USING STATISTICAL TESTS

Richard Salisburyrichardasalisbury@gmail.com

What I’m going to cover

Key concepts What test when? Examples

Key concept 1: The null hypothesis

I predict that any difference seen between two groups is due to chance alone.

Use 95% cut off in medicine P > 0.05 = accept null hypothesis P < 0.05 = reject null hypothesis as

difference is NOT due to chance. There is a statistically significant difference between groups.

Key concept 2: Data types

Continuous eg. height Discrete - integers Ordinal - ranked Categorical eg. Hair colour Dichotomous/Binary eg. Yes/no

Key concept 3: Normal/Gaussian distribution

Value

Cumulative frequency

Mean =median=mode

Central Limit TheoremShapiro Wilk test

Common statistical testsContinuous and Gaussian distributed

Continuous or discrete and NOT Gaussian distributed

Binary/Categorical

Comparison of Independent 2 groups

Box plotT-testZ-test

Box plotCross-tabulationMann-Whitney U-test

2x2 frequency tableChi-squared testFisher’s exact test

Comparison of more than 2 groups

Analysis of variance (ANOVA)

Kruskal Wallis Cross-tabulationChi-squared test

Comparison of 2 related outcomes

Paired t-test Wilcoxon matched pairs

McNemar’s test

Relationship between a dependent variable and one or more independent variables

Scatter plotRegression analysisPearson’s correlation coefficient

Spearman correlation or Kendall’s correlation coefficient

Phi coefficientLogistic Regression

Which test to use?

Is data normally

distributed?

Is data categorical?

2 groups or less?

Chi-squared test

Mann-Whitney U

test

Is n > 30 ANOVA

Yes

No

Yes

No

NoYe

s

Yes

No

Z-test T-test

Which test to use?

Is data normally

distributed?

Is data categorical?

2 groups or less?

Chi-squared test

Mann-Whitney U

test

Is n > 30 ANOVA

Yes

No

Yes

No

NoYe

s

Yes

No

Z-test T-test

Normally distributed data - T-test

Comparison of means taking into account spread

Allows comparison 2 groups OR a comparison of one group and an expected mean

1 tailed Vs 2 tailed – what question are you asking?

Independent groups Vs Dependent/Paired groups

Example 1

I have audited BMI of 20 patients undergoing gastric banding, I want to compare this with the national average.

Data - BMI is a continuous variable and therefore will be normally distributed about the mean.

Groups - 2 groups Number - n<30 T-test using mean and variance of my group compared to

mean and variance of national average. 2 tail t-test as I am interested in knowing whether the BMI

is different therefore either smaller or larger 1 tail t-test could be used if I wanted to ask is the BMI

larger in patients undergoing gastric banding compared to national average

Example 2

Does CBT change the mood (measured by visual analogue scale) of 50 depressed individuals? – Comparison of before and after scores

Data – Normally distributed Groups – 2; before Vs after CBT Number – n>30 BUT groups are not

independent – repeated measures 2-tail paired T-test 1-tail paired t-test would be for a question that

asks if CBT increases mood.

Alternatives to t-test

Z-test for independent variables where n > 30

ANOVA for more than 2 groups – multiple comparisons (the more comparisons you do, the more likely you are to get a false positive)

ANOVA tests for difference between all groups A post test eg Bonferroni then tests for

differences between individual groups Eg. RCT Placebo Vs Drug A Vs Drug B

Which test to use?

Is data normally

distributed?

Is data categorical?

2 groups or less?

Chi-squared test

Mann-Whitney U

test

Is n > 30 ANOVA

Yes

No

Yes

No

NoYe

s

Yes

No

Z-test T-test

Mann-whitney U test

Non-parametric test (Parameter-free test)

Not normally distributed Small sample size (n<10) Discrete (integers)/Ordinal (ranked) data Upper or lower limits

• 2 Independent groups• Uses ranking to analyse data (not

important)

Categorical Data

Data which can be put into categories Best displayed by a frequency table

Exposure to dust

No exposure to dust

Total

Asthma sympts

59 62 121

No asthma sympts

4 11 15

63 73 136

Chi squared and Fisher’s exact test

Used to compare categorical data against expected data (probabilities eg. Mendellian crosses) OR against other independent categorical data.

Fisher’s exact test is more accurate, especially if n is small, but is harder to calculate.

Regression Analysis

Compares how an independent variable changes the value of a dependent variable, independent of any other independent variables.

This is as complicated as it sounds. Seek help early!

Examples to finish

Example 1(Kostov DV, Kobakov GL.Segmental liver resection for colorectal metastases. J Gastrointestin Liver Dis. 2009 Dec;18(4):447-53)

56 colorectal liver metastasis patients had two types of operations for their liver metastasis: 38 patients had major liver resection with 16 of them having surgical wound infection later. 18 patients had segmentectomy and only 7 of them experienced wound infection later.

• Objective: is the occurrence of wound infection different in these two types of operations?

(Kostov DV, Kobakov GL.Segmental liver resection for colorectal metastases. J Gastrointestin Liver Dis. 2009 Dec;18(4):447-53)

Analysis: comparison Variable: wound infection categorical Comparison across segmentectomy and

major liver resection

Chi Sqaure Test

yes/no

2 independent groups

Example 2 (Siregar P, Setiati S., Urine osmolality in the elderly. Acta Med Indones. 2010 Jan;42(1):24-6.)

A study recorded the urine osmolality of 13 and 15 respectively female and male elderlies.

Objective: is the urine osmolality different in males and females?

• Analytical statistics: comparison• Variable: urine osmolality• Comparison across females and males 2 independent

groups • If data not normally distributed

Mann Whitney U test

• If data normally distributed 2 Sample T test

continuous

Questions