(1) STUDY DESIGN: This study is perhaps more complex than what you are used to. It is experimental, with pre-test and post-test measurements in four independent groups. The outcome measure (MIQ), appears to be a standardized continuous score, although its source and validity remains somewhat unclear. We must take it on good faith that this outcome is justifiable. Also, it is unclear why the researchers used the current sample sizes. Our analysis plan should include separate considerations of differences between groups and changes within groups.
(2) DATA ENTRY AND VALIDATION: Take care in naming files and in creating variables.
(3) DATA DOCUMENTATION & EXCHANGE: Exporting the data to the fixed-length field file format is useful when exchanging data among various programs. After creating the file, look at it in a text editor to make sure it is of the proper type and structure. Does it contain 23 records? It's clear that the data file must be carefully documented in order to decipher its meaning. See the EPI6 Basics chapter for additional information concerning data conversion and documentation.
(4) GROUPS AT BASELINE: The research problem is to see whether there is a relationship between treatment type and BASELINE scores. As one astute student noted, "There should there be no difference since the groups were randomized!" Still, it is sometimes important to check this assumption to make certain that the randomization achieved its goal. Below, please find the statistics requested by the problem. Statistics were computed with a MEANS BASELINE GROUP command.
Summary Statistics, Monkey Intelligence Quotients at Base Line
| Alcohol Consumption Score |
Monkey Groups | |||
| 1
(n =6 ) |
2
(n = 6) |
3
(n = 5) |
4
(n = 6) | |
| Mean | 162.0 | 119.3 | 168.0 | 156.7 |
| Standard Dev. | 71.4 | 46.2 | 49.9 | 73.4 |
| (Minimum, Maximum) | 103, 298 | 92, 212 | 80,202 | 68, 252 |
Test for Inequality of Means
The ANOVA test is used to test the means. Recall that the null hypothesis addresses the potential inequality of population means. The F test statistic has 3 and 19 degrees of freedom and = 0.73 (p = .55) (APA format for this statement is F(2,19) = 0.73; p = .55.) One might ask why I've reported the leading zero for the F statistic, but not for the p value. Briefly, the F statistic can be any positive value, so the leading zero lets the reader know that there are zero units in the statistic. The p value, however, is a probability, bounded by 0 and 1. The leading zero is unnecessary, therefore, because it must occur. See the APA manual p. 104, section 3.46 for information on the reporting of decimal fractions and number of decimal places to that should be reported. In any event, our test suggests that we must retain the null hypothesis and conclude that there is no significant difference between group mean. The average Monkey IQ is no different among groups at baseline.
A good case can be made for checking our results by the nonparametric K-W test. The K-W chi-square value is chi-square(3, N = 23) = 2.27; p = .52, thereby deriving a similar conclusion of no significant difference among groups.
Standard Errors of Means
We will assume that groups are homoscedastic. The MS Within (Variance Within) from the ANOVA table = 3844.772 with df = N - k = 19. Since Group 1, Group 2, and Group 4 all have n = 6, and we are assuming homoscedasticity, the sem for these groups = sqrt (3844.772 / 6) = 25.314. Since Group 3 has only 5 subjects, sem3 = sqrt (3844.772 / 5) = 27.730. Accordingly, means � sems:
Group 1: 162.0 � 25.3
Group 2: 119.3 � 25.3
Group 3: 168.0 � 27.7
Group 4: 156.7 � 25.3
This information can be plotted to display visually relationships.
(5) Change in MIQ Scores Within Group 1
STEM-&-LEAF
|-2|5
|-1|6421
|-0|
|+0|
|+1|1
SUMMARY STATS
Mean change = -110.7
SD = 118.5
n = 6
CONFIDENCE INTERVAL
95% confidence interval for �d = (-235.1, 13.7)
HYPOTHESIS TEST
H0: �d = 0 vs. H1: �d not = 0, alphla = .05, t(5) = 2.29, p = .070, retain Ho (but data are "almost" significant; so-called marginal significance).
(6) CHANGE WITHIN OTHER GROUPS
Analyses not shown. Follow a procedure similar to above.
(7) ANALYSIS OF GROUP DIFFERENCES AT 12 WEEKS POST INTERVENTION
I am going to cut right to the quick here. Let's just report the summary statistics, results of the test for inequality of variances, and results of the tests for inequality of means (parametric ANOVA and K-W). I generally don't like to do this at this because it might give us the false and simplistic impression that there is nothing interesting in the data. However, in practice, this is how things are often done. Here are the results, in summary form:
Summary Statistics of Monkey Intelligence Quotients After 12 Weeks on Their Respective Programs
| Alcohol Consumption Score |
Monkey Groups | |||
| 1
(n =6 ) |
2
(n = 6) |
3
(n = 5) |
4
(n = 6) | |
| Mean* | 272.7 | 186.7 | 360.0 | 303.7 |
| Standard Dev.** | 63.0 | 103.3 | 92.6 | 161.8 |
* ANOVA Test Results: F(3,19) = 2.33; p = .11
** Bartlett's Test Results: Chi-square(3, N = 23) = 4.05; p = .26
Discussion: The "shorthand" discussion might be "there are no significant differences among groups at week 12." However, this must not be interpreted to mean that there is nothing that we might learn from the data - data are replete with information. First notice that all groups have increased their MIQ from baseline. For example, Group 1 has gone from an average MIQ at baseline of 162 to 272 at week 12, a nearly doubling in monkey intelligence! Similar increases were found among all groups. We can see, then, that the most important part of our analysis has, so far, been descriptive. If we had relied too heavily on the p values and whatnot, this information would have been lost. This teaches us a valuable lesson: Do not get too fancy and try to stay within a comfortable and intuitive level of interpretation before moving on toward the more arcane. (Comment: In the next section of the course, immediately following the exam, we will learn how to test whether the increases in MIQ that might be attributed to the interventions are significant, but this was not the current question.) Also, notice that the analysis presented above provides no firm evidence of a difference among treatment groups, but there is a hint that Group 2's improvements are not as large as that of the other groups.
Happy studying, and if you have any questions as you approach the test, please do not hesitate to ask them of me. Please understand that Email responses necessarily require a lag time, and that I do not check my Email every day. (I check it at least every other day, whenever possible.) Also, sometimes I like to think about your questions for a day or two before I respond, so answers may be forthcoming anywhere from half a day to three days hence.
Also, please do study DAWEI, since this provides your primary basis for understanding. Do not let the computer do you thinking for you, for will it inevitably fail you. You may also need to study notes from your prerequisite course to help fill in gaps in knowledge - especially if you are having trouble understanding summary statistics, confidence intervals, and hypothesis testing, and so on. Always seek to achieve the big picture by asking "What am I hoping to learn from these data" but also pay attention to the particulars, for this too is essential for true understanding.
Finally, the Can You Questions can be used as a study guide, but these are by necessity somewhat sketchy Let DAWEI be your guide, and do review the HW posting for a complete listing of areas of study.We've covered a lot of ground, but this background will help make the rest of the course a rewarding experience. Do a careful good studying the basics, and the payoff will be profound.
Best of luck and happy computing!
...BBG...