Statistical Data Analysis Flashcards

Flashcards covering bootstrapping, confidence intervals, and the Mann-Whitney U test.

Bootstrapping Method (Confidence Intervals)

Used when the sample size is small (n < 30) and the underlying distribution is not normal.

Default Resamples in Bootstrap Confidence Intervals

1000

R code for 99% BCa and Percentile Bootstrap Confidence Intervals

boot.ci(name of bootstrap output, conf=0.99, type=c(“bca”,“perc”)

95% Bootstrap Confidence Interval (using normal approximation)

x̄ ± 1.96 * standard error

99% Bootstrap Confidence Interval (using normal approximation)

x̄ ± 2.58 * standard error

Mann-Whitney U Test

A test used to compare two independent groups when the sample size is small and the data is not normally distributed.

Null Hypothesis (H0) in Mann-Whitney U Test

The medians of the two groups are equal.

Alternative Hypothesis (H1) in Mann-Whitney U Test

The medians of the two groups are not equal.

U Statistic Calculation

U1 = R1 − n1(n1 + 1) / 2 and U2 = R2 − n2(n2 + 1) / 2 , where U = Min{U1, U2}

Decision Rule for Mann-Whitney U Test (Reject H0)

Reject H0 if U < Ucrit (critical value)