Statistical Tests



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Statistical Tests

  • Karen H. Hagglund, M.S.






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





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



Mystat: http://www.systat.com/MystatProducts.aspx

  • Mystat: http://www.systat.com/MystatProducts.aspx

  • List of Free Statistics Software: http://statpages.org/javasta2.html



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


Scales of Measurement

  • Nominal

  • Ordinal

  • Interval

  • Ratio



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


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


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


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


Scales of Measurement

  • Nominal

  • Ordinal

  • Interval

  • Ratio



Two Branches of Statistics

  • Descriptive

    • Frequencies & percents
    • Measures of the middle
    • Measures of variation
  • Inferential

    • Nonparametric statistics
    • Parametric statistics


Descriptive Statistics

  • First step in analyzing data

  • Goal is to communicate results, without generalizing beyond sample to a larger group



Frequencies and Percents

  • Number of times a specific value of an observation occurs (counts)

  • For each category, calculate percent of sample



Measures of the Middle or Central Tendency

  • Mean

  • Median

    • 50th percentile score
      • half above, half below
    • Use when data are asymmetrical or skewed


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


Measures of Variation or Dispersion

  • Variance

    • Square of the standard deviation
  • Range

    • Difference between the largest & smallest value






Inferential Statistics

  • Nonparametric tests

  • Parametric tests

    • Used for analyzing interval & ratio variables
    • Makes assumptions about data
      • Normal distribution
      • Homogeneity of variance
      • Independent observations


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?


Key Inferential Statistics

  • Chi-Square

    • Fisher’s exact test
  • T-test

    • Unpaired
    • Paired
  • Analysis of Variance (ANOVA)

  • Pearson’s Correlation

  • Linear Regression



p < 0.05

  • p < 0.05

  • p < 0.01

    • 1 in 100 or 1% chance of error
  • p < 0.001

    • 1 in 1000 or .1% chance of error


Research Hypothesis

  • Topic research question

  • Research question hypothesis

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






Are These Categorical Variables Associated?



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


Let’s Test For Association



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




Do These Groups Differ?



Unpaired t-test or Student’s t-test

  • Frequently used statistical test

  • Use when there are two independent groups



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



Let’s Test For A Difference



Do These Groups Differ?



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



Let’s Test For A Difference



Is there a relationship between the variables?



Pearson’s Correlation

  • 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


Scatterplots r = -1.0 ---- +1.0



Let’s Test For A Relationship





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”


Don’t Lie With Statistics !



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