Question

A researcher is interested in assessing male and female dentists have equal amounts of leisure time. Because women have not been widely represented in the field of dentistry until recently, almost all the older dentists are male. Therefore, you divide your sample into three groups: younger or novice female dentists (group 1), younger or novice male dentists (group 2), and older or more experienced male dentists (group 3). Each dentist is then asked to report the number of hours devoted to leisure time activities in a week. The three female dentists have 1,2, and 3 hours of leisure time; the three younger male dentists have 4, 5, and 6 hours of leisure time per week: and the three older male dentists have 7,8, and 9 hours of leisure time each week. The researcher wants to determine whether these differences in leisure time between the three groups of dentists are statistically significant or are likely to be due to chance.

Enter the following data in SPSS. Using SPSS conduct a one-way ANOVA; write the hypothesis; test for homogeneity of variances; conduct post-hoc tests (for this case use Tukey HSD if  Equal variances are assumed or Dunnett T3 C if Equal variances are not assumed). Include the SPSS output and write the results in APA format.

The assumptions for this test are:

1. Scores are independent of each other
2. The data is normally distributed for all groups
3. The groups have equal variances

Group	1	1	1
Scores	1	2	3
Group	2	2	2
Scores	4	5	6
Group	3	3	3
Scores	7	8	9

Write the null hypothesis:

On the results, identify the following:

1. F ratio for the group effect: _____   Explain what it means.
2. Sums of squares between and within groups: _______Explain what it means.
3. Mean scores for each group = _____
4. P value  = ______
5. Levene’s test results : F(, ) =_____, p =_____
6. Conduct post-hoc tests. Include the SPSS output and write the results in APA format.

Answer 1

Step-1: Firstly put the data in spss software taking group as a nominal variable and score as a scale variable.

Step-2: follow the 1 and 2 point as it is as given in this screen shot.

Hypothesis testing-

H0- There is a no statistically significant difference in leisure time between the three groups of dentists or There was a no statistically significant difference between groups1 group2 and group 3.

H1- There is a statistically significant difference in leisure time between the three groups of dentists or There was a statistically significant difference between groups1 group2 and group 3. or atleast 2 are significantly differ to each other.

As per follow the step 1 and step 2 we got the following output -

This is the table that shows the output of the ANOVA analysis and whether there is a statistically significant difference between our group means. We can see that the significance value is 0.001 (i.e., p = .001), which is below 0.05. and, therefore, there is a statistically significant difference in leisure time between the three groups of dentists This is great to know, but we do not know which of the specific groups differed. since this we can find out in the Multiple Comparisons table which contains the results of the Tukey post hoc test( as per assumption groups have equal variances) .

Ans(a)- F ratio = 27.000 this the calculated value of F test.

Ans(b)- sum of square between groups = 54

sum of square with in the groups = 6

Ans (c)- mean square for between groups = 27

mean square for between groups = 1

Ans (d)- p value = 0.001

Ans(e)- Levene’s test results :

F(2,6) = 0.000 , p = 1.000

Ans (f)- post hoc test

From The anova result it is clear that there are statistically significant differences between the groups as a whole. The table below, post hoc test shows which groups differed from each other. The Tukey post hoc test is generally the preferred test for conducting post hoc tests on a one-way ANOVA.  We can see from the table below that there is a statistically significant difference in leisure time between the all the three groups of dentists( p value < 0.05)