Hypothesis Testing

Question 1

In hypothesis testing, what do we always assume is true?

Answer 1

The null hypothesis

Question 2

What is the null hypothesis?

Answer 2

This states there is no difference between the variables of interest

Question 3

What value is used to calculate the likelihood or probability that the difference observed happened by chance?

Answer 3

The p value

Question 4

What does a p-value of 0.02 signify?

Answer 4

That the probability your scenario happened by chance is only 2 in 100

Question 5

When is the null hypothesis rejected?

Answer 5

When the p-value is below the significance threshold

Question 6

What does it mean if the p-value is large/above significance threshold?

Answer 6

You fail to reject your null hypothesis therefore no evidence exists for the difference - it is likely due to chance

Question 7

What is the commonly used cut-off for p-value? Why is this not a universal figure?

Answer 7

0.05

For studies such as GWAS, a much lower p-value is required

Question 8

What is a type I error also known as and when does this happen?

Answer 8

This is a false positive and occurs when you reject the null hypothesis even though it is actually true

Question 9

What is the frequency of having a type I error/false positive?

Answer 9

This is the same as the value you use for significance cut off

Question 10

What is a type II error also known as and when does it occur?

Answer 10

This is a false negative and occurs when you fail to reject the null hypothesis even though it is actually false

Question 11

What is type II error or false negative dependent on?

Answer 11

Sample size

Question 12

The choice of statistical test used to determine your p-value depends on what three key factors?

Answer 12

1. Study design (paired or independent)
2. Outcome variable (continuous or categorical)
3. Distribution (normal or non-normal)

Question 13

how is a t-statistic calculated?

Answer 13

For independent data, it is calculated by taking the observed mean difference and dividing this by the standard error of difference between the means

Question 14

What three assumptions does a t-test make?

Answer 14

1. Data is continuous
2. Data is normally distributed
3. Variance in the two groups is equal (levene’s test)

Question 15

What does levene’s test do and why is it important?

Answer 15

Levene’s test helps assess whether the variance between two groups is equal. This is used when interpreting t-test results:

• If levene’s test is >0.05 then we accept the null hypothesis and interpret the results relating to ‘equal variances assumed’

Question 16

What are your options if the assumptions for a parametric are untrue?

Answer 16

1. Transform the data
2. Check the normality again. If ok - use a parametric test
3. If not ok, use a non-parametric test

Question 17

What transformations can you attempt if your data is:

• moderately positively skewed
• strongly positively skewed
• weakly positively skewed

Answer 17

• log transform (logx)
• reciprocal (1/x)
• square root (rootx)

Question 18

What transformation method would you use if your data was:

• moderately negatively skewed
• strongly negatively skewed
• unequal variation

Answer 18

• square (x2)
• cube (x3)
• log/reciprocal/squareroot

Question 19

What are the advantages of a non-parametric test? What are the disadvantages?

Answer 19

• make no assumption about underlying distribution of data
• less powerful than parametric
• difficult to get CIs

Question 20

What is the non-parametric equivalent of a t-test?

Answer 20

Wilcoxon rank sum test or Mann-Whitney u test

Question 21

Describe how a wilcoxon rank sum test works

Answer 21

• two independent groups: group1 and 2 where group1 is the smallest size group
• rank all observations into ascending order
• sum ranks for group 1 = test statistic T
• look up T on wilcoxon rank sum table of critical values to get P-value

Question 22

What non-parametric is used for skewed data with more than two independent exposure groups? What is its parametric equivalent?

Answer 22

Kruskal-Wallis test

Parametric equivalent = ANOVA

Question 23

What test is used to compare two binary categorical variables and obtain a p-value?

Answer 23

Chi squared test

Question 24

What does the p-value of a chi-squared test tell us?

Answer 24

How likely the differences between our variables would have occurred by chance if there was truly no association

Question 25

How do you calculate the chi-square test statistic?

Answer 25

This involves working out how close the observed values in your table are to the values expected if there was no true association You first have to work out the expected numbers for each cell of your table. General formula: (row total x column total)/overall total The next step is to then calculate the chi-square statistic for each cell then total these together. General formula: (O-E)squared/E

Question 26

How do you interpret your chi-square statistic?

Answer 26

The larger the chi-square value, the less consistent the data are with the null hypothesis Usually use a stats package to obtain a p-value but can use stats tables based in degrees of freedom

Question 27

How do you calculate your degrees of freedom?

Answer 27

Degrees of freedom = (Rows-1) x (Columns-1) E.g. For a 2x2 table it would be (2-1) x (2-1) = 1 d.f

Question 28

Why do we we need both the Odds ratio AND the p-value?

Answer 28

The OR tells us the magnitude of an association whilst the p-value tells us the significance of this

Question 29

What are the assumptions of chi-squared?

Answer 29

- Each subjects contributes data to only one cell (I.e. You can't be a smoker AND a non-smoker) - The expected count in each cell should be at least 5 (SPSS will give you a warning)

Question 30

If your expected count are not all >5 in your table, should you use a chi-squared test? If not, what should you do instead?

Answer 30

1. Yes - but you must then use the Yates Continuity Correction 2. No - you should use Fishers Exact Test instead

Question 31

When using chi-squared test for tables bigger than 2x2, what could you do if you don't meet the assumptions?

Answer 31

Combine the rows or columns with small numbers, if biologically plausible

Question 32

What is chi-squared test for trend?

Answer 32

This is a special test for when the exposure variable is ordered (not nominal) and the outcome is binary For example, looking at disease (yes/no) across ordered age groups (

Question 33

How do you visualise correlation?

Answer 33

Scatter diagram

Question 34

On a scatter diagram, on which axis is the outcome plotted?

Answer 34

Vertical/y-axis

Question 35

What does correlation measure? What do the correlation coefficients (r) mean?

Answer 35

Measures the closeness or degree of association between two continuous variables ``` +1 = perfect positive association -1 = perfect negative association 0 = no association ```

Question 36

What are the two main types of correlation coefficient and when would you use each of them?

Answer 36

Pearsons correlation coefficient and Spearmans correlation coefficient Pearsons is used when the variables are normally distributed. If they aren't you can transform them and then use this, or instead you can use Spearmans

Question 37

What does correlation NOT take into account?

Answer 37

The gradient/steepness of slope

Question 38

What does the r-squared value do? Please give an example

Answer 38

This is the proportion of the variance of the outcome variable which is explained by the exposure variable E.g. An r-squared of 0.64 for correlation between BP and stress means 64% of the variation in BP is explained by stress

Question 39

Does correlation equal causation?

Answer 39

No. Possibilities are: 1. X influences or causes Y 2. Y influences X 3. Both X and Y are influenced by one or more other variables (confounders)

Question 40

Why should you interpret correlation results from large cohorts with caution?

Answer 40

Because you can get a significant result for a very weak correlation

Question 41

What is the difference between correlation and regression?

Answer 41

Correlation is used to assess if two variables are related and how closely Regression is used to describe/model the rship or make predictions

Question 42

What does linear regression do?

Answer 42

States how much y (outcome) increases/decreases as X (exposure) increases Estimates a best-fit straight line through the data

Question 43

What is the equation used in linear regression?

Answer 43

Y=a+bx a=the intercept, i.e. the value of Y when X=0 b=the slope of the line that tells us on average how much Y increases/decreases for each unit increase in X. It is an estimate of the magnitude of effect

Question 44

What do the values of regression coefficient 'b' mean?

Answer 44

Positive B = outcome increases as exposure increases Negative B = outcome decreases as exposure increases B=0: outcome and exposure not related

Question 45

Consider two variables weight and systolic BP. Your values of a and b are 98.5 and 0.43 (95% CI 0.34-0.51), respectively. Your p-value is

Answer 45

Estimates that for every kg increase in weight, BP increased on average by 0.43 mmHg You are 95% confident this increase is between 0.34 and 0.51 mmHg This is highly statistically significant

Question 46

When is multiple linear regression used?

Answer 46

When you want to include two or more exposure variables For example, to look at age and weight in reference to BP and obtain an age-adjusted regression coefficient