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STATISTICAL ANALYSIS FOR THE MATHEMATICALLY-CHALLENGED Associate Professor Phua Kai Lit School of Medicine & Health Sciences Monash University (Sunway Campus, Malaysia) December 2012

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How do you select an appropriate Statistical Test to analyse your data? Relax! This is easily done with the help of the following table:

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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)

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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

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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

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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

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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 H 0 and accept H 1. If the p-value is less than 0.01, it is highly statistically significant. You will then reject H 0 and accept H 1. Note: H 0 is the “null hypothesis” and H 1 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)

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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 H 0 and accept H 1 if the 95% Confidence Interval does not contain 1 For the t-test of difference between two population means, reject H 0 and accept H 1 if the 95% Confidence Interval does not contain 0 (zero)

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Additional Resources (to help you understand Statistics) http://phuakl.tripod.com/biostatistics1.html http://phuakl.tripod.com/biostatistics2.html http://www.statsoft.com/textbook/elementar y-statistics-concepts/button/1/ http://www.statsoft.com/textbook/elementar y-statistics-concepts/button/1/

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

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Thanks for watching ! (Love statistics, hate computers – when they fail to run )

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