ANOVA: Mixed Design ANOVA Mixed Design ANOVA: ANOVA

Mixed Design ANOVA

None of the questions used in the week 1 assignment qualify for the mixed-design ANOVA; for this reason, I have selected an entirely new question from an entirely different subject -- back pain. Chronic back pain has become a serious problem for the health fraternity in America -- it is estimated that approximately 31 million Americans experience chronic back pain at any given time, and that over 80% of adults are poised to experience some form of backache at some point in their lives. Currently, back pain stands as the leading cause of disability in the country, with the economy losing over 450 billion dollars as a direct result of the same every year. In this paper, we focus on the treatment aspect of back pain. Acupuncture and massage are the two leading treatment modalities for back pain -- we are interested in finding out which of the two approaches is more effective at addressing back-related problems over time. We have formulated the following research question:

"Which of the two treatment approaches is more effective at reducing back-related problems over time?"

We can deduce, from the research question, that back-related problems is the dependent variable, 'time' is the within-subjects factor, and 'treatment approaches' is the within-subject factor. The two treatment approaches are the acupuncture program (treatment A) and the massage program (treatment B) -- these are the two groups of the between-subjects factor. This only implies that the question lends itself effectively to the use of the mixed-design ANOVA -- the mixed ANOVA is used when one is interested in comparing the mean differences between groups that have been split on the basis of two independent variable/factors, where one factor is a between-subjects factor and the other is a within-subjects factor (Sukal, 2013). The main purpose of conducting a mixed ANOVA in our case is to determine whether there is a significant interaction between the two factors -- time and treatment approach -- on the dependent variable (back pain).

Variables: as already mentioned, 'back pain' is the dependent variable, whereas 'time' and treatment approach' are the independent variables, only that the former is a within-subject variable and the latter a between-subject variable. The dependent variable will be defined in terms of how much a person suffers and hurts as a result of their back problems, that is how much their daily activity, movement, work, and play are affected by their back problems. The McGill pain questionnaire, a 13-item questionnaire, which requires patients to describe the intensity and quality of the pain that they are experiencing as i) mild, ii) discomforting, iii) distressing, iv) horrible, and v) excruciating, based on how much their daily activities are affected will be used to measure participants' pain levels before and after treatment. We will attach numerical values ranging from -2, -1, 1, 2, and 3, and the intensity of pain will be arrived at by summing the numerical values from all the 13 questions. This would make the variable a continuous, interval variable. The within-subjects factor, time, will be categorized into three (time point one -- at the start of the program, time point two -- after four weeks, and time point three -- after 8 weeks). This would make it a categorical, ordinal variable. The between-subjects factor, on the other hand, will be categorized into two as mentioned earlier on (treatment 1 -- acupuncture and treatment 2- massage), which would make it a categorical, nominal variable.

We could select 30 patients to take part in the study -- fifteen could be subjected to the acupuncture program and 15 to the massage program for a period of 8 weeks; the intensity of their pain before the program, four weeks into the program and upon completion could then be obtained and recorded.

Variable Qualification: the mixed ANOVA requires the dependent variable to be measured at the continuous...

Our variable, back pain, satisfies this condition (a continuous, interval variable). Moreover, the within-subjects factor ought to comprise of two or more related groups, such that the same participants are present in both groups. In our case, this is satisfied as the participants in time point one are the same ones in time point 2 and in time point 3. Finally, the within-subjects factor ought to comprise of two or more categorical, independent groups -- our two groups are the treatment 1(acupuncture) and treatment 2 (massage) groups.
Hypotheses: the null and alternative hypotheses guiding the study can be stated as follows:

We will have three null hypotheses:

H0: µ A1= µA2= µA3 - there is no difference in the means of factor A (acupuncture)

H0: µ B1= µB2= µB3 -- there is no difference in the means of factor B (massage)

H0: C12 = 0 -- there is no interaction between factors 1 and 2 (time and treatment approach)

And three alternative hypotheses:

HA: µ A1? µA2? µA3 -- there is a significant difference in at least two of the means of factor A HA: µ B1? µB2? µB3 -- there is a significant difference between at least two of the factor B means

HA: CAB?0 -- there is a significant interaction between factors A and B.

Possible Errors: type 1 and type 2 errors are both possible in this case. The risk of type II error could be minimized by raising the significance level; however, this only increases the chances of committing a type II error.

Part 2: Stroop Interference Case Study

The case study was based on three distinct research questions:

RQ1: do males and females differ in the time it takes to correctly conduct the stroop tasks?

H0: µ A= µB -- males and females do not differ in the time it takes to conduct the tasks

HA: µ A? µB -- males and females differ in the time it takes to conduct the tasks

RQ2: are there differences in the time it takes to correctly conduct the various stroop tasks -- words, colors or interference?

H0: µ AW = µBW -- there is no difference in the time males and females take to conduct the words task

HA: µ AW? µAW -- there is a significant difference in the time males and females take to conduct the words task

H0: µ AC = µBC -- there is no difference in the time males and females take to conduct the colors task

HA: µ AC? µBC -- there is a significant difference in the time males and females take to conduct the colors task

H0: µ AI = µBI -- there is no difference in the time males and females take to conduct the interference task

HA: µ AI? µBI -- there is a significant difference in the times males and females take to conduct the interference task

RQ3: does the effect of the stroop task type depend on the gender?

H0: C12= 0 -- there is no interaction between factors 1 and 2 (gender and stroop task type)

HA: C12 ? 0 -- there is a significant interaction between factors 1 and 2

Variables: 'task time' is the dependent variable -- it is measured in terms of how long it takes a participant to conduct a particular task. This makes it a continuous, interval variable. The study has two independent variables -- gender and stroop task type. Stroop-task type is the within-subject variable whilst gender is the between-subjects factor. Both gender and stroop task type are measured as categorical, nominal variables.

Data Analysis: the mixed-design ANOVA was used to test the hypothesis -- this test was appropriate because the study was made up of two independent variables, one of which was a within-subjects variable and the other a between-subjects variable. At a significance level of p