Hypothesis Testing

Question 1

What do hypothesis test do?

Answer 1

Test whether a single value is the true parameter

Determine the strength of evidence against the proposition that the singular value is the true value

Question 2

What is the research hypothesis?

Answer 2

The hypothesis the research is designed to investigate

Question 3

What do you need to test a research hypothesis?

Answer 3

The null hypothesis and the alternative hypothesis

Question 4

What is the null hypothesis?

Answer 4

The hypothesis we test and determine how much evidence there is in the data to support this hypothesis
Denoted as H_0

Question 5

What is the alternative hypothesis?

Answer 5

It specifies a departure from the null hypothesis

If the null hypothesis is μ=3 then the alternative hypothesis isn’t equal to 3 (can be greater or less than)

Question 6

What is a one tailed test?

Answer 6

When you use a two sample test (comparing two groups) and specify a direction H1 :μA < μB or H1 :μA > μB

Question 7

How do hypothesis test work?

Answer 7

Estimate obtained from data and compared to what we expect to find assuming the null hypothesis is true
Evidence against null hypothesis provided by large discrepancy between data estimate and null

Question 8

What does a true difference between means mean?

Answer 8

More compelling if the values within group are tightly clustered

Question 9

Why would you use a test statistic?

Answer 9

Quantify how much our data estimate differs from the value in our null hypothesis

Question 10

How is a one sample t-test conducted?

Answer 10

Compare the data estimate to a known value

Question 11

How is the t-test statistic found?

Answer 11

(Data estimate - hypothesised value)/se(data estimate)

Question 12

When is the null hypothesis true?

Answer 12

The test statistic should be small as difference between test stat and hypothesised value is small

Question 13

When is the null hypothesis false?

Answer 13

Test stat is large as difference between test stat and hypothesised value is small

Question 14

How would you determine if the test statistic is typical under the null hypothesis?

Answer 14

Compare test stat to a reference distribution

Use t-distribution

Question 15

What is the p-value?

Answer 15

The probability of observing a test statistic at least as extreme as the one observed, given the null hypothesis is true

Question 16

What does the p-value measure?

Answer 16

Measures the strength of evidence against the null hypothesis?

Question 17

What value of the p-value would you reject the null hypothesis?

Answer 17

When p-value is really small, 0.001. If the p-value is 0.1 there is no evidence against the null hypothesis

Question 18

What does rejecting the null hypothesis mean?

Answer 18

Small p-value indicates the test stat is very unlikely to be obtained when the null hypothesis is true. Reject null in favour of alternative

Question 19

What is happening in a two sample t-test?

Answer 19

Comparing means from two groups (eg density for phase A and phase B)

Question 20

What would it mean if the p-value is very small in a two sample test?

Answer 20

Unlikely to obtain a test stat at least as extreme when the true underlying means are the same
Strong evidence that the means are not the same

Question 21

What tests should be used if the data is non-norma?

Answer 21

Non#parametric or distribution-free methods

Question 22

What test is the non-parametric alternative to the two sample t-test?

Answer 22

Mann-Whitney test

Question 23

In the Mann-Whitney test, what do the null and alternative hypothesis represent?

Answer 23

Null - no difference between the ranks of each group

Alternative - this is a difference between the ranks of each group