Sample size and common statistical tests There are three kinds of lies- lies, dammed lies and statistics…… Benjamin Disraeli

Variables: Qualitative – Nominal Quantitative – ordinal, interval, ratio.

Variables: Nominal scale - Blood group - Psychiatric diagnosis - Sex, race. Ordinal: - Apgar score - Cancer staging

Variables: Interval - No true zero point temp  C,  F Ratio - True zero point - Length, time, mass, volume.

GoalMeasurement (from Gaussian Population) Rank, Score, or Measurement (from Non- Gaussian Population) Binomial (Two Possible Outcomes) Describe one group Mean, SDMedian, interquartile range Proportion Compare one group to a hypothetical value One-sample t test Wilcoxon testChi-square or Binomial test Compare two unpaired groups Unpaired t testMann-Whitney test Fisher's test (chi-square for large samples)

Compare two paired groups Paired t testWilcoxon testMcNemar's test Compare three or more unmatched groups One-way ANOVAKruskal-Wallis test Chi-square test Compare three or more matched groups Repeated- measures ANOVA Friedman testCochrane Q Quantify association between two variables Pearson correlation Spearman correlation Contingency coefficients

Predict value from another measured variable Simple linear regression or Nonlinear regression Nonparametric regression Simple logistic regression Predict value from several measured or binomial variables Multiple linear regression or Multiple nonlinear regression Multiple logistic regression

Type I error: (  ) Incorrectly rejecting null hypothesis. Type II error:(  ) Incorrectly failing to rejecting null hypothesis. (1-  ) = power.

Sample size determinants: 1) Power: 80% 2) Significance level: P< 0.05 – 5% P< 0.01 – 1% 5% or 1% probability of a chance difference mistakenly being considered a real difference.

Sample size determinants: 3) Clinical event rate 4) Expected effect size 5) Compliance & dropout rate 6) Subject allocation ratio

S.NoDeterminates  power  power 1Sample sizeIncreaseDecrease 2VarianceDecreaseIncrease 3Significance levelIncreaseDecrease 4Normality  power  power 5Test tailsOne tailTwo tail 6Exptl. designsWithin subject Between subjects 7Normal distributionYesNo 8Effect sizeLargeSmall

Z score Standard normal distribution Z = X -  Z in the Standard normal value  X is the original value  = mean  = S.D Z represents no. of SD s a value is away from the mean. Z=1=1 SD away from mean

Z = M diff  / √N

Suppose we are trying to measure the mean glucose level in a population and wanted to know the sample size that would give us 95% confidence (which corresponds to a Z-score of 1.96) in the result. If the standard deviation for glucose measurements is 15 and the we are willing to accept an error of 3, then: Z²  ² e² s

Z²  ² e² s Sample Size [( /3)] So, we would need 97 subjects

Suppose we want to determine with 95% confidence (Z1.96) the proportion of patients who will respond to a treatment. If we estimate that 70% (p0.70) will respond to the medication and are willing to accept a / 10% (e0.10) error, then: Z² p (1- p) e²

Z² p (1- p) e² Sample Size [(1.96) ] /(0.10) So, we would need 81 subjects