Statistical Tests

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

• 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

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

• 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

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

• 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

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 !