Example –A radio station manager wants to know if the amount of time his listeners spent listening to a radio per day is about the same every day of the week. –200 teenagers were asked to record how long they spend listening to a radio each day of the week Radio.xls). Radio.xls Solution –The problem objective is to compare seven populations. –The data is quantitative. Randomized Blocks ANOVA - Example

Solution –Each day of the week can be considered a treatment. –Each 7 data points (per person) can be blocked, because they belong to the same person. –This procedure eliminates the variability in the “radio-times” among teenagers, and helps detect differences of the mean times teenagers listen to the radio among the days of the week. Randomized Blocks ANOVA - Example

Checking the required conditions Observing the histograms of the seven populations we can assume that all the distributions are approximately normally distributed. Sunday Monday The population variances seem to be equal. See the sample variances :

BlocksTreatmentsK-1b-1 MST / MSE MSB / MSE Conclusion: At 5% significance level there is sufficient evidence to reject the null hypothesis, and infer that mean “radio time” is different in at least one of the week days. Randomized Blocks ANOVA – Excel solution