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Statistical Tests Karen H. Hagglund, M.S.

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**Research: How Do I Begin???**

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**Take It “Bird by Bird” Anne Lamott**

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**Let’s Take it Step by Step...**

Identify topic Literature review Variables of interest Research hypothesis Design study Power analysis Write proposal Design data tools Committees Collect data Set up spreadsheet Enter data Statistical analysis Graphs Slides / poster Write paper / manuscript

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**Confused by Statistics ?**

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Goals To understand why a particular statistical test was used for your research project To interpret your results To understand, evaluate, and present your results

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**Free Statistics Software**

Mystat: List of Free Statistics Software:

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**Before choosing a statistical test…**

Figure out the variable type Scales of measurement (qualitative or quantitative) Figure out your goal Compare groups Measure relationship or association of variables

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**} } Scales of Measurement Nominal Ordinal Qualitative Interval Ratio**

Quantitative

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**Nominal Scale (discrete)**

Simplest scale of measurement Variables which have no numerical value Variables which have categories Count number in each category, calculate percentage Examples: Gender Race Marital status Whether or not tumor recurred Alive or dead

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Ordinal Scale Variables are in categories, but with an underlying order to their values Rank-order categories from highest to lowest Intervals may not be equal Count number in each category, calculate percentage Examples: Cancer stages Apgar scores Pain ratings Likert scale

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**Interval Scale Quantitative data Can add & subtract values**

Cannot multiply & divide values No true zero point Example: Temperature on a Celsius scale 00 indicates point when water will freeze, not an absence of warmth

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**Ratio Scale (continuous)**

Quantitative data with true zero Can add, subtract, multiply & divide Examples: Age Body weight Blood pressure Length of hospital stay Operating room time

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**} } Scales of Measurement Nominal Ordinal**

Interval Ratio Lead to nonparametric statistics } Lead to parametric statistics

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**Two Branches of Statistics**

Descriptive Frequencies & percents Measures of the middle Measures of variation Inferential Nonparametric statistics Parametric statistics

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**Descriptive Statistics**

First step in analyzing data Goal is to communicate results, without generalizing beyond sample to a larger group

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**Frequencies and Percents**

Number of times a specific value of an observation occurs (counts) For each category, calculate percent of sample

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**Measures of the Middle or Central Tendency**

Mean Average score sum of all values, divided by number of values Most common measure, but easily influenced by outliers Median 50th percentile score half above, half below Use when data are asymmetrical or skewed

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**Measures of Variation or Dispersion**

Standard deviation (SD) Square root of the sum of squared deviations of the values from the mean divided by the number of values Standard error (SE) Standard deviation divided by the square root of the number of values SD = sum of (individual value – mean value) 2 ________________________________________________ number of values

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**Measures of Variation or Dispersion**

Variance Square of the standard deviation Range Difference between the largest & smallest value

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**Inferential Statistics**

Sample Population Nonparametric tests Used for analyzing nominal & ordinal variables Makes no assumptions about data Parametric tests Used for analyzing interval & ratio variables Makes assumptions about data Normal distribution Homogeneity of variance Independent observations

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**Which Test Do I Use? Step 1 Know the scale of measurement**

Step 2 Know your goal Is it to compare groups? How many groups do I have? Is it to measure a relationship or association between variables?

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**Key Inferential Statistics**

} Chi-Square Fisher’s exact test T-test Unpaired Paired Analysis of Variance (ANOVA) Pearson’s Correlation Linear Regression Nonparametric Association/Relationship } Parametric Compare groups } Parametric Compare groups } Parametric Association/Relationship

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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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**Research Hypothesis Topic research question**

Research question hypothesis Null hypothesis (H0) Predicts no effect or difference Alternative hypothesis (H1) Predicts an effect or difference

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Example

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**Topic: Cancer & Smoking**

Research Question: Is there a relationship between smoking & cancer? H0: Smokers are not more likely to develop cancer compared to non-smokers. H1: Smokers are more likely to develop cancer than are non-smokers.

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**Are These Categorical Variables Associated?**

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**2 Chi-Square Most common nonparametric test**

Use to test for association between categorical variables Use to test the difference between observed & expected proportions The larger the chi-square value, the more the numbers in the table differ from those we would expect if there were no association Limitation Expected values must be equal to or larger than 5

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**Let’s Test For Association**

Low SES 38.9%, Middle SES 20.3%, High SES 26.1%

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**Alternative to Chi-Square**

Fisher’s exact test Is based on exact probabilities Use when expected count <5 cases in each cell and Use with 2 x 2 contingency table R A Fisher

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Do These Groups Differ?

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**Unpaired t-test or Student’s t-test**

William Gossett Frequently used statistical test Use when there are two independent groups

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**Unpaired t-test or Student’s t-test**

Test for a difference between groups Is the difference in sample means due to their natural variability or to a real difference between the groups in the population? Outcome (dependent variable) is interval or ratio Assumptions of normality, homogeneity of variance & independence of observations

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**Let’s Test For A Difference**

Smokers’ BMI = ± 5.27 Non-Smokers’ BMI = ± 5.48

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**Do These Groups Differ? Light smoker < 1 pack/day**

Heavy smoker > 1 pack/day

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**Analysis of Variance (ANOVA) or F-test**

Three or more independent groups Test for a difference between groups Is the difference in sample means due to their natural variability or to a real difference between the groups in the population? Outcome (dependent variable) is interval or ratio Assumptions of normality, homogeneity of variance & independence of observations

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**Let’s Test For A Difference**

Non-Smokers’ BMI = ± 5.48 Light Smokers’ BMI = ± 4.96 Heavy Smokers’ BMI = ± 5.62

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**Is there a relationship between the variables?**

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**Pearson’s Correlation**

Karl Pearson Measures the degree of relationship between two variables Assumptions: Variables are normally distributed Relationship is linear Both variables are measured on the interval or ratio scale Variables are measured on the same subjects

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**Scatterplots r = -1.0 ---- +1.0**

Perfect positive correlation Perfect negative correlation No correlation

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**Let’s Test For A Relationship**

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**Interpretation of Results**

The size of the p value does not indicate the importance of the result Appropriate interpretation of statistical test Group differences Association or relationship “Correlation does not imply causation”

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**Don’t Lie With Statistics !**

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