The selected statistical test for the research question is a one-way Analysis Of Variance Analysis (ANOVA).  In order for the research question to employ the use of ANOVA, the study must have a null and an alternative hypothesis, respectively.  It should also have a dependent variable and one independent variable.  The independent variable must further have three or more different levels or samples, each with multiple observations (Plonsky, 2014).  The question is appropriate for the use of a one-way ANOVA because it fits all the requirements for a research study that necessitates the use of a one-way ANOVA and possesses the ability to generate results which are more reliable and valid than a regression analysis or t-test.

In addition, the research question has one dependent variable, and that is, the complete treatment of depression and one explanatory variable, the different treatments available for depression.

The independent variable (IV) has three levels. Each of these three levels has multiple observations. This is to say, the independent variables are the three main known treatments for depression, that is: Psychotherapy for depression treatment, Medication treatment for depression, and Alternative and Complementary treatment for depression (American Psychological Association, 2014).  Within these levels there are multiple observations, for instance, under Alternative and Complementary treatment for depression, it includes the use of herbal and vitamin supplements as well as the use of acupuncture and relaxation techniques such as tai chi, meditation and yoga.  The presence of various levels of the IV allows the study to carry out a one-way ANOVA analysis.

The research question has a null hypothesis (H₀) and an alternative hypothesis (H₁).  The null hypothesis states that there is no one particular most effective treatment for depression while the alternative hypothesis states that there exists one most effective treatment for depression.  This can be reflected in the following statistical notation:

H_o: µ₁₌ µ₂₌µ_3:

The treatment method has no effect on depression level

H_1: µ_1≠ µ_2≠ µ_3: 

Treatment X will be more effective in reducing depression levels when comparing to the other two groups.

The main errors that are likely to arise when using a one-way ANOVA analysis, is the lack of independence between the samples and the existence of outliers. The lack of independence between the independent samples often arises out of correlated samples; this usually results in the researcher making an incorrect inference from the findings.  This can however, be addressed through the use of a one-way blocked ANOVA.  The presence of outliers in the data usually has the effect of increasing the estimated sample variance, and thus decreases the calculated F statistics for the ANOVA and in extent lowering the likelihood of rejecting the null hypothesis or the values being from a non-normal population or poor recording of data.  Thus, it can be corrected through meticulous and careful collection of data.

Method

Participants

In this study, the population of interest from which the participants would be selected for the proposed study would predominantly be people who have at one point in their life gone through depression and through seeking and undergoing the one or a combination of the available treatment options able to completely recover from depression. The demographic characterization of the participants will be that they be between the ages of 18 and above, all other demographic variables would be assumed to have no influence on the findings of the study, and in the occasion they have any influence, it is presumed to be insignificant enough to influence the findings of the study. Additionally, further specifying of the population of interest will limit the findings of the study in terms of generalizability.

The participants will not be sampled based on any demographic characteristics, such as gender or age or racial background.  They will be previous patients of depression.  The participants however, will be selected from a pool of individuals who have previously suffered from depression.  The unit of differentiation would be the treatment option that the individual employed.  The participants however, will be differentiated based on which of the three broad available treatment option of depression was used during their treatment.  Thus, they will be purposely chosen so that the number of final participants would be equally distributed based on the treatment option they employed.  That is, the number of participants who used psychotherapy for depression treatment is equal to the number of participants who used medication for depression, as well as those who used alternative and complimentary treatments for depression.  the participants can be a sample of 300 individuals divided into three groups based on the treatment option they used to treat depression.

Procedure

            The primary objective of the proposed study is to identify the most effective treatment for treating depression.  The dependent variable in the study is the treatment of depression, while the independent variables in the study are the various treatments options available for depression.  The independent variable can further be divided into three levels and thus this research question fits for the use of a one-way ANOVA analysis.

According to Huck (2012) and Thorndike and Thorndike-Christ (2009) a variable is defined as anything that varies or changes in value.  In this study, the independent variable has three levels, which are the three broad treatment options available for treating depression. Each of these treatment options has multiple observations.

There are four types of scale of measurement data, which are ordinal, nominal, ratio and interval (Huck, 2012; Thorndike & Thorndike-Christ, 2009).  The nominal scale is used for distinguishing by name.  For example, 1=male and 2=female.  Ordinal scales are used to rank objects in order.  The interval and ratio scales indicate order as well as distance, for instance, the magnitude of difference between the heights of two players.  The difference between them is that interval scale has relative measurements (where there is no absolute zero) while ratio scale has absolute measurement (where zero value does signify absence of a given attribute).  Thus, in this study, the number of available treatment options is a categorical variable, since they can take on one of a limited and usually fixed number of possible values and it is measureable using a nominal scale.  A categorical variable is used to categorize objects and responses into different sets such as level of education.  As such, the treatment of depression is a categorical variable that is measureable using a dichotomous scale.  The patient is either feeling better or the treatment did not treat the depression.           The independent variable is the variable that represents the input and is affected by any other variable whereas the dependent variable represents output and is affected by the independent variable.  As such, the dependent variable in this study is the treatment from depression.  Treatment of depression is defined as the practice of the diagnosis, medication and prevention of depression, as well as the restoration and promotion of good health, and recovery from depression.

The independent variable is the various treatment options available for the treatment of depression.  In the context of this study, it is defined as the widely approved and accepted methods for the treatment of depression which are recognized by the American Psychological Association.  Therefore, they include: Psychotherapy for depression treatment, Medication treatment for depression, and Alternative and Complimentary treatment for depression (American Psychological Association, 2014).

Results

            The study employed a one-way ANOVA test.  A one-way ANOVA is a statistical test by which a researcher can test whether three or more means are equivalent or not.  It tests whether the value of a single individual variable is significantly different among three or more levels of a factor.  That is, for a one-way ANOVA analysis to be conducted there must be a single factor or single independent variable with three or more levels and multiple observations at each level.

The role of Post-hoc tests in a one-way ANOVA is invaluable.  For example,

the ANOVA will inform the researcher about the overall difference between the various levels in the independent variable.  However, it fails to inform the researcher which of the particular levels are different (Laerd Statistics, 2014).  On the other hand, through the use of the post-hoc tests this difference can be specified to a specific group.  These tests are conducted to confirm the particular place where the difference occurred between the levels.

When using a one-way ANOVA, the interest of subjecting the data to this analysis is to accept or reject the null hypothesis.  ANOVA is used for the comparison and contrasting of the means from different samples (Plonsky, 2014).  It employs the use of the data that is entered into the mean and standard variation.  The mean that would be obtained from the various levels would be compared to each other to find out if their differences are statistically significant or differ more than would be expected by chance.  Through the use of the one-way ANOVA an F-Ratio statistics is obtained which is an inferential statistic, but is not the end goal of the study (Sommer, 2006).  However, the F-ratio assists in the computation of the p value which is a probability estimate which determines whether or not a researcher accepts or rejects the hypothesis of the existence of a difference.

Discussion

The significant strengths of a one-way ANOVA is that it can control for type 1 error and it is considered a stronger and more powerful parametric test.  The control of type 1 error makes the findings from a one-way ANOVA more reliable and valid and a higher confidence level can be attached to the findings.  In addition, one-way ANOVA provides an overall test of equality of group mean.  This makes it a valuable statistical tool for this proposed study.  Whereas the use of a one-way ANOVA has advantages such as the simplicity of the layout of the design as well as the advantage that this technique does not require that the number of observations in each individual sample be the same, it also has some shortcoming which take the form of very sensitive assumptions.  Firstly, it assumes that the population from which the participants sample is obtained is standard, this more often is not always achievable.  Secondly, it assumes that the samples are independent.  Lastly, it assumes that the population variance is equal.

A one-way ANOVA has the weakness that in the occasion that the null hypothesis is rejected, it does not determine the particular group that is different from the other groups.  Thus, in the case of the research question, in the employment of a one-way ANOVA, the outcome can only be useful in providing an inference that there is one most effective treatment of depression.  The findings however, cannot specify which among the three different treatment options is the most effective.

The results from the propose study will be beneficial to practitioners in the field of psychology because the results will be able to identify the existence of one particular treatment option that is ideal in the treatment of depression.  However, the test will confirm the presence of one most effective treatment, but will not identify the particular treatment option.  As a result, the need exists to subject the data to other statistical tests which will assist in identifying the specific treatment.  This notwithstanding, the one-way ANOVA will be an important statistical analysis tool for this proposed study, and other studies in the field of psychology.

References

American Psychological Association. (2014). Depression and How Psychotherapy and other Treatments can Help People Recover. Retrieved September 17, 2014, from American Psychological Association: http://www.apa.org/topics/depress/recover.aspx?item=1

Huck, S. W. (2012). Reading Statistics and Research (6 Edition ed.). Columbus, OH: Allyn & Bacon.

Laerd Statistics. (2014). One-way ANOVA. Retrieved September 17, 2014, from Laerd Statistics: https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide-2.php

Plonsky, Ph.D, M. (2014, April 19). Psychological Statistics: One way analysis of variance (ANOVA). Retrieved September 18, 2014, from University of Wisconsin: http://www4.uwsp.edu/psych/stat/12/anova-1w.htm

Sommer, B. A. (2006, August 1). Inferential statistics: Analysis of Variance (ANOVA). Retrieved September 18, 2014, from University of California, Davis: http://psychology.ucdavis.edu/faculty_sites/sommerb/sommerdemo/stat_inf/infcont.htm

Thorndike-Christ, T. M., & Thorndike, R. M. (2009). Measurement and Evaluation in Psychology and Education. Upper Saddle River, NJ: Prentice Hall.

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