Example of Friedman Test

A marketing analyst wants to compare the relative effectiveness of three types of advertising: direct mail, newspaper, and magazine. The analyst performs a randomized block experiment. For 12 clients, the marketing firm used all three types of advertising over a 1-year period and recorded the year's percentage response to each type of advertising.

To determine whether the median treatment effect differs for the type of advertising, the analyst uses the Friedman test.

  1. Open the sample data, AdvertisingEffectiveness.MTW.
  2. Choose Stat > Nonparametrics > Friedman.
  3. In Response, enter Response.
  4. In Treatment, enter Advtype.
  5. In Blocks, enter Company.
  6. Click OK.

Interpret the results

Because the p-value for the advertising data is less than the significance level of 0.05, the analyst rejects the null hypothesis and concludes that at least one of three types of advertising has a different effect. Also, the median responses for direct mail (6.100) and magazine (8.150) are close to the overall median (9.183), but the median response for newspaper advertising (13.300) is substantially higher. These results indicate that newspaper advertising might be more effective than the other types of advertising.

Friedman Test: Response vs Advtype, Company

Method Treatment = Advtype Block = Company
Descriptive Statistics Advtype N Median Sum of Ranks direct-mail 12 6.1000 16.0 magazine 12 8.1500 24.0 newspaper 12 13.3000 32.0 Overall 36 9.1833
Test Null hypothesis H₀: All treatment effects are zero Alternative hypothesis H₁: Not all treatment effects are zero

DF Chi-Square P-Value 2 10.67 0.005

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