Statistical Tests

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Statistical Tests

• Karen H. Hagglund, M.S.

Karen.Hagglund_at_stjohn.org
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ResearchHow Do I Begin???
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Take It Bird by BirdAnne Lamott
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Lets 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 http//www.systat.com/MystatProducts.aspx
  
• List of Free Statistics Software
  http//statpages.org/javasta2.html

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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
• Interval
• Ratio

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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

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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
• Fishers exact test
• T-test
• Unpaired
• Paired
• Analysis of Variance (ANOVA)
• Pearsons Correlation
• Linear Regression

Nonparametric Association/Relationship

Parametric Compare groups

Parametric Compare groups

Parametric Association/Relationship
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Probability and p Values

• p lt 0.05
• 1 in 20 or 5 chance groups are not different
  when we say groups are significantly different
• p lt 0.01
• 1 in 100 or 1 chance of error
• p lt 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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Chi-Square
2

• 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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Lets Test For Association
Low SES 38.9, Middle SES 20.3, High SES 26.1
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Alternative to Chi-Square

• Fishers exact test
• Is based on exact probabilities
• Use when expected count lt5 cases in each cell and
• Use with 2 x 2 contingency table

R A Fisher 1890-1962
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Do These Groups Differ?
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Unpaired t-test or Students t-test
William Gossett 1876-1937

• Frequently used statistical test
• Use when there are two independent groups

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Unpaired t-test or Students 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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Lets Test For A Difference
Smokers BMI 25.18 5.27 Non-Smokers BMI
26.22 5.48
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Do These Groups Differ?
Light smoker lt 1 pack/day Heavy smoker gt 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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Lets Test For A Difference
Non-Smokers BMI 26.22 5.48 Light Smokers
BMI 26.18 4.96 Heavy Smokers BMI 23.31
5.62
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Is there a relationship between the
variables?
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Pearsons Correlation
Karl Pearson 1857-1936

• 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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Lets 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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Dont Lie With Statistics !