect size

Question 13

What are the four values involved in power analysis?

Answer 13

Need 3 of:

▪️Power (1-β) - usually 0.80
▪️α = 0.05 (probability of error allowed)
▪️Effect size
▪️Sample size (n)

Question 14

What is an a-priori power analysis?

Answer 14

Using a power analysis BEFORE the experiment to calculate the sample size needed to have at least 80% power to detect a difference with error margin of 0.05

(ES is based on past research)

Question 15

What is an a-posterior power analysis?

Answer 15

Using a power analysis AFTER our experiment to compute the power we actually had to detect a difference with error margin of 0.05

If we didn’t find the treasure, were we powerful enough to find it?

(Already have the sample size and ES)

Question 16

What is the rejection area?

Answer 16

The area where the probability of having an observation there is very low, if the null hypothesis is true (95% of times we wouldn’t observe a value here)

If the value is here, we reject the null hypothesis.

Question 17

What is the p-value?

Answer 17

The probability of observing a value equal or more extreme than our sample value under that null hypothesis

The probability of type 1 error (false positive)

Question 18

What do we conclude if the p-value is equal or less than 0.05?

Answer 18

We reject the hypothesis (the value is in the rejection zone, outside of the standard error 95% confidence interval)

Question 19

What do we conclude if the p-value is larger than 0.05?

Answer 19

We do not reject the null hypothesis (our value is not in the rejection area - it is not sufficiently different from the expected null hypothesis mean to believe it’s different)

Question 20

When hypothesis testing, which hypothesis do you use to create the sampling distribution?

Answer 20

The null hypothesis

(Using the null hypothesis mean but the sample statistics to estimate standard error)

Question 21

What test would we use to see whether our observed mean is equal to what is expected?

Answer 21

A one sample t-test

Is the population mean equal to a certain value?

t = (x-μ0)/SE, df = n-1

Question 22

What is the test value?

Answer 22

The value we our testing our sample again (the population mean if the null hypothesis is true)

Question 23

What test would you use to see whether the population proportion (π) is equal to a certain value (π0)?

Answer 23

One sample χ2 test (chi-square)

(e.g. is the frequency of women born in the same city they work in the same as the frequency of women born in a different city?)

Question 24

What type of test is chi-square?

Answer 24

Non-parametric

Question 25

What is the degree of freedom in a one sample t-test?

Answer 25

Sample size minus 1 (n-1)

Question 26

What is the degree of freedom in a one sample χ2 test?

Answer 26

Number of categories minus 1 (c-1)