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

STATISTICS David Pieper, Ph.D.

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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 Inferential**

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**

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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**Analysis of Variance (ANOVA)**

p < 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 = p < 0.01

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**Pearson’s Correlation Coefficient**

r = 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? ANOVA Chi-Square Paired t-test * Unpaired t-test

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

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**Pearson’s correlation * Repeated measures ANOVA Chi-Square**

Name the Statistical Test Is there a relationship between length of hospitalization and number of medications prescribed when patient is discharged? Logistic regression Pearson’s correlation * Repeated measures ANOVA Chi-Square

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**Free Statistics Software**

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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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