Inferring differences between groups

Question 1

what questions must be asked when identified which test is appropriate for each research question?

Answer 1

1. what are the two concepts in the research question?
2. what is the level of measurement of the two variables that store information on the two concepts?
3. what is the focus of the research question?
4. for a continuous variable: is it sufficiently normally distributed?

Question 2

what are some important notes to make when thinking about concepts?

Answer 2

○ Multiple categories does not indicate multiple concepts e.g. categories of non-smokers and smokers are 2 categories that indicate 1 concept
○ Concepts can be measured in multiple ways e.g. smoking could be measured as smoker or non-smoker or by measuring number of cigarettes smoked

Question 3

how do you carefully consider your variables on SPSS?

Answer 3

○ Look at data view
○ Consider information of the study
○ Use descriptive statistics to make a reasoned judgement as to what the levels of measurement are

Question 4

what are the different focuses of a research question?

Answer 4

difference between groups
difference over time
association

Question 5

what does it mean if you are looking at a difference between groups?

Answer 5

categorical (binary) variable divides sample into different groups
groups are compared in terms on their average score on a second variable

Question 6

what does it mean if you are looking at a difference over time?

Answer 6

concept is measured on two (or more) occasions
comparing whether an average score has changed over time

Question 7

what does it mean if you are looking at an association?

Answer 7

looking at the tendency for the scores on two variables to change in a common manner

Question 8

what assumption do we make about continuous variables and why?

Answer 8

We assume that the scores on a continuous variable are normally distributed because if not then we cannot trust the results of the test
If this assumption is not true, then a different bivariate statistical test will need to be carried out

Question 9

what are the different ways to determine whether a continuous variable is normally distributed?

Answer 9

• Visual inspection of histogram and boxplots - not very scientific
• Rules of thumb for acceptable kurtosis and skewness values
• Z test on the kurtosis and skewness
• Complex statistical tests of non-normality e.g. Kolmogorov-Smirnov; Shapiro-Wilk)

Question 10

what are the two statistics to look at when assessing if a continuous variable is normally distributed?

Answer 10

skewness - whether the curve is closer to the left or right side
kurtosis - whether the bell-shaped curve is wide or thin

Question 11

how far from zero are skewness and kurtosis allowed to get?

Answer 11

close to 0 but does not need to be exactly 0

Question 12

if the sample contains 50 or more sampled units…

Answer 12

treat the variable as if it were normally distributed (Ghasemi & Zahediasl, 2012)

Question 13

if the sample contains less than 50 sampled units…

Answer 13

carry out Z test on the skewness and kurtosis values to evaluate whether the values of skewness and kurtosis are close enough to 0 for the distribution to be deemed normal (Kim, 2013)

Question 14

steps of carrying out a Z test

Answer 14

○ Divide skewness value by its standard error
○ Divide kurtosis value by its standard error

Question 15

if the values obtained from a Z test are between -1.96 and +1.96…

Answer 15

this shows a variable with normally distributed scores (Kim, 2013)

Question 16

if the values obtained from a Z test are not between -1.96 and +1.96…

Answer 16

this shows a variable with non-normally distributed scores
use alternative non-parametric bivariate statistical test

Question 17

what are the different kinds of statistical tests?

Answer 17

parametric statistical tests
non-parametric statistical tests
- For most bivariate parametric statistical test there is an equivalent and alternative non-parametric test

Question 18

what are parametric statistical tests?

Answer 18

bivariate inferential statistical test used with continuous variables that are normally distributed

Question 19

what are non-parametric statistical tests?

Answer 19

bivariate inferential statistical test used with continuous variables that are not normally distributed

Question 20

when should independent t-test be used?

Answer 20

when looking at a difference between two groups with continuous variables that are normally distributed (parametric test)

Question 21

if you are looking at a difference between two groups with continuous variables that are normally distributed, which statistical test should you use?

Answer 21

independent t-test

Question 22

what is an independent t-test?

Answer 22

• Gives a p-value which tells us how likely it is that the null hypothesis is true
• Less than 5% chance that null hypothesis is correct to be able to accept the alternative hypothesis

Question 23

when should a Mann Whitney U test be used?

Answer 23

when looking at a difference between two groups with continuous variables that are not normally distributed (non-parametric test)

Question 24

if you are looking at a difference between two groups with continuous variables that are not normally distributed, which statistical test should you use?

Answer 24

Mann Whitney U test

Question 25

if you are looking at a difference between two groups with ordinal variables, which statistical test should you use?

Answer 25

Mann Whitney U test

Question 26

if you are looking at a difference between two groups with nominal variables, which statistical test should you use?

Answer 26

Chi square

Question 27

what is the Mann Whitney U test?

Answer 27

- Ranks the scores of the continuous variable - Then analyses the ranked data - Compares two groups and tests the null hypothesis (p < 0.05) - 'the mean rank of the two groups is the same in the population' or 'there is no difference in the mean rank of the two groups' - There is some loss of data when using ranked data

Question 28

steps of carrying out bivariate statistical tests using SPSS:

Answer 28

1. report p-values 2. SPSS output & report

Question 29

how do you report p-values?

Answer 29

If p-value is more than 0.05 then the result is not significant so you accept the null hypothesis as it is likely to be true in the population i. n.s. (not significant) If p-value is less than 0.05 then look closer at p-value: ii. p<0.05 iii. p<0.01 iv. p< 0.001 Never report P=0.00 instead use p< 0.001

Question 30

how do you carry out SPSS output & report for independent t-test?

Answer 30

Which group has the highest mean? Look at Levene's test for equality of variances to explore whether the data is homogenous or not: i. If value of Sig is more than 0.05 --> value is significant --> look at first row of table ii. If value of Sig is less than 0.05 --> value is not significant --> look at second row of table Report and write up: whether there is a significant difference between mean and standard deviation of both variables, followed by results of t-test in the form: t('df') = 't-value', p < 'p-value'

Question 31

What elements from the SPSS table is needed when reporting the results of an independent samples t-test?

Answer 31

mean, standard deviation, t-statistic, degrees of freedom and significance value

Question 32

how do you carry out SPSS output & report for Mann Whitney U test?

Answer 32

Which group has the highest mean rank? Look at p-value from test statistics: i. If p-value is more than 0.05 --> accept null hypothesis ii. If p-value is less than 0.05 --> reject null hypothesis Report and write up: whether there is a significant difference between the mean rank of both variables, followed by the value of U and p-value

Question 33

If p-value is above 0.05...

Answer 33

then report as n.s.

Question 34

What elements from the SPSS table is needed when reporting the results of a Mann Whitney U test?

Answer 34

mean rank, p-value, Mann-Whitney U value

Question 35

what are the two types of research questions?

Answer 35

one-tailed two-tailed

Question 36

how do you know if a research question is one-tailed?

Answer 36

If research question is concerned with the direction of the difference between groups OR difference over time only one way the question can be answered only one way the null hypothesis can be tested

Question 37

how do you know if a research question is two-tailed?

Answer 37

If research question is concerned with the possibility of some difference between groups vs no difference OR difference over time vs no difference two ways the question can be answered two ways the null hypothesis can be tested

Question 38

If you are looking at a one-tailed research question and only a two-tailed p-value is given...

Answer 38

then you must divide it by 2