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STATISTICS David Pieper, Ph.D. [email protected] Types of Variables Categorical Variables • • • • Organized into category No necessary order No quantitative measure Examples • • • • male, female race marital status treatment A and treatment B Types of Variables Ordinal Data • Ranked or ordered • Examples: – strongly agree, agree, disagree – worse, no change, better – 1st place, 2nd place, 3rd place Types of Variables Continuous Variables • Have specific order • Examples: – – – – weight temperature blood pressure time • May be converted to categorical or ordinal Types of Statistics • Descriptive – summarize data for clearer understanding • Inferential – generalize results from sample to population – make probability decisions Descriptive Statistics • Measures of central tendency – mean – mode – median • Measures of variability – – – – range variance standard deviation standard error Research Hypothesis • Null hypothesis: relationship among phenomena does not exist • Example: kids who attend daycare have no greater incidence of colds than kids who do not attend daycare Probability and p Values • p < 0.05 – 1 in 20 or 5% chance groups are not different when we say groups are significantly different • p < 0.01 – 1 in 100 or 1% chance of error • p < 0.001 – 1 in 1000 or .1% chance of error Type of Statistical Test to Use • Continuous variable as end point – 2 groups: t-test – 3 or more groups: ANOVA • Relation between 2 categorical variables: – Chi-square test – Fisher’s Exact test (2 x 2) • Relation between 2 continuous variables: – Regression analysis or correlation T-test • When comparing 2 independent groups and end-point variable (dependent variable) is continuous • Purpose is determine if the difference between the 2 groups is unlikely due to chance • May be paired or unpaired T-test • Example: • Blood pressure before and after exercise program (paired t-test) • Compare blood pressure in a group undergoing cardiac rehab to a control group not undergoing rehab (unpaired t-test) Analysis of Variance (ANOVA) When comparing 3 or more groups (independent variables) and end-point (dependent variable) is continuous. Analysis of Variance (ANOVA) Treatment A Treatment B Treatmnet C Patient 1 25 10 23 Patient 2 30 13 28 Patient 3 32 15 30 Patient 4 26 14 32 Patient 5 24 15 25 Analysis of Variance (ANOVA) mean SE Treatment A Treatment B Treatmnet C 27.4 1.5 13.4 0.9 27.6 1.6 p < 0.001 overall there is a difference between groups - does not tell us which groups are different from one another Post-hoc analysis with Tukey’s multiple comparison test A vs B p < 0.001 A vs C p > 0.05 (not significantly different) B vs C p < 0.001 Chi-square Test • When comparing 2 or more groups and the dependent variable is categorical • Minimum frequency in any cell must be at least 5 • If less than 5 and a 2 x 2 analysis - use Fisher’s Exact Test Male Female Hypertensive 35 17 Not Hypertensive 22 68 Is there a relationship between hypertension and gender? Chi square analysis - p < 0.001 Correlation or Regression • When determining if there is a linear relationship between 2 continuous variables • Ranges from -1 to 1 • Assumptions: – Relationship is linear – Random variables Pearson’s Correlation Coefficien Diastolic BP (mm) Weight (kg) 90 82 140 114 68 56 110 62 100 83 95 110 Is Diastolic BP related to Weight? r = 0.805 p < 0.01 Pearson’s Correlation Coefficient • r = 0.805 does not mean weight gain causes increase in BP or vice versa • Correlation does not prove cause and effect Type of Variable Descriptive Statistics Central Tendency Nominal (Categorical) (Non-parametric) Variability Compare Groups 3 groups 1 or 2 groups 2 2 Mode Relationship of Groups Fisher’s Exact Test Mode Ordinal (Ranks) Standard deviation Kruskal-Wallis Spearman’s Rank Order Confidence Interval t-test ANOVA Pearson’s r Median Mean (Continuous) (Parametric) Mann-Whitney Wilcoxon Median Mode Interval or Ratio Range Standard error Variance Range Regression Name the Statistical Test Do students improve their knowledge after a lecture, as measured by the number of correct answers on a quiz before and after the lecture? a. b. c. d. ANOVA Chi-Square Paired t-test * Unpaired t-test Name the Statistical Test Is there an association between smoking status and 3 levels of socioeconomic status? a. b. c. d. Mann-Whitney U-test Pearson’s correlation Turkey’s test Chi-Square * Name the Statistical Test Is there a relationship between length of hospitalization and number of medications prescribed when patient is discharged? a. Logistic regression b. Pearson’s correlation * c. Repeated measures ANOVA d. Chi-Square Free Statistics Software http://freestatistics.altervista.org/click/fclick.php?fid=4 Illustrations • • • • Graphs - not tables Replace keys with direct labels Use color Each axis must have a label with units • Each graph must have a legend 4 3 p < 0 . 0 1 CFR 2 1 0 B a s e l i n e A f t e r C o r o n a r y I n t e r v e n t i o n Exam Score (%) 100 Girls 80 60 Boys 40 20 0 Jan Feb Mar Month April