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STATISTICS David Pieper, Ph.D. dpieper@med.wayne.edu

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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

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Types of Variables Ordinal Data Ranked or ordered Examples: –strongly agree, agree, disagree –worse, no change, better –1st place, 2nd place, 3rd place

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Types of Variables Continuous Variables Have specific order Examples: –weight –temperature –blood pressure –time May be converted to categorical or ordinal

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Types of Statistics Descriptive –summarize data for clearer understanding Inferential –generalize results from sample to population –make probability decisions

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Descriptive Statistics Measures of central tendency –mean –mode –median Measures of variability –range –variance –standard deviation –standard error

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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

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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

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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

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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

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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)

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Analysis of Variance (ANOVA) When comparing 3 or more groups (independent variables) and end-point (dependent variable) is continuous.

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Analysis of Variance (ANOVA)

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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

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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

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Is there a relationship between hypertension and gender? Chi square analysis - p < 0.001

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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

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Pearson’s Correlation Coefficient Is Diastolic BP related to Weight? r = 0.805 p < 0.01

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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

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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.ANOVA b.Chi-Square c.Paired t-test * d.Unpaired t-test

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Name the Statistical Test Is there an association between smoking status and 3 levels of socioeconomic status? a.Mann-Whitney U-test b.Pearson’s correlation c.Turkey’s test d.Chi-Square *

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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

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Free Statistics Software http://freestatistics.altervista.org/click/fclick.php?fid=4

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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

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Girls Boys

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