STATISTICAL REVIEW FOR THE OITE
Richard E. Hughes, Ph.D.
OUTLINE
• • • • The assumption of normality What test should I use? Type I and Type II errors Statistical power
EXAMPLE DATA
68 27 74 12 31 22 43 63 22 51 57 50 43 49 42 23 36 51 38 27 12 27 24 42 12 21 49 30 25 28 32 16 28 36 44 31 49 24 23 28 65 28 38 69 19 32 43 25 42 47 46 79 25 45 27 23 30
HISTOGRAM
NORMAL DISTRIBUTION (“parametric statistics”)
OUTLINE
• • • • The assumption of normality What test should I use? Type I and Type II errors Statistical power
STATISTICAL ANALYSIS
Response
Continuous
Normally distributed and large sample size? No
Discrete
Yes
# experimental groups 1 group repeated measures Paired t-test
Nonparametric Chi-squared Wilcoxon Friedman Kruskal-Wallis ANOVA
2 groups t-test
> 2 groups
You have a large population of patients who have had surgery on one shoulder. You want to compare the mean shoulder abduction strength of the shoulders that had surgery to the contralateral side. The data is normally distributed. Which test do you use?
• • • • • Kolmologorov-Smirnov Logistic regression Two-way frequency analysis Paired t-test Student’s t-test
STATISTICAL ANALYSIS
Response
Continuous
Normally distributed and large sample size? No
Discrete
Yes
# experimental groups 1 group repeated measures Paired t-test
Nonparametric Chi-squared Wilcoxon Friedman Kruskal-Wallis ANOVA
2 groups t-test
> 2 groups
You have a large population of patients who have had surgery on one shoulder. You want to compare the mean shoulder abduction strength of the shoulders that had surgery to the contralateral side. The data is normally distributed. Which test do you use?
• • • • • Kolmologorov-Smirnov Logistic regression Two-way frequency analysis Paired t-test Student’s t-test
What analytical technique would be used to test the hypothesis of equal [put your favorite continuous dependent measure here] in 2 groups tested in the laboratory? (The data are distributed normally in each group, and group variances are equal) • • • • • Two-way analysis of variance Wilcoxon two-sample test Two-way frequency analysis Paired t-test Student’s t-test
STATISTICAL ANALYSIS
Response
Continuous
Normally distributed and large sample size? No
Discrete
Yes
# experimental groups 1 group repeated measures Paired t-test
Nonparametric Chi-squared Wilcoxon Friedman Kruskal-Wallis ANOVA
2 groups t-test
> 2 groups
What analytical technique would be used to test the hypothesis of equal [put your favorite continuous dependent measure here] in 2 groups tested in the laboratory? (The data are distributed normally in each group, and group variances are equal) • • • • • Two-way analysis of variance Wilcoxon two-sample test Two-way frequency analysis Paired t-test Student’s t-test
You are testing the stiffness of four reconstructions and want to determine if the mean stiffness depends on reconstruction type. A large number of cadavers are tested and the data is normally distributed. What test would you use?
• • • • • Chi-square ANOVA Spearman correlation Paired t-test Regression
STATISTICAL ANALYSIS
Response
Continuous
Normally distributed and large sample size? No
Discrete
Yes
# experimental groups 1 group repeated measures Paired t-test
Nonparametric Chi-squared Wilcoxon Friedman Kruskal-Wallis ANOVA
2 groups t-test
> 2 groups
You are testing the stiffness of four reconstructions and want to determine if the mean stiffness depends on reconstruction type. A large number of cadavers are tested and the data is normally distributed. What test would you use?
• • • • • Chi-square ANOVA Spearman correlation Paired t-test Regression
Two groups of patients have been treated, and each patient outcome has been graded as poor, good, or excellent. You want to test for association between treatment group and outcome. Which test do you use?
• • • • • Chi-square Logistic regression Regression Paired t-test Student’s t-test
STATISTICAL ANALYSIS
Response
Continuous
Normally distributed and large sample size? No
Discrete
Yes
# experimental groups 1 group repeated measures Paired t-test
Nonparametric Chi-squared Wilcoxon Friedman Kruskal-Wallis ANOVA
2 groups t-test
> 2 groups
Two groups of patients have been treated, and each patient outcome has been graded as poor, good, or excellent. You want to test for association between treatment group and outcome. Which test do you use?
• • • • • Chi-square Logistic regression Regression Paired t-test Student’s t-test
GUESSING
Parametric tests
• • • • t-test Paired t-test ANOVA Regression • • • • • • • Nonparametric tests Chi-squared Wilcoxon signed-rank Mann-Whitney Kolmolgorov-Smirnov Kruskal-Wallis Spearman correlation Friedman two-way ANOVA
What analytical technique would be used to test the hypothesis of equal [put your favorite continuous dependent measure here] in 2 groups tested in the laboratory? (The data are distributed normally in each group, and group variances are equal)
• • • • • Two-way analysis of variance Wilcoxon two-sample test Two-way frequency analysis Paired t-test Student’s t-test
What analytical technique would be used to test the hypothesis of equal [put your favorite continuous dependent measure here] in 2 groups tested in the laboratory? (The data are distributed normally in each group, and group variances are equal)
• • • • • Two-way analysis of variance Wilcoxon two-sample test Two-way frequency analysis Paired t-test Student’s t-test
OUTLINE
• • • • The assumption of normality What test should I use? Type I and Type II errors Statistical power
TYPE I ERROR (Alpha or p-value)
Saying there is a difference when there really isn’t
TYPE II ERROR (beta)
Saying there isn’t a difference and there really is a difference
Which of the following terms best describes the probability of making a decision that a treatment has an effect on an outcome in an experiment when in reality there is no effect?
• • • • • Alpha Type II error Power Beta Effect size
Which of the following terms best describes the probability of making a decision that a treatment has an effect on an outcome in an experiment when in reality there is no effect?
• • • • • Alpha Type II error Power Beta Effect size
OUTLINE
• • • • The assumption of normality What test should I use? Type I and Type II errors Statistical power
STATISTICAL POWER (1 - Prob[Type II error])
is the probability that you will find an effect if there really is one
The main reason for performing a power analysis before a study is to
Supply an appropriate control group Avoid bias so that conclusions are not questionable Obtain a sample that represents the population Determine the probability of detecting scientifically meaningful effects • Ensure that treatment groups are handled equally • • • •
The main reason for performing a power analysis before a study is to
Supply an appropriate control group Avoid bias so that conclusions are not questionable Obtain a sample that represents the population Determine the probability of detecting scientifically meaningful effects • Ensure that treatment groups are handled equally • • • •
THANK YOU