Comparing means and proportions

Question 1

If the value is more than 0.05 is this value significant statistically?

Answer 1

If its bigger than 0.05 it is NOT statistically significant.

If it is less than 0.05 it is statistically significant

Question 2

Is 0.67 significant?

Answer 2

No - more than 0.05

Question 3

Is 0.003 significant?

Answer 3

Yes - less than 0.05

Question 4

If data is categorical, what are the 3 types of test we would carry out?

Answer 4

One sample X2 test - one sample
Pearsons chi-square test - two independent samples
McNemar test - two paired samples

Question 5

If data is numerical, what are the 3 types of test we would carry out?

Answer 5

One sample t-test
Independent sample t-test
Paired sample t-test

Question 6

What is the symbol for the ‘known population’

Answer 6

U0

Question 7

When we conduct a test to compare means or proportions, we use the result to work out if we can reject the null hypothesis or not. How?

Answer 7

Compare against the P value, if less than 0.05 it is significant, if it is above 0.05 then it is not statistically significant

Question 8

With this hypothesis, what test would we use?
H0: μ=μ0
Ha: μ≠μ0

Answer 8

Is the population mean (μ) equal to a certain value (μ0) ?

One Sample T-test

Question 9

With this hypothesis, what test would we use?
H0: π=π0
Ha: π≠π0

Answer 9

Is the population proportion (π) equal to a certain value (π0) ?
One sample X2 test

Question 10

With this hypothesis, what test would we use?
H0: μA=μB
Ha: μA≠μB

Answer 10

In the population, is the mean of group A (μA) equal to the mean of group B (μB) ?
Two Independent samples t-test

Question 11

With this hypothesis, what test would we use?
H0: πA=πB
Ha: πA≠πB

Answer 11

In the population, are the proportions for each group (πΑ & πΒ) equal across the categories of the characteristic?
Pearsons chi-squared test

Question 12

With this hypothesis, what test would we use?
H0: μ1=μ2
Ha: μ1≠μ2

Answer 12

In the population, is the mean of a group in one condition (μ1) equal to the mean of the same (or
paired) group in another condition (μ2) ?
Two paired samples t-test

Question 13

With this hypothesis, what test would we use?
H0: π1=π2
Ha: π1≠π2

Answer 13

In the population, are the proportions for each group (π1 & π2) equal before and after?
McNemar test

Question 14

What is meant by parametric test?

Answer 14

Parametric testsas the sample mean is an estimator of a population parameter

Question 15

Give an example of…

a. one sample
b. independent sample
c. paired sample

Answer 15

a. Do prisoners have more divorced parents?
b. Do prisioners in the USA have more divorced parents than prisioners in the UK
c. Does sleeping pills make someone sleep better?

Question 16

Who came up with the 3 t-tests?

Answer 16

William S. Gosset

Question 17

What are the three main assumptions we must have before conducting a one sample t-test?

Answer 17

1. The observations are randomly and independently drawn
2. There are no outliers
3. Symmetrical data (approximately normally distributed)

Question 18

When interpreting the one sample t-test SPSS table what values do we need to look at?

Answer 18

The test value and the mean difference value. We look at the p-value to see if it is a significant finding. We also report the t value, df and CI

Question 19

What are the three main assumptions we must have before conducting a two independent sample t-test?

Answer 19

The observations are randomly and independently drawn
• Symmetrical data, within each group
• There are no outliers, within each group

Question 20

When interpreting the independent sample t-test SPSS table what values do we need to look at?

Answer 20

Need to look at the Levene test to see if the p value is significant. If it is significant, then we use the second/bottem line of the SPSS table. If it is not significant then we use the top line. We report the mean difference, t value, CI, P value and DF

Question 21

What are the three main assumptions we must have before conducting a paired sample t-test?

Answer 21

The (paired) observations are randomly and independently drawn
• The (paired) difference are is symmetrical continuous variable
• There are no outliers in the difference

Question 22

When interpreting the paired sample t-test SPSS table what values do we need to look at?

Answer 22

Look at the mean and the P value. We need to report the t value, CI, P value and DF

Question 23

What are the three main assumptions we must have before conducting a one sample chi-square (X2) test?

Answer 23

• The observations are randomly and independently drawn
- The number of cells with expected frequencies less than 5, are less than 20%
• The minimum expected frequency is at the very least 1.

Question 24

When interpreting the one sample chi-squared table what values do we need to look at?

Answer 24

SPSS prints a table with descriptive statistics and one with the one sample t-test.
We report the X2 value, df and p-value (this is the asymp. sig)
We need to make sure the cell expected frequency is below 20% and the minimun expected frequency needs to be larger than 1

Question 25

What did Karl Pearson invent?

Answer 25

Pearsons chi-square test

Question 26

What are the four main assumptions we must have before conducting the pearsons chi-square test?

Answer 26

• The observations are randomly and independently drawn
• The number of cells with expected frequencies less than 5, are less than 20%
• The minimum expected frequency is at the very least 1.
• The observations are not paired

Question 27

When interpreting the pearsons chi-square test table what values do we need to look at?

Answer 27

• SPSS prints a double entry table with descriptive statistics and one with the χ2-test
• We can either report the ‘row’ data e.g. woman reported Y% before and Y% after, with men reporting Y% before and Y% after
  OR we can report the ‘colum’ data e.g. woman reported Z% and men reported Z% before, and woman reported Z% and men reported Z% after
  Report which is more appropriate
• Chi-square test table: report the value, DF and P-value

Question 28

What is the golden rule when comparing results of a pearsons chi-square test?

Answer 28

NEVER compare percentages which add up to 100%!

Question 29

What are the three main assumptions we must have before conducting the McNemar test?

Answer 29

• The observations are randomly and independently drawn
• There are at least 25 observations in the discordant cells
• The data are paired

Question 30

When interpreting the McNemar test table what values do we need to look at?

Answer 30

Need to compare the two percentages that you want to know using ‘% of total’ e.g. The percentage of those who ‘exercised after’ (44.3%) is higher than the percentage of those who ‘exercised before’ (26.0%).
We then use the McNemar test result to see if the finding is significant (this is the p value)