chapter 10

• Mann-Whitney U-Test is often referred to as the Wilcoxon rank-sum test
• Statistical tests are chosen for a specific data analysis based on the types of clinical data to be analyzed and the research design
• Factors to consider in choosing a statistical test

  • Type of data (type of variable)
  • Number of variables
  • Metric used (e.g., means, rates, etc.)
  • A prespecified analysis plan is necessary in the research proposal
  • Identifying the statistical test used is part of methodology
• Steps in Mann-Whitney U-Test

  1. First, get the rank of ALL the variables

  2. If you have similar variables, add the designated ranks and divide based on the number of the same variables
• Bivariate analysis

  Typically assigns one variable as independent variable and one as dependent variable
• DO NOT REJECT THE NULL HYPOTHESIS in Mann-Whitney U-Test if: The average ranks of the two samples are similar
• Mann-Whitney U-Test is a test for ordinal data that is similar to the two-sample t-test
• Statistical Analysis

  1. Observed differences in research may be due to random chance or due to meaningful associations

  2. Statistical tests analyze relationships of variables in analytic research

  3. Appropriate statistical test should match the research objectives and the research design as well as other factors
• The statistical test must be appropriate for the scientific metrics used
• Mann-Whitney U-Test defines the null hypothesis as a 50:50 chance that a randomly selected observation from one population (x) would be larger than an observation from the population (y)
• Steps in statistical analysis

  1. Data of individual variables first studied

  2. Distributions and outliers determined

  3. Errors looked for

  4. Bivariate analysis performed to test hypothesis and determine relationships

  5. Multivariable analysis subsequently done if there are more than one independent variable to consider
• Statistical testing is NOT REQUIRED when the results of interest are purely descriptive because you are simply describing your sample without making any inferences to the population from which the sample was thought to be taken
• Nonparametric Tests Using Ordinal Data

  • Mann-Whitney U-Test
  • Wilcoxon Matched-Pairs Signed-Ranks Test
  • Kruskal-Wallis Test
  • Spearman and Kendall Correlation Coefficients
  • Sign Test
  • Mood Median Test
• REJECT THE NULL HYPOTHESIS in Mann-Whitney U-Test if: The average rank of one sample is considerably greater than the other sample
• There is no significant difference on the satisfaction ratings of low, middle, and upper class
• There is a significant difference in the Pre-test and Post-test scores in using Traditional learning in teaching Biostatistics
• Example: Age and Sleep correlation
• KRUSKAL-WALLIS TEST is comparable to ONE WAY ANOVA (F TEST)
• Spearman and Kendall Correlation Coefficients


  • For ordinal data, these tests are used to assess associations between variables
  • Similar to regression analysis and correlation analysis in relating continuous variables
  • Spearman rank correlation coefficient (rho)
  • Kendall rank correlation coefficient (tau)
  • rho vs r: Pearson correlation coefficient (r) measures the strength of linear associations of variables, while rho measures the strength of any strictly increasing or decreasing relationship between variables, even if it is nonlinear
• KRUSKAL-WALLIS TEST

  • All the data are ranked numerically and the rank values are summed in each of the groups compared
  • Determines if the average ranks from three or more groups differ from one another more than expected if by chance alone
  • Is an example of a critical ratio: magnitude of the difference measure of random variability
  • Null hypothesis (H0) is rejected if ratio is sufficiently large
• Ranking

  Rank 1: 18
• Sign Test

  Used to compare results of experimental studies, determine significant change in response of experimental group in paired data
• Calculating Rank

  1. Rank (x): 2, 3, 1, 4.5, 4

  2. Rank (y): 1.5, 4.5, 3, 1.5, 4.5
• Inferences from Dichotomous and Ordinal Data
• Age and Sleep correlation

  • Subject A: 25 years, 6 hrs sleep
  • Subject B: 18 years, 7 hrs sleep
  • Subject C: 32 years, 5 hrs sleep
  • Subject D: 18 years, 7 hrs sleep
  • Subject E: 62 years, 5 hrs sleep
• Concepts

  • Sign of r: (+) direct relationship, (-) inverse relationship
  • Values of rho: 0.0-0.20 No correlation, 0.21-0.40 Low corr., 0.41-0.70 Moderate corr., 0.71-0.90 High corr., 0.91-0.99 Very high corr., 1.00 Perfect correlation
• Ranking of Age and Sleep

  • AGE RANK: 18, 25, 28, 32, 62
  • SLEEP RANK: 5 hrs, 5 hrs, 6 hrs, 7 hrs, 7 hrs
• 2 x 2 Contingency Table is used to determine if the distribution of one variable is conditionally dependent on the other variable
• Conclusion: Age (x) and duration of sleep (y) show inverse and moderate correlation
• Mood Median Test

  Compares two independent samples to determine if they have the same median, uses a 2x2 table and Chi-square test
• Value of rho calculated as -0.70
• 2 x 2 Contingency Table


  • It is used to determine whether the distribution of one variable is conditionally dependent on the other variable
  • 2 x 2 tables are constructed with the outcome or dependent variable in the columns and the exposure in the rows
• Goodness-of-Fit Test

  1. Comparing the observed counts with the expected counts

  2. Goal is to see how well the observed counts in a contingency table fit the counts expected on the basis of the model
• Chi-Square Test

  Denoted as x2
• H0 is rejected if medians are not the same
• Calculation of Percentages

  Divide the number of individuals in a specific category by the total number of individuals in that category, then multiply by 100 to get the percentage
• Calculation for Expected Counts

  Expected count = Row total x Column total / Study total
• The expected counts in each cell of a 2 x 2 contingency table should equal to 5 or more, or the assumptions and approximations inherent in the chi-square test are not valid
• Data is randomly selected, Frequency counts and E of at least 5
• When to use Chi-Square

  • Categorical data ONLY
  • Measures how expectations vs. actual observed data
  • Test relationships between categorical variables
  • Test hypothesis about distribution of observations in different categories
  • Estimate how distribution of a categorical variable closely matches an expected distribution, or whether two categorical variables are independent of one another