STATISTICAL ANALYSIS FOR THE MATHEMATICALLY-CHALLENGED

Associate Professor Phua Kai LitSchool of Medicine & Health Sciences

Monash University (Sunway Campus, Malaysia)

December 2012

How do you select an appropriate Statistical Test to analyse your data?

• Relax! This is easily done with the help of the following table:

Note: This table has been adapted from Table 37.1 “Selecting a Statistical Test” presented in the website http://www.graphpad.com

Measurement (from an underlying Normal Distribution)

Rank or Measurement (from an underlying population which is not a Normal Distribution

Binomial (only two outcomes are possible)

Describe one sample

Mean, standard deviation, variance

Median, interquartile range

Proportion

Compare a sample to a hypothetical value or hypothetical distribution

Student’s t-test for one sample(use the Z-test for a large sample, i.e. n > 29)

Wilcoxon signed-rank test

Chi-square goodness-of-fit test

Compare two unpaired or unmatched samples

Student’s t-test for unpaired samples (use the Z-test for samples > 29)

Mann-Whitney test or the Wilcoxon rank sums test

Chi-square test of association (Use Fisher’s exact test for small samples)

Note: This table has been adapted from Table 37.1 “Selecting a Statistical Test” presented in the website http://www.graphpad.com

Measurement (from an underlying Normal Distribution)

Rank or Measurement (from an underlying population which is not a Normal Distribution

Binomial (only two outcomes are possible)

Compare two paired/matched samples

Student’s t-test for two paired samples

Wilcoxon matched-pairs signed-rank test

McNemar’s test

Compare three or more unmatched samples

One-way ANOVA (analysis of variance)

Kruskal-Wallis one-way analysis of variance test

Chi-square test of association

Compare three or more matched samples

Repeated measures ANOVA

Friedman’s two way analysis of variance test

Cochrane Q test

Note: This table has been adapted from Table 37.1 “Selecting a Statistical Test” presented in the website http://www.graphpad.com

Measurement (from an underlying Normal Distribution)

Rank or Measurement (from an underlying population which is not a Normal Distribution

Binomial (only two outcomes are possible)

Measure association between two variables

Pearson’s correlation coefficient

Spearman’s rank correlation coefficient

Contingency coefficients

Predict value of one variable from another variable

Simple linear regression

Nonparametric regression

Simple logistic regression

Predict value of one variable from several other variables

Multiple linear regression

Multiple logistic regression

After choosing your stats test ….

• Input your data and run the stats test – here is an online site where you can run your stats test

• www.graphpad.com/quickcalcs/index.cfm

How to interprete the output from your chosen Stats Test (1)

• 1. Look at the p-value : if the p-value is less than 0.05, it is statistically significant. You will then reject H0 and accept H1. If the p-value is less than 0.01, it is highly statistically significant. You will then reject H0 and accept H1.

• Note: H0 is the “null hypothesis” and H1 is the “research hypothesis”. The null hypothesis is the hypothesis you wish to reject. It is usually stated in a negative manner, e.g. “no association between Variable X and Variable Y” (for the Chi-square test of association) or “no difference between Population Mean X and Population Mean Y” (for the t-test of difference between two means)

How to interprete the output from your chosen Stats Test (2)

• 2. Look at the 95% Confidence Interval (if it is in the output):

• For Relative Risk analysis or Odds Ratio analysis (two kinds of stats tests used in epidemiology), reject H0 and accept H1 if the 95% Confidence Interval does not contain 1

• For the t-test of difference between two population means, reject H0 and accept H1if the 95% Confidence Interval does not contain 0 (zero)

Additional Resources(to help you understand Statistics)

• http://phuakl.tripod.com/biostatistics1.html

• http://phuakl.tripod.com/biostatistics2.html

• http://www.statsoft.com/textbook/elementary-statistics-concepts/button/1/

Helpful books …… some written by me and my co-authors

Thanks for watching !

(Love statistics, hate computers – when they fail to run )