Click to start/reset.
Compare one sample with target value(s)
Compare population median to a target value
Distribution of parent population is symmetrical
Create second sample all of the target median value
Wilcoxon signed-rank test
Distribution of parent population is NOT symmetrical
No valid process in AH Statistics course
Compare population mean to a target value
Distribution of parent population is normal
Parent population variance NOT known
Estimate population variance from sample variance
Perform hypothesis test
t-test for a single sample mean
Construct confidence interval
Use Student's t-distribution
Parent population variance known
Perform hypothesis test
z-test for a single sample mean
Construct confidence interval
Use z-distribution
Distribution of parent population is NOT normal
Parent population variance known
Sample size > 20
Use central limit theorem to obtain approximate normal distribution of sample mean
Perform hypothesis test
z-test for a single sample mean
Construct confidence interval
Use z-distribution
Sample size <20
No valid process in AH Statistics course
Parent population variance NOT known
Sample size > 20
Estimate population variance from sample variance
Use central limit theorem to obtain approximate normal distribution of sample mean
Perform hypothesis test
t-test for a single sample mean
Construct confidence interval
Use Student's t-distribution
Sample size <20
No valid process in AH Statistics course
Compare population proportion to a target value
Model with binomial distribution
Hypothesis test
Either proceed using the binomial distribution, or approximate to normal if np > 5 and nq > 5
Confidence interval
Approximate to normal if np > 5 and nq > 5
Construct confidence interval using z-distribution
Compare sample to a theoretical distribution
Chi-squared goodness-of-fit test
Distribution parameter known
Check expected frequencies: at least 80% ≥5 and none <1, else combine categories and start again.
Use degrees of freedom = categories - 1
Distribution parameter NOT known
Estimate the unknown parameter from the observed frequencies
Check expected frequencies: at least 80% ≥5 and none <1, else combine categories and start again.
Use degrees of freedom = categories - 2
Compare two samples with each other
Two samples of paired data
Compare difference of population medians
Distribution of parent population of differences is symmetrical
Wilcoxon signed-rank test
Distribution of parent population of differences is NOT symmetrical
No valid process in AH Statistics course
Compare population means
Calculate values of paired differences
Proceed as if a one sample process, with the focus upon the distribution of the differences.
Two samples of non-paired data
Compare population medians
Distributions of both parent populations have the same shape and spread
Mann-Whitney test
Distributions of both parent populations do NOT have same shape and spread
No valid process in AH Statistics course
Compare population means
Distribution of both parent populations are NOT normal
Parent population variances known
Sample size > 20
Use central limit theorem to obtain approximate normal distribution of sample means
z-test for a difference in population means
Sample size < 20
No valid process in AH Statistics course
Parent population variances NOT known
Sample size > 20
Parent population variances assumed to be equal
Estimate population variance from pooled sample variance
Use central limit theorem to obtain approximate normal distributions of sample means
t-test for a difference in population means
Parent population variances assumed to be NOT equal
Both sample sizes large (ie both > 20)
Estimate population variances from sample variances
Use central limit theorem to obtain approximate normal distributions of sample means
z-test for a difference in population means
Either sample size small
No valid process in AH Statistics course
Sample size < 20
No valid process in AH Statistics course
Distribution of both parent populations are normal
Parent population variances both NOT known
Parent population variances assumed to be equal
Estimate population variance from pooled sample variance
t-test for a difference in population means
Parent population variances assumed to be NOT equal
Both sample sizes large (ie both > 20)
Estimate population variances from sample variances
z-test for a difference in population means
Either sample size small
No valid process in AH Statistics course
Parent population variances both known
z-test for a difference in population means
Compare population proportions
Model with binomial distribution
Check criteria for approximating binomial with normal
z-test for a difference in population proportions
Establish a relationship between two variables
Establish if an association exists between two categorical variables, using frequencies
Chi-squared test for association in a contingency table.
Check expected frequencies: at least 80% ≥5 and none <1, else combine rows or columns and start again.
Use degrees of freedom = (rows-1) x (cols-1).
Compare paired continuous variables
Linear correlation and regression analysis
View a scatterplot to establish if there is a plausible linear correlation
Conduct hypothesis test on correlation coefficient, ρ
Calculate least squares regression equation
Conduct hypothesis test on slope, β (if required)
Construct a residual plot for analysis
Construct prediction/confidence intervals