Parametric and Nonparametric Tests Flashcards
Population Parameter
A number that describes something about an entire group or population
The number in the population is usually high, so it will probably have a normal distribution!
How is the sample size distributed when a parametric test is used?
Normally distributed
Which parameters should be used for skewed data?
Median, IQR (25th percentile, 75th percentile)
Data: Sex number in %
Parametric or Non-parametric
Non-parametric
-bc it is a yes or no answer and no means are used and there represented in categories
-means are continuous and more likely to be represented in a normally distributed curve
What is considered descriptive statistics?
Mean, median, SD, IQR
-used to describe data
What are Inferential Statistics?
Inference = Conclusion (reached based on evidence)
-used to test hypotheses and draw interferences
-Inferential Statistics can be parametric or non-parametric
What are the criteria for Parametric Tests?
-Samples are drawn from a normal distribution
-Variances (SD) in both groups compared are approximately equal (both normally distributed)
-Data are continuous (BP, LDL) !!!
What are non-parametric Tests?
-Statistics that do not test hypotheses concerning population parameters
-assumptions for parametric tests are not met
-they do not assume normal distribution and are distribution-free tests
What type of data is used in non-parametric Tests?
-Nominal data (Male/female, race, dead/alive)
-Ordinal data
-small sample size -> likely to have skewed data
What are common Parametric Tests?
-Student’s T-Test -> often used for continuous data
-Analysis of Variance (ANOVA)
What are common Non-Parametric Tests?
-Mann Whitney U
Nonparametric form of Student’s t-test
-Chi-Square Test / Fisher’s Exact Test
Used for nominal data
Students T-test
-parametric
-comparing two population means (or drug and placebo group)
-most common in the medical literature (more than 50%)
What are the assumptions of the Student t-test?
-Normal distribution
-SD in the 2 groups is approximately equal
-continuous data
-Randomly selected, independent samples
-> There are two different groups (drug vs placebo, compared to dependent in cross-over studies - with the same patients used for drug and placebo -> paired data)
Purpose of Student T-test
-determine the probability of the findings being due to chance
-creating a p-value
What is a t-score?
not on EXAM
-similar to Z-score
-Z-score is the number of SD away from the mean
-t-score is expressed in an estimated SD away from the mean
-Z-scores are stable
-t-scores will vary depending on sample size
Example:
randomized, placebo-controlled, double-blinded study (n=300)
the drug arm of the study reduced LDL by 18±4% and the placebo arm reduced LDL by 13±3%
Student’s t-test was used to compare lipid
reduction, p =0.02
Is the student’s t-test appropriate?
Criteria:
Normally distributed - Y bc the SD is not high relative to the mean
Variances should be approximately equal - Y
Continuous data Y- LDL values are continuous data
Independent groups - Y bc placebo-controlled
Why are Student t-tests not appropriate when comparing multiple groups?
Because the probability of committing a type I error (alpha) sums up each time we compare different groups
Which test is appropriate to test multiple groups?
ANOVA
When to use Non-parametric t-tests?
-When the assumptions for a Student’s t-test (parametric test) are not me
-when we have ordinal data
What are the Non-parametric t-tests?
-Mann Whitney U
-Wilcoxon Rank Sum
-with median
-they tell us whether the medians are different
Which test should be used when the conditions for a parametric t-test are not met?
Mann Whitney U
Which test to use for a nonparametric paired t-test
Wilcoxon Signed Rank test
ANOVA
-ANOVA = Analysis of Variance
-ANOVA is a “group comparison”
-ANOVA is a parametric test
When is an ANOVA test appropriate?
-When comparing the means of three or more groups
-parametric tests
-normally distributed data
What is the null for 3 or more groups?
H0: Group 1 = Group 2 = Group 3
-no difference between the groups
-if there is a difference between any of the means the p-value will be <0.05 for ANOVA
-but it doesn’t tell me between which group the statistical difference is
After discovering a difference between 3 groups
-conduct a “posthoc” test and analyze where the difference in mean between the 3 groups is
-pairwise comparison:
Group 1 vs Group 2
Group 2 vs Group 3
Group 1 vs Group 3
(a priori = before)
One-way ANOVA
-assessing the effect of a single variable (factor) on a single response variable (change of condition)
-multiple groups (it is ANOVA)
-f.e.: women with osteoporosis is assigned into 3 groups: std treatment, new drug, placebo
-the response variable is: a change in bone density
-single variable is: the new drug
Two-way ANOVA
-assesses the effect of two variables (factors)
-multiple groups
-the response variable is the change in condition
-two variables (factors): f.e. drug and age
Multi-way ANOVA - MANOVA
-assesses the effect of multiple variables (factors)
-multiple groups
-the response variable is the change in condition
-two variables (factors): f.e. drug, diet and alcohol consumption
Analysis of Covariance - ANCOVA
-same as ANOVA
-but controlling for the effects of some explanatory variable
-f.e. : we have the two variables (factors): drug, age
-the covariable could be: the severity of the disease
Repeated Measures ANOVA
-assessing several or repeated measurements of the same participant -> different conditions or different times
-BP taken while sitting, standing, supine
-Measurement of bone density at different times (6 months, 12 months)
Multiple Comparison Test or Posthoc Test
(NOT ON EXAM)
-for repeated tests
-Bonferroni t procedure
-prevents aggregation of p-values (alpha) like a Studtent’ds test would do
-increases the critical value -> it makes each comparison more rigorous -> and decreases each p-value
-the sum of the p-values will still be under 0.05 and significant
Different Comparison Test, Posthoc Test
(NOT ON EXAM)
important for research
-Bonferroni t Procedure
-Tukey test
-Scheffe’s Procedure
-Dunnett’s Procedure
When are posthoc tests done?
-After we determined a difference with the ANOVA
-we want to find out where the difference is with: the post hoc test
Nonparametric Comparison of 3 or more Groups
-Remember for parametric test we need: normal distribution, equal SD, continuous data
-for parametric test comparing multiple groups we would use ANOVA
-if one of these criteria is not met or the data is ordinal when comparing multiple groups: we use the nonparametric form of ANOVA
-Kruskal Wallis test: ANOVA on ranks
-Friedman test: ANOVA on ranks for paired (related) data –> f.e. cross-over studies
Which test is used for Categorical Variables (nominal data)?
Chi-square test
nominal data: race, color, sex
Chi-square test
-compares expected frequency vs observed frequency
-determines a p-value: what is the probability that this frequency of findings is due to chance alone
-2x2 table: 2 groups (drug, placebo) x 2 categories (male, female) -> fill with the percentages
-the test compares the actual numbers (in percentage) vs the expected numbers due to random variation
When is a Chi-square test considered statistically significant?
-NOMINAL DATA
-FREQUENCY TEST: is the amount of participants similar enough (significantly equal)
-p-value is less than 0.05 when the observed frequency is outside of the expected frequency
When is the Fisher’s Exact Test used?
-Nominal Data
-like Chi-square Test
-if at least one of the cells in the table has a value of 5 or less
-Yates correction for sample size of 25-40
What is the McNemar’s Test
-examines the frequency of data when the cases are dependent or related
-Chi-square test for dependent or paired samples
-several data points obtained from the same patient (repeated measures)
What is the Mantel-Haenszel test used for?
-adjust for confounding variables when comparing two INDEPENDENT categorial groups
-so it has to be independent groups
-nominal data
