1. Statistical Tests
Karen H. Hagglund, M.S.

2. Research: How Do I Begin???

3. Take It “Bird by Bird” Anne Lamott

4. 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

5. Confused by Statistics ?

6. 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

7. Free Statistics Software
Mystat:
List of Free Statistics Software:

8. 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

9. } } Scales of Measurement Nominal Ordinal Qualitative Interval Ratio
Quantitative

10. 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

11. 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

12. 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

13. 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

14. } } Scales of Measurement Nominal Ordinal
Interval
Ratio
Lead to nonparametric statistics }
Lead to parametric statistics

15. Two Branches of Statistics
Descriptive
Frequencies & percents
Measures of the middle
Measures of variation
Inferential
Nonparametric statistics
Parametric statistics

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

17. Frequencies and Percents
Number of times a specific value of an observation occurs (counts)
For each category, calculate percent of sample

18. 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

19. 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

20. Measures of Variation or Dispersion
Variance
Square of the standard deviation
Range
Difference between the largest & smallest value

23. 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

24. 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?

25. 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

26. 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

27. Research Hypothesis Topic research question
Research question hypothesis
Null hypothesis (H0)
Predicts no effect or difference
Alternative hypothesis (H1)
Predicts an effect or difference

28. Example

29. 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.

30. Are These Categorical Variables Associated?

31. 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

32. Let’s Test For Association
Low SES 38.9%, Middle SES 20.3%, High SES 26.1%

33. 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

35. Do These Groups Differ?

36. Unpaired t-test or Student’s t-test
William Gossett
Frequently used statistical test
Use when there are two independent groups

37. 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

38. Let’s Test For A Difference
Smokers’ BMI = ± 5.27
Non-Smokers’ BMI = ± 5.48

39. Do These Groups Differ? Light smoker < 1 pack/day
Heavy smoker > 1 pack/day

40. 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

41. Let’s Test For A Difference
Non-Smokers’ BMI = ± 5.48
Light Smokers’ BMI = ± 4.96
Heavy Smokers’ BMI = ± 5.62

42. Is there a relationship between the variables?

43. 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

44. Scatterplots r = -1.0 ---- +1.0
Perfect positive correlation
Perfect negative correlation
No correlation

45. Let’s Test For A Relationship

47. 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”

48. Don’t Lie With Statistics !