KNR 445
Statistical Applications in Science & Technology

Assignment 24
Oneway Analysis of Variance (Oneway ANOVA)

The purpose of this assignment is to introduce the concept of the oneway analysis of variance, used to compare the means among two or more independent sets of data. The exercise also requires you to run and interpret a post hoc test, used to identify which means are significantly different if the F ratio of the ANOVA is statistically significant.

Homework

The data to be used are listed on this page. The data represents ankle joint range of motion (ROM) during landing with three ankle brace conditions.

1. Enter the data set listed below into an SPSS data file. Code the three groups with 1 for No support, 2 for tape and 3 for brace.
    a. Run a Oneway ANOVA on the data, specifying Tukey-b (sometimes called Tukey's Honestly Significant Difference (HSD)) as the post hoc test.
    b. Off the ANOVA table
        i. What does the Between Groups Sum of Squares represent?
        ii. What does Within Group Sum of Squares represent?
        iii. What does df stand for? How are the df Between and df Within terms calculated?
        iv. How are the values in the column MS calculated?
        v. How is the F ratio calculated?
        vi. What is the critical F value in this experiment ( alpha = 0.05)?
        vii. Is the F ratio statistically significant
                (1) at the alpha = 0.10 level of significance?
                (2) at the alpha = 0.05 level of significance?
                (3) at the alpha = 0.01 level of significance?
                (4) If the p value was to be listed as 0.000, what does that mean?
        viii. If the F ratio is significant
                (1) identify which of the three groups are (is) significantly different.
        ix. Write up the results of the ANOVA and the post hoc test as if they were to be presented in the text of a thesis or manuscript.
SPSS Output

ROM data
NO_SUP    TAPE    BRACE
31.53         18.51         29.92
41.72         29.79         45.55
38.63         27.11         38.07
47.35        42.27         46.99
53.22        34.95         52.75
33.18        27.49         34.29
45.87        35.96         44.17
40.36        40.60         39.96
47.63        36.59         45.15
52.19        35.77         51.86
41.90        23.31         39.37
26.74        25.14         44.10
33.87        23.71         30.03
41.39        27.99         35.90