# Non-parametric Tests Notes

### Osmosis High-Yield Notes

This Osmosis High-Yield Note provides an overview of Non-parametric Tests essentials. All Osmosis Notes are clearly laid-out and contain striking images, tables, and diagrams to help visual learners understand complex topics quickly and efficiently. Find more information about Non-parametric Tests:

Chi-squared test

Fisher's exact test

Kaplan-Meier survival analysis

Kappa coefficient

Mann-Whitney U test

Spearman's rank correlation coefficient  NOTES NOTES NON-PARAMETRIC TESTS NON-PARAMETRIC TESTS ▪ For data that is assumed to not be distributed normally ▪ For nominal/ordinal level variables CHI-SQUARED TEST osms.it/chi-squared_test ▪ Chi-square (𝜲2) goodness-of-ﬁt test ▪ Test compares categorical variables ▫ Assesses for signiﬁcant association ▪ Examines whether collected data is signiﬁcantly different than theoretical model ▫ How “good is the ﬁt” between data, what is expected ▪ Null hypothesis: no signiﬁcant difference between theorized/expected, observed ratios ▫ 𝜲2 = sum of [(observed – expected)2/ expected] ▪ Use 𝜲2 table to ﬁnd critical 𝜲2 ▫ Adjusted for degrees of freedom [n – 1], at selected p-value ▪ Accept null hypothesis if 𝜲2 < critical 𝜲2 CHI-SQUARE TEST OF INDEPENDENCE ▪ For analysis of contingency tables (or crosstabs tables) ▪ Investigates whether two/more categorical variables are statistically signiﬁcant ▪ Used for multiple variables ▪ Degrees of freedom = (# of rows – 1) x (# of columns – 1) ▪ Requires > 5 data points in all cells of table; whole numbers ▪ Higher 𝜲2 results in lower p-value FISHER'S EXACT TEST osms.it/Fisher_exact_test ▪ Variant of chi-square test ▫ Used with small sample size ▪ Used to determine exact probability of association between two categorical variables (i.e. signiﬁcance of association [contingency] between classiﬁcations) 62 OSMOSIS.ORG ▫ Use for 2 x 2 contingency tables (< 5 in a cell) ▫ p-values calculated exactly ▫ p < 0.05, unlikely to be random association  Chapter 9 Biostatistics & Epidemiology: Non-parametric Tests KAPLAN-MEIER SURVIVAL ANALYSIS osms.it/Kaplan-Meier_survival_analysis ▪ Estimates survival from lifetime data; measures fraction of survivors over treatment time; simplest method of computing survival over time ▫ Plot of percent survival versus time; generated from status at last observation, time to event ▫ Large sample size → approaches population effect ▫ Accounts for censored data; withdrawn from study, lost to follow-up; alive at last follow-up (i.e. right-censoring—data above a certain value, but otherwise unknown) ▫ Limited capacity to estimate survival adjusted for covariates KAPPA COEFFICIENT osms.it/kappa-coefficient ▪ AKA Cohen’s kappa coefﬁcient ▪ Measure of inter-rater agreement ▪ Compares ability of different raters to classify categorical variables ▪ Interobserver agreement: accounts for agreement that occurs by chance, when raters measure same thing, using same observation method ▪ Calculated from observed, expected frequencies from diagonal of contingency table ▪ If kappa = 1 ▫ Agreement is perfect ▪ If kappa = 0 ▫ Agreement is no better than if agreement happened by chance ▪ Example for interpreting agreement based on kappa coefﬁcient ▫ None: < 0 ▫ Fair: 0.20–0.40 ▫ Moderate: 0.40–0.60 ▫ Good: 0.60–0.80 ▫ Very good: 0.80–1.00 MANN-WHITNEY U TEST osms.it/Mann-Whitney_u_test ▪ Nonparametric test equivalent to unpaired t-test ▪ Compares differences between two unpaired groups that are not normally distributed ▫ Uses number ranks rather than raw data ▫ Provides p-value indicating whether or not groups are signiﬁcantly different from each other (p < 0.05; unlikely to happen by chance) OSMOSIS.ORG 63  SPEARMAN'S RANK CORRELATION COEFFICIENT osms.it/Spearmans-rank-correlation-coefficient ▪ Spearman’s rho (𝞺) ▪ Non-parametric equivalent of Pearson’s correlation coefﬁcient ▪ Measure strength, direction of monotonic association between two ranked variables ▫ Monotonic association means variables increase together (i.e. as value of one variable increases value of other variable increases also/as value of one variable increases, other variable value will decrease) ▫ Does not have to be linear, but must be entirely increasing/entirely decreasing (may include plateaus) ▫ Use for continuous/discrete ordinal, interval, ratio variables 64 OSMOSIS.ORG ▪ Sign indicates direction of association ▫ x and y increasing → +ve 𝞺; x and y decreasing → –ve 𝞺 ▪ 𝞺 increases as correlation approaches perfect monotone relationship between variables ▪ Two formulas ▫ One for when there are no tied ranks ▫ One for tied ranks ▪ Use critical values (rs) from Spearman’s rank coefﬁcient tables to determine signiﬁcance of r (Spearman’s coefﬁcient of sample)

### Osmosis High-Yield Notes

This Osmosis High-Yield Note provides an overview of Non-parametric Tests essentials. All Osmosis Notes are clearly laid-out and contain striking images, tables, and diagrams to help visual learners understand complex topics quickly and efficiently. Find more information about Non-parametric Tests by visiting the associated Learn Page.