[SOLVED] game statistic ANOVA in SPSS statstutor Community Project stcp-marshall- ANO V A

ANOVA in SPSS statstutor Community Project stcp-marshall- ANO V A
One-way (between-groups) ANOVA Dependent variable: Continuous (scale/interval/ratio),
Independent variable: Categorical (at least 3 unrelated/ independent groups)
Common Applications: Used to detect a difference in means of 3 or more independent groups. It can be thought of as an extension of the independent t-test for and can be referred to as between-subjects ANOVA.
Data: The data set Diet.sav contains information on 78 people who undertook one of three diets. There is background information such as age, gender and height as well as weight lost on the diet (a positive value means they lost weight). The aim of the study was to see which diet was best for losing weight so the independent variable (group) is diet.
The following resources are associated:
Statistical Hypothesis testing, Checking normality in SPSS and the SPSS dataset Diet.sav
Female = 0
Diet 1, 2 or 3
Before carrying any analysis, summarise weight lost by diet using a confidence interval plot or box-plot and some summary statistics. Do the group means and standard deviations look similar or very different?
Diet 3 seems better than the other diets as the mean weight lost is greater. The standard deviations are similar so weight lost within each group is equally spread out.
Ellen Marshall www.statstutor.ac.uk University of Sheffield
Reviewer: Alun Owen University of Worcester
Weight lost after 10 weeks

ANOVA in SPSS statstutor Community Project
ANOVA stands for Analysis of variance as it uses the ratio of between group variation to within group variation, when deciding if there is a statistically significant difference between the groups. Within group variation measures how much the individuals vary from their group mean. Each difference between an individual and their group mean is called a residual. These residuals are squared and added together to give the sum of the squared residuals or the within group sum of squares (SSwithin). Between group variation measures how much the group means vary from the overall mean (SSbetween).
Steps in SPSS
To carry out an ANOVA, select AnalyzeGeneral Linear ModelUnivariate
Put the dependent variable (weight lost) in the Dependent Variable box and the independent variable (diet) in the Fixed Factors box. Then click on the Save and Options buttons for additional options.
Ask for standardised residuals to be added to the data set
Ask for the test of equality of variances
The ANOVA output
F = Test statistic
Tests of Between-Subjects Effects MSDiet = 35.547 =6.197
Dependent Variable: Weight lost on diet (kg)
MSerror 5.736
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Corrected Model Intercept
71.094a 1137.494
2 1
35.547 1137.494
6.197 198.317
.003 .000
Diet SSBetween
71.094
2
35.547
6.197
.003
Error SSwithin
T otal Corrected Total
430.179 1654.350 501.273
75
78 77
5.736
When writing up the results, it is common to report certain figures from the ANOVA table.
F(dfbetween, dfwithin)= Test Statistic, p = F(2, 75)= 6.197, p =0.003
There was a significant difference in mean weight lost [F(2,75)=6.197, p = 0.003] between the diets.
Ellen Marshall Reviewer: Alun Owen www.statstutor.ac.uk University of Sheffield University of Worcester
P = p-value = sig = P(F > 6.197)
p = 0.003

ANOVA in SPSS statstutor Community Project
Post Hoc Tests
ANOVA tests the null hypothesis all group means are the same so the resulting p-value only concludes whether or not there is a difference between one or more pairs of groups. Further post hoc tests have to be carried out to confirm where those differences are. The post hoc tests are mostly t-tests with
an adjustment to account for the multiple testing.
Repeat the ANOVA making the following adjustments in the post hoc window
Move the independent variable (factor) from the Factor to the Post hoc Tests for box at the top, then choose from the available tests. Tukeys and Scheffes tests are the most commonly used post hoc tests. Hochbergs GT2 is better where the sample sizes for the groups are very different.
Diet 3 Diet 1
Report each of the three pairwise comparisons e.g. there was a significant difference between diet 3 and diet 1 (p = 0.02). Use the mean difference between each pair e.g. people on diet 3 lost on average 1.85 kg more than those on diet 1 or use individual group means to conclude which diet is best.
Ellen Marshall Reviewer: Alun Owen www.statstutor.ac.uk University of Sheffield University of Worcester

ANOVA in SPSS statstutor Community Project Checking the assumptions for one-way ANOVA
Assumptions
How to check
What to do if the assumption is not met
Residuals should be normally distributed
Use the Save menu within GLM to request the standardised residuals for each subject to be added to the dataset and then use AnalyzeDescriptive StatisticsExplore to produce histograms/ QQ plot / Shapiro Wilk tests of residuals.
If the residuals are very skewed, the results of the ANOVA are less reliable. The Kruskall- Wallis test should be used instead of ANOVA.
For more details on checking normality, see the Checking normality in SPSS resource. For help carrying out a Kruskall-Wallis test, refer to the Kruskall-Wallis in SPSS resource.
Homogeneity (equality) of variance: The variances (SD squared) should be similar for all the groups.
The Levenes test is carried out if the Homogeneity of variance test option is selected in the Options menu.
If p > 0.05, equal variances can be assumed.
If p < 0.05, the results of the ANOVA are less reliable. The Welch test is more appropriate and can be accessed via the Options menu using AnalyzeCompare MeansOne- way ANOVA. The Games Howell post hoc test should also be used instead of Tukeys.Checking the assumptions for this dataCheck equality of variancesCheck normalityAs p > 0.05, equal variances can be assumed
The residuals are normally distributed.
Reporting ANOVA
A one-way ANOVA was conducted to compare the effectiveness of three diets. Normality checks and Levenes test were carried out and the assumptions met.
There was a significant difference in mean weight lost [F(2,75)=6.197, p = 0.003] between the diets. Post hoc comparisons using the Tukey test were carried out. There was a significant difference between diets 1 and 3 (p = 0.02) with people on diet 3 lost on average 1.85 kg more than those on diet 3. There was also a significant difference between diets 2 and 3 difference (p = 0.005) with people on diet 3 lost on average 2.12 kg more than those on diet 2.
Ellen Marshall Reviewer: Alun Owen www.statstutor.ac.uk University of Sheffield University of Worcester