Choosing statistics

Question 1

What is needed to test the hypothesis?

Answer 1

Choice of statistical test

Patient population/study sample selected allows for comparison (i.e. inclusion/exclusion criteria)

Patient outcome measures (i.e. variables)

Question 2

When the hypothesis proposes a correlation, what are the possible stats tests based on the variables?

Answer 2

Discrete
- Chi-Square

Continuous

• Pearson (normally distributed)
• Spearman rank (not normally distributed)

Question 3

When the hypothesis proposes a comparison between groups, what stats test do you use for discrete data?

Answer 3

Chi-Square

Question 4

When the hypothesis proposes a comparison between groups, what stats test do you use for continuous, normally distributed data based on number of groups?

Answer 4

> 2 groups
- ANOVA (one variable)

2 groups

• paired t-test
• independent t-test

Question 5

When the hypothesis proposes a comparison between groups, what stats test to you use for continuous, NOT normally distributed data based on number of groups?

Answer 5

> 2 groups
- Kruskal Wallis

2 groups

• Wilcoxon (paired)
• Mann Whitney (independent)

Question 6

Which statistical analysis tests for differences?

Answer 6

Chi-square
ANOVA
T-tests
Kruskal-Wallis
Wilcoxon
Mann-Whitney U-Test

*hypothesis proposes a comparison between groups

Question 7

Which statistical analysis tests for similarities?

Answer 7

Chi-Square
Pearson
Spearman rank

*hypothesis proposes a correlation

Question 8

What is quantitative data?

Answer 8

Numerical information about quantities

• MEASURED: information can be measured and have continuous dimensions (height, temperature, BP)
• COUNTED: information can be counted but not continuous (no. of children in family, no. of patients in clinic)

Question 9

What is qualitative data?

Answer 9

Information about qualities, it can’t actually be measured

Deals with descriptive information such as free-text comments to open-ended question/response to interview

Question 10

What is categorical data?

Answer 10

In-between quantitative and qualitative

• ORDINAL aspects can be easily converted into numerical data (i.e. scale on happiness can be given in numbers instead of words)
• NOMINAL aspect consists of individual terms rather than sentences like in qualitative data

Question 11

Broadly compare quantitative, qualitative, and categorical data

Answer 11

Quantitative = when you measure something and give it a number value

Categorical = when you classify something

Qualitative = when you judge something

Question 12

Compare discrete and continuous data

Answer 12

Discrete data; counted

• cannot be made more precise
• i.e. number of children

Continuous data; measured

• can be divided and reduced to finer and finer levels
• i.e. height of a person

Question 13

Compare nominal and ordinal data

Answer 13

Nominal = items that are assigned individual named categories that do not have an implicit or natural value or rank
i.e. gender, fracture incidence

Ordinal = items which are assigned to categories that do have some kind of implicit or natural order
i.e. describe patients’ characteristics: stage of hypertension, pain level, and satisfaction

Question 14

Broadly describe the mean and standard deviation

Answer 14

Mean is an average of the data

Standard deviation describes the width

Question 15

What is normality?

Answer 15

It measures the central tendency and dispersion of data, and is used to decide how to describe the properties of large data-sets

Question 16

Describe the relative mean, median, and mode for the following skews:

a) positive skew
b) symmetrical distribution
c) negative skew

Answer 16

a) mode > median > mean
b) mean = median = mode
c) mode < median < mean

• positive: >
• negative <

Question 17

What is kurtosis?

Answer 17

Describes data that are heavy-tailed or light-tailed relative to a normal distribution

Question 18

Compare high and low kurtosis

Answer 18

High kurtosis
- tend to have heavy tails, or outliers that create a very wide distribution

Low kurtosis
- ten to have light tails, or lack of outliers that create a very narrow distribution

Question 19

What statistical tests are used to test for normality?

Answer 19

Shapiro-Wilks test
- small sample size (n<50)

Kolmogorov-Smirnov
- large sample size (n>50)

Question 20

What is a descriptive statistics?

Answer 20

Mean, mode or median

- used to categorise large data-sets into a tangible format

Question 21

Compare range, variance and standard deviation

Answer 21

Range
- measures how fat a set of numbers are spread out from their average value
Variance
- measure of the spread of the numbers away from the mean value
Standard deviation
- measure the spread of a set of data

Question 22

Compare IQR, standard error of mean, and confidence intervals

Answer 22

Interquartile range
- UQ - LQ
Standard error of mean
- measures how well the sample mean approximates to the population mean
Confidence intervals
- range of values in which true mean value might be found

Question 23

How do you determine whether groups are paired or independent?

Answer 23

Look at whether each group is composed of the same subjects of interest or if they are different

Paired = two data-sets come from the same individual
- measure same variable in same subject at different time points (longitudinal study)

Independent = two data-sets from different individuals
- comparing two groups with no common factors (cross-sectional study)

Question 24

Compare when to use parametric and non-parametric statistics

Answer 24

Parametric = normally distributed

Non-parametric = not

Question 25

Name parametric tests

Answer 25

Paired/independent t-tests

ANOVA

Question 26

Name non-parametric tests

Answer 26

Wilcoxon Signed Rank
Mann-Whitney U
Friedman (non-parametric equivalent of repeated measures one-way ANOVA)
Kruskal-Wallis

Question 27

When would you use the different t-tests?

Answer 27

Paired: different variables are compared with the same sample

Independent: same variable is compared by from different samples

Question 28

What does a one-way ANOVA tell you?

Answer 28

Used to compare the means from more than two samples with a normal distribution and will only tell you if a difference exists between your samples

Further stat tests (i.e. post hoc test) are needed to calculate exactly where the difference is

Question 29

What can the Pearson correlation coefficient tell you about correlation?

Answer 29

How strong the relationship is

Varies between -1 to +1 (from perfect negative to perfect positive correlation)

Question 30

Approximately what are the r-values for the following correlations:

a) very low,
b) low,
c) reasonable,
d) high,
e) very high?

Answer 30

a) 0.0-0.2
b) 0.2-0.4
c) 0.4-0.6
d) 0.6-0.8
e) 0.8-1.0

*can be +/-

Question 31

What is the r^2-value from a Pearson correlation?

Answer 31

Represents how closely your data is fitted to the correlation line

The higher the value, the more reliable your conclusion can be

Question 32

Compare correlation and regression

Answer 32

Correlation = indicates the strength of the relationship between two variables

Regression = quantifies the association between the two variables, i.e. tells us the impact that changing one variable will have on the other variable

Question 33

How is regression defined?

Answer 33

gcse

y = a + bx

a = the y-axis intercept value
b = the gradient of the line, i.e. the regression coefficient

Question 34

What does the chi square test measure?

Answer 34

It is a measure of the differences between observed and expected frequencies

Represented as X/X^2

Question 35

What does it mean when X^2 = 0?

Answer 35

The observed and expected frequencies are the same

Question 36

What does it mean the higher the X^2 value?

Answer 36

The bigger the difference between the observed and expected frequencies

Question 37

How can the size of a study affect the p-value?

Answer 37

Very small studies with few samples might not return a reliable p-value

Very large studies with many samples might be over powered and find a significant difference where none exists

Question 38

What is a type I error?

Answer 38

Incorrectly reject the null hypothesis when it is true (significance level, a-value)

False positive

Question 39

What is a type II error?

Answer 39

Incorrectly fail to reject the null hypothesis when it is false

False negative

*the greater the power of the test, the lower type II error rate (power = 1-beta; the closer the power is to 1, the better the test is at detecting a false null hypothesis)