Choosing statistics

Question 1

Give important points to remember when selecting a study design, including the choice of statistical test.

Answer 1

The stats must test the hypothesis.
The patient population or study sample (i.e. inclusions and exclusion criteria) must be selected to allow for a comparison that will test the hypothesis.
The patient outcome measures (i.e. variables) must also be useful for testing the hypothesis.

Question 2

What is the best way to select the most appropriate statistical test for the hypothesis once the data has been collected (or even before)?

Answer 2

Use a statistical decision tree.

Question 3

When is a Pearson statistical test used?

Answer 3

The hypothesis proposes a correlation, the variables are continuous and have a normal distribution.

Question 4

When is a Spearman rank statistical test used?

Answer 4

The hypothesis proposes a correlation, the variables are continuous and do not have a normal distribution.

Question 5

When is a Chi-squared statistical test used?

Answer 5

The hypothesis proposes either a correlation or a comparison between groups, and the variables are discrete.

Question 6

When is ANOVA used?

Answer 6

The hypothesis proposes a comparison between groups, the variables are continuous and have a normal distribution, there are >2 groups and only one variable.

Question 7

When is a t-test used?

Answer 7

The hypothesis proposes a comparison between groups, the variables are continuous and have a normal distribution, there are 2 groups of either paired or independent data.

Question 8

When is a Kruskal-Wallis statistical test used?

Answer 8

The hypothesis proposes a comparison between groups, the variables are continuous and do not have a normal distribution, there are >2 groups.

Question 9

When is a Wilcoxon statistical test used?

Answer 9

The hypothesis proposes a comparison between groups, the variables are continuous and do not have a normal distribution, there are 2 groups of paired data.

Question 10

When is a Mann-Whitney statistical test used?

Answer 10

The hypothesis proposes a comparison between groups, the variables are continuous and do not have a normal distribution, there are 2 groups of independent data.

Question 11

What are the 2 main types of data that may be analysed?

Answer 11

Quantitative and qualitative (categorical).

Question 12

What is quantitative data?

Answer 12

Numeric information about quantities. Information that can be measured and written down with numbers, including dimensions such as height, width, length and mass or other measured variables such as temperature, blood pressure and price etc.

Question 13

What is qualitative data?

Answer 13

Information about qualities. Information that can’t actually be measured. Qualitative data deals with categories such as gender (male or female), life status (alive or dead) and stages of disease (e.g. hypertension).

Question 14

Give an example of a variable that could be measured either quantitatively or qualitatively.

Answer 14

Eye colour can be measured quantitatively by assessing the RGB scale or qualitatively by categorising into blue, brown or green etc.

Question 15

What are the different types of quantitative data?

Answer 15

Continuous and counted (discrete).

Question 16

What are the different types of qualitative (categorical) data?

Answer 16

Nominal (unordered) and ordinal (ordered).

Question 17

Give examples of nominal (unordered) data.

Answer 17

Gender (male/female/other).
Life status (alive/dead).

Question 18

Give examples of ordinal (ordered) data.

Answer 18

Fitness (not fit, quite fit, very fit).

Stages of hypertension.

Question 19

Give examples of continuous data.

Answer 19

Age.

Heart rate.

Question 20

Give examples of counted (discrete) data.

Answer 20

Number of males/females in a group.

Number of people with hypertension.

Question 21

What types of data are parametric?

Answer 21

Continuous quantitative data.

Question 22

What types of data are nonparametric?

Answer 22

Nominal and ordinal qualitative data.

Counted (discrete) quantitative data.

Question 23

What does ‘normality’ measure, and what is it used for?

Answer 23

The central tendency and dispersion of data, used to decide how to describe the properties of large data-sets i.e. the descriptive statistics which are presented instead of the raw data.

Question 24

What are the features of a normal distribution?

Answer 24

Normal distribution has a symmetric distribution with well-behaved tails i.e., many data points at the central region of the range and a symmetrical disruption either side, a.k.a. ‘bell curved’ or ‘Gaussian’.

Question 25

What are the features of a skewed data distribution?

Answer 25

Asymmetric with many data points in the high or low end of the range and an uneven tail (long on one side and short on the other).

Question 26

What are the features of a kurtosis data distribution?

Answer 26

Heavy-tailed or light-tailed relative to a normal distribution. Data sets with high kurtosis tend to have heavy tails, or outliers that create a very wide distribution. Data sets with low kurtosis tend to have light tails, or lack of outliers that create a very narrow distribution.

Question 27

What are the statistical tests of normality?

Answer 27

Shapiro-Wilks test: used to test for normality with small sample sizes (n<50).
Kolmogorov-Smirnov: used to test for normality with large sample sizes (n>50).

Question 28

How do paired data arise?

Answer 28

Typically, paired observations arise from measuring the same variable in the same subject at different time-points (this could be referred to as a longitudinal experiment).

Question 29

How do independent data arise?

Answer 29

Unpaired, or independent, observations are seen when comparing two groups with no common factors (this could be referred to as a cross-sectional study).

Question 30

What are parametric statistics?

Answer 30

A parametric statistical test is one that makes assumptions about the parameters (defining properties) of the population distribution(s) from which the data are drawn, while a non-parametric test is one that makes no such assumptions.
Parametric statistics (e.g. t-test, ANOVA) are used when the data from the population is well described by the mean and standard deviation- normally distributed.

Question 31

What are non-parametric statistics?

Answer 31

Non-parametric tests (e.g. Mann-Whitney, Wilcoxon signed rank test) are adopted when the population is not well described by the mean and standard deviation. For example, when quantitative data is not normally distributed. Non-parametric are also used when the data is qualitative.

Question 32

What are the measures of centrality?

Answer 32

Mean, median and mode.

Question 33

What are the measures of dispersion?

Answer 33

Standard deviation, standard error of the mean, CI.