SPSS LAP assignment
Danyah
stat_lab_5_sp15.pptxLAB 5 :
Comparison of Means II (ANOVA)
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The main purpose of this lab is to learn when, why, and how to perform One-Way ANOVA, and how to correctly interpret the results.
One-Way ANOVA
Is used when comparing the averages of a quantitative variable between more than two groups
Is an extension of Two- Independent Samples t-Test
Involves one quantitative and one qualitative (more than two categories) variables
Assumptions:
Normality: The quantitative variable is normally distributed in each group
Independent samples: The samples must be independent of each other
Homogeneity of variance (equality of variances): The within-group variances are the same for each of the groups
Introduction
See Chapter 6 for more details
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One-Way ANOVA
The null hypothesis
The population means of the all groups are the same
The alternative hypothesis:
The population means of at least two groups are different
Decision rule for ANOVA:
If the decision is to reject the null hypothesis, then at least one of the means is different. However, the ANOVA does not tell us where the difference lies. Further investigation using Post Hoc Multiple Comparisons test (such as Tukey) is needed to identify where the group differences lie.
A significant ANOVA should be followed by the result of a Post Hoc Multiple Comparisons test
Scenario when you would use ANOVA:
A researcher wishes to see whether there is any difference in the weight gains of athletes following one of three special diet.
Three different relaxation techniques are given to a randomly selected patients in effort to reduce their stress levels
| Comparison of Means | ||||
| Type of Test | Number of Variables | Variables Type | Writing the Null / Alternative Hypothesis | The Value of the Test Statistics |
| One Sample t-test | 1 | Quantitative variable | t- value | |
| Independent Samples t-Test | 2 | One quantitative and one qualitative (two categories only) | t- value | |
| Paired t-Test | 2 | Two related quantitative variables | t- value | |
| ANOVA Analysis of variance | 2 | One quantitative and one qualitative (has more than two categories) | F- value |
Comparison
of
Means
One-Sample t-Test
For comparing sample result with a known value
Independent Samples t-Test
To determine whether the unknown means of two population are different from each other based on independent samples
Paired t-Test
For data in which the two samples are paired in some way.
One-Way ANOVA
To determine whether there are differences among more than two group means
| Evidence or Proof | |
| P-value (Sig.) | If p-value ≤ 0.05, we reject the null hypothesis |
| If p-value > 0.05, we fail to reject the null hypothesis | |
| Confidence Interval (CI) | If CI includes the value of zero, we fail to reject the null hypothesis (Check to see if the interval goes from negative to positive ) |
| If CI does not include the value of zero, we reject the null hypothesis |
Question. Is the mean baseline systolic blood pressure different for people with different categories of BMI?
Answer:
Hypothesis:
Since we have one quantitative and one qualitative (more than two categories) variables, One-Way ANOVA should be used to answer this research question.
Note: Make sure to check that you have enough sample size in each group .
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Is the mean baseline systolic blood pressure different for people with different categories of BMI?
Answer:
Since we have one quantitative and one qualitative ( more than two categories) variables, One-Way ANOVA should be used to answer this research question.
What kind of a variable is BMI in this case? Qualitative ( 3 groups only)
To Obtain One-Way Analysis of Variance (ANOVA):
From the menus choose:
Analyze Compare Means One-Way ANOVA Select baseline systolic blood pressure as the dependent variable Select BMI categories as the factor variable Under POST HOC option, select Tukey (used to know which groups are different) Under options, select descriptive Click continue then ok
Note: The factor variable is always the qualitative variable while the dependent variable is always the quantitative variable.
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SPSS outputs:
Since the p-value (<0.001) for ANOVA is significant (<0.05), we conclude that there is a significant difference in means between the groups.
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SPSS Post Hoc Test outputs:
The mean difference between group 1 vs 2, group vs 3, and group 2 vs 3
Since the p-value is significant, we conclude that the means of all groups are significantly different from each other
Since all the 95% confidence interval do not include “zero difference” of the null hypothesis, we conclude that the means of all groups are significantly different from each other
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| N | Mean | Std. Deviation | P-value (Sig.) | ||
| BMI Categories | Normal | 106 | 121.39 | 17.32 | <0.001 |
| Over weight | 175 | 130.67 | 19.51 | ||
| Obese | 125 | 137.46 | 21.91 | ||
| Dependent variable: Systolic blood pressure at baseline F (2, 403) = 19.04, p-value <0.001 |
Summary Table:
Decision:
Fail to reject the null hypothesis (FTR) √ Reject
Since P-value less than alpha = 0.05, we reject the null hypothesis.
Conclusion (Interpretation):
The mean baseline systolic blood pressure is statistically different for people with different categories of BMI.
Tukey multiple comparisons test indicated that the average baseline systolic blood pressure is different for all BMI categories
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