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Analysis of Variance (ANOVA)
Analysis of variance (ANOVA) is a commonly used approach in testing of the equality of various means using variance (Derrick, 2008). This analysis of often based on a number of assumptions including: independence of the samples, equal variance in populations and that the populations from which the sample is extracted has a normal or near normal distribution (Derrick, 2008). This paper applies ANOVA analysis in development of statistical assumptions defining the situation of HIV/AIDS related psychiatric depression in Africa. The paper compares the impact different therapeutic approaches in management of psychiatric depression among patients with HIV/AIDS. Using selected variables, this paper will successfully illustrate how ANOVA analysis is applicable in analysis of such scenario. To achieve this, a null and an alternative hypothesis will be developed and tested with the help of SPSS statistical analysis tool. The null and alternative hypothesis provides a rational basis upon which conclusions are drawn.
In comparing the relationship between therapy administration and psychiatric depression amongst aids patients, the paper will seek to establish whether the means of several groups are equal as well as determine if there exist any significant differences. In general, this paper aims to illustrate the logic used in ANOVA. The null hypothesis evaluated by one way ANOVA is that the mean of two or more populations are equal (Stuttgart, 2007).
It questions whether (H0) the population means for all groups bear equality and that the differences observed are a result of variations from random sampling (Brian, 2009). When null hypothesis is not true, the alternative hypothesis (Ha) supposes that the observed differences between means of sample being evaluated are real differences in the mean of the populations. The logic applied in ANOVA in mean comparison is similar to comparison of means adopted in t-tests (Green &Salkind, 2008). The data set used in this study is based on three therapy groups. One groups is subjected to journal therapy, the other group is subjected to counseling therapy while the last group is subjected to a combination of journal and counseling therapy. The data used is obtained from the General Social Survey disk. The data measures the psychiatric depression average levels suffered by HIV/AIDS patients in respective groups prior to treatment and after treatment.
In order to determine the impact of different types of treatments in management of depression related to HIV/AIDS, researches are first developed. The null hypothesis states that there is no significant difference in means of different treatment approaches adopted in depression management among HIV/AIDS infected persons in Africa. The alternative hypothesis is just the opposite of this; it states that there is a significant difference in the means of different treatment approaches adopted in depression management among HIV/AIDS infected persons in Africa. Mathematically, the expressions are expressed as follows:
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H0: µ1 = µ2 = µ3
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H1: µ1 ` µ2 ` µ3
Whereby µ1, µ2, ^ µ3 are the means for journal, counseling, and a combination of journal and counseling respectively. To further evaluate the significance of the test, the statistic F value is obtained. The F value is tested with a P value of 0.05 and as such an F value less than the p value will lead to outright rejection of the hypothesis being evaluated. Given that the primary ANOVA analysis does not give the actual mean differences for the groups evaluated, this study conducts further post-hoc studies to define the group differences. Tukey B is adopted for this study.
Results
The SPSS output displays the findings established based on the criteria defined earlier in the study.
Table 1: Descriptive statistics.
From the research study, each dependent variable i.e. treatment approach there is an associated mean as well as a standard deviation. As earlier mentioned two scenarios are evaluated: firstly, the state prior to treatment and secondly, the state after treatment. The respective means and variances are shown in table 1 attached. The returned means, for instance after treatment administration shows that the means µ1, µ2, ^ µ3 fail to satisfy the criteria defined by the null hypothesis i.e.
H0: µ1 = µ2 = µ3
Whereby µ1, µ2, ^ µ3 are 70.30, 65.85, and 71.10 respectively. However, the null hypothesis is not immediately rejected. Rather a further evaluation for statistical significance is sought.
Table 2: Test for homogeneity of variances.
To reject the findings of the null, the F statistic value is determined. Given the F value of.699 and.753 obtained for pre and post treatment respectively, it is sufficient to reject the null hypothesis (see table 2). The F values shows that the result are statistically significant because they are larger than the p value of.05 earlier stated. There is a strong evidence suggesting that the there is a significant difference between the means of variables being evaluated.
The ANOVA results further reinforce the earlier defined results. It provides the results between groups as well as within groups. In both cases, the results reveal that there are indeed differences between the groups as well as within groups.
The overall SPSS and syntax files illustrating the discussion illustrated in the study are attached hereafter:
SPSS Syntax and output
Post Hoc Tests
Homogeneous Subsets
References
Brian, S. (2009). Introduction to Statistics. London: McGraw Hill.
Derrick, A. (2008). Research methods applicable to quantitative analysis of data (2th ed.). Worth publishers: New York.
Green, S.B. & Salkind, N.J. (2008) Using SPSS for Windows and Macintosh: Analyzing and Understanding Data (5th ed.) Pearson Prentice Hall: New Jersey.
Stuttgart, W. (2007). ANOVA application to case analysis.Journal of Statistics 14(2), pp. 123-126.
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