PSYC1040 Week 9

Question 1

Null hypothesis testing logic: decision outcomes and statistical power

Answer 1

• we want to assess the plausibility of chance as an explanation for our results (here, the different between SM and the population mean)
• so we assume the null hypothesis that only chance (sampling error) is operating and then calculate how often the mean as extreme as ours (or more) would be obtained, given our SS and the population parameters
• by convention, if we estimate that sampling error would produce a mean like our less than 5% of the time, we reject the Null hypothesis and accept the alternative hypothesis that something other than sample error was also involved; otherwise, we retain the Null Hypothesis

Question 2

Significance testing: decision outcomes and statistical power

Answer 2

• at the end of any Null Hypothesis Significance Test; we make a binary decision to either retain or reject the Null Hypothesis
• any binary decision can be described as having four outcomes:
• if the Null Hypothesis is true:
  ~ retaining H0 is the correct decision, called a true decision
  ~ rejecting H0 is the incorrect decision, called a false positive
• if the Null Hypothesis is fake:
  ~ retaining H0 is an incorrect decision, called a false negative

Question 3

Significance testing: decision outcomes and statistical power: true positive

Answer 3

• rejecting H0 is a correct decision, called a True Positive
• if H0 is true:
  ~ the false positive rate is equal to the significance decision threshold, normally 0.05 or 5% probability
  ~ the true negative rate is the complement of the threshold, typically 0.95
• when only sampling error is occurring, we’ll probably be wrong 5% of the time

Question 4

Significance testing: decision outcomes and statistical power: false

Answer 4

• if H0 is false: the true positive rate is called statistical power
• power depends on:
  ~ SS (through the SE)
  ~ the distance between means, measured in SD’s
  ~ the significance decision threshold
• increase power by:
  ~ increasing SS
  ~ reducing raviance
  ~ lowering your standards (relaxing the significance threshold)
  ~ increasing the mean difference

Question 5

Inferential tests: single sample z-tests

Answer 5

• purpose: testing a difference between a SM and a population mean
• requires a known or specified population variance

Question 6

Inferential tests: single sample t-tests

Answer 6

• like a z-test but uses estimated population variance and a t-table instead of a z-table

Question 7

Inferential tests: the repeated measures t-test

Answer 7

• typical purpose: testing whether a within-participants difference is larger than zero
• just a single sample t-test where the data are ‘difference scores’

Question 8

The independent groups t-test

Answer 8

• purpose: testing whether a between-participants difference is larger than zero, that is, testing a difference between the means of two groups of participants

Question 9

The single sample z-test: conditions and steps

Answer 9

Conditions ~
- we want to test how easily sampling error could explain the difference between our SM and a known population mean
- the population variance/SD is known
Steps ~
1. state the statistical hypothesis
2. calc the SE of the mean
3. calc the z-score for our obtained mean
4. compare the z-score to the critical z-score
5. interpret the result

Question 10

t-tests: when the population variance must be estimated

Answer 10

• usually we don’t know the population variance and we must estimate it from the sample scores
• by estimating the variance comes with two problems:
  1. sample variance tests to be smaller than population variance
  2. sample variance is subject to sampling error, so sample-based estimates of population variance are uncertain, especially from small samples

Question 11

Degrees of freedom

Answer 11

• for our purposes, just a number used to adjust test results for the number of scores and (later) the n.o of groups or conditions in the analysis

Question 12

The single sample t-test conditions and steps

Answer 12

conditions ~ same as the single sample z-test but the population variance is not known
Steps ~
1. state the statistical hypothesis
2. calc the sample-estimated SD
3. calc the sample-estimated SE of the mean
4. calc the t-score for our obtained mean
5. use the t-table to find the critical t-value based on df
6. compare t-obtained to t-critical
7. interpret results

Question 13

Repeated measures t-test

Answer 13

• for each participant, we find a difference score by subtracting their score in one situation from their score in the other
• we then treat those difference scores as a sample from a hypothesis population distribution of difference scores
• even if the true average difference between situations is zero, most difference scores won’t by zero and a sample mean difference score often won’t be either
• to see how often sampling error would produce an average difference score like the one we obtained in a study, we can run a t-test comparing our mean difference score to a hypothetical population mean difference score of 0.