Practical 4 - Comparing two groups

Question 1

Describe how the following types of data should be described/represented

a) Categorical - nominal/ordinal
b) Continuous - continuous/discrete

Answer 1

a) Descriptive - frequencies/percentages
Dispersion - bar chart / pie chart

b) Descriptive - mean (median if skewed
Dispersion - SD (min/max or IQR if skewed)

Question 2

One sample - to compare mean of our sample to external specific value

Question 3

Outline when you would use the three different t tests

Answer 3

One sample t tests - to compare mean of our sample to external specific value already proposed (mew symbol). For example does the sample mean = 25

Independent sample t test - does the mean of one group differ to the mean of another group (where individuals can only relate to one group). (young vs old // city a vs city b)

paired sample t test - where individuals can belong to both groups i.e. mean at one time vs mean at another time. (before / after)

Question 4

For the three t tests (one sample, independent groups, paired sample) - we need to check if the data is normally distributed

Can you name the alternative t tests for the respective above tests if the data is not normally distributed

Answer 4

One sample -
Independent sample - Mann Whitney U Test
Paired samples - Wilcoxon Matched Pair Test

Question 5

How would we check the distribution of numerical data?

Answer 5

Check the histogram and see if there is a bell shaped curve

Some numerical tests that can be used - Kolmogorov-Smirnov tests - however these tests can be too conservative and will easily say the data is not normally distributed when at times it should be regarded so.

For normal distribution - Kolmogorov-Smirnov test is p > 0.05 (asymp. statistic)
Null is no difference between your data and normality - therefore if significant value would side with alternative hypothesis and reject the null

Question 6

What p value would indicate you reject the null hypothesis

Answer 6

< 0.05

Question 7

What symbol indicates…

a) the sample mean?
b) the population mean

Answer 7

a) X

b) mew

Question 8

What are the assumptions of the one sample t test?

Answer 8

1. Observations are randomly and independently drawn
2. There are no outliers

3, The data is normally distributed

Question 9

What format would a 1 sample t test be reported?

Answer 9

Based on our sample the expected age of males was 4.5 years less than 65 (95% CI). This difference was/was not statistically significant (t test, df, p value)

Question 10

What are the assumptions of two groups (independent samples) test

Answer 10

Observations and randomly and independent drawn (participants only belong to one of two groups)

Symmetrical observations in each group - normal distribution

No outliers in each group

Question 11

What is Levenne’s test for equality of variance?

Answer 11

Determines if the variance in each group of an independent samples t test is different

If the test is significant then there is a difference in variable of two groups and we read from “equal variance not assumed” - i.e. if significant read from 2nd/bottom row

Question 12

What are the assumptions for a paired sample t test

Answer 12

1. Independently and randomly drawn paired observations
2. Normally distributed difference in the data
3. No outliers

Question 13

In a paired sample t test how would check if the data is suitable?

Answer 13

Need to check if the difference between groups is normally distributed.

Compute variable: weight after - weight before

Do analyse descriptives - frequencies - normal distribution curve?

Question 14

Describe the different chi square tests?

Answer 14

One sample chi sqaure test - used to test if the proportion in a population is equal a certain value

Independent chi square tests (Pearson’s) - tests if proportion of a condition in one group is different to the proportion of a group in another group

Paired samples chi square tests (McNemar) - is proportion of a group in one condition

Question 15

What are the assumptions for one sample chi square

Answer 15

Randomly and independently drawn observations
Number of cells with expected frequencies less than 5 < 20%
Minimum expected frequencies is 1

Question 16

How would one sample chi test be reported?

Answer 16

Based on our sample the proportion of men and women is not equal (chi square, df, p)

Question 17

When do we use Pearson’s square?

Answer 17

If two categorical variables are related - are there different proportions of one variable in one group compared to another

i.e. men vs women (height)

Assumptions as before (independently and random observations, not paired, minimum expected frequencies at least 1, < 20% of cells have expected frequencies less than 5)

Question 18

How do you run Pearson’s (independent samples) chi square

Answer 18

Analyse - crosstabs - choose column for how you want to interpret - dependent in column

Statistic –> Chi Square

Cells –> observed

Remember - do not compare percentages that add up to 100%

Question 19

What are the assumptions of McNemar test?

Answer 19

Paired samples chi square

1. The data are paired
2. The observations are randomly and independently drawn
3. There are at least 25 observations in the discordant cells (this refers to the change categories)

Concordant cells would be yes/yes (before - after) and no/no (before -after)

Discordant cells are the other ones - add these up and they should be > 25

Question 20

How do you run the McNemar tests?

Answer 20

Analyse - crosstabs - put before/after or each condition in

Statistics - Chi Square & McNemar

Cells - observed (ticket) but for percentages tick total

Question 21

How does the comparison of Pearson interpretation differ from McNemar total?

Answer 21

The interpretation of McNemar total uses total percentages - i.e. total of yes before vs total yes after (these are found in the total sections of the table)

For Pearson’s the comparison would use values within rows/columns