This paper proposes a study that will be carried out using one-way analysis of variance (One-way ANOVA). One-way ANOVA is a statistical test that is applied in cases with three or more groups or levels of independent variables (Pallant, 2005). The proposal outlines the statistical applications of one-way ANOVA, the study participants, the variables, study methods, expected results and biases, and the practical significance of the expected results. The proposed study will endeavor to answer this research question:
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Is there a difference in TB cases among the young, middle-aged, and old persons who smoke cigarettes?
The research question is appropriate for one-way ANOVA because it satisfies the conditions for the test. First, the research question has one categorical independent variable. The independent variable has three different groups, i.e. young, middle-aged, and old persons. The three groups of persons are continuous variables. For example, the study will have participants in three age groups. Young persons will be participants aged between 18 to 25 years middle-aged persons will be aged between 30 to 40 years, and old persons will be aged 60 years and above. The research question also fits to be analyzed by one-way ANOVA because it has one dependent variable (the TB cases). The study will attempt to assess whether there are statistically significant differences in TB cases in three groups of smokers. Statistical notation for the linear model is:
yi, j = µj + ∑i, j (Means model) or yi,j = µi + Tj + ∑I, j (effects model)
- i = 1,…, I refers to groups that are in the experiment
- j = 1,…, J refers to groups that are being manipulated
- Ij refers to the groups in an experiment that are being manipulated in the jth group
- I =∑ Ij refers to the total groups in an experiment
- yi,j = total number of changes observed in an experiment
- µj= the average of changed observed in an experiment for the jth group (which was manipulated), and
- µ= total number of averages of responses obtained in an experiment.
- The null and alternative hypotheses are explained as follows:
- H0 (Null Hypothesis): There is no difference in TB cases in the young, middle-aged, and old cigarette smokers.
- H1 (Alternative hypothesis): There is a difference in TB cases in the young, middle-aged, and old cigarette smokers.
The errors that will mostly occur in the study will occur in the variances calculated by the one-way ANOVA statistical test.
The study will recruit 150 participants, 50 participants for each group of smokers. For each group of smokers, half of the participants will be females while the other half will be males. The study participants will be assigned to the study groups depending on their ages. Young smokers will be participants aged between 18 to 25 years, middle-aged smokers will be aged between 30 to 40 years, and old smokers will be aged 60 years and above.
The age of the study participants will be the categorical independent variables in the study. They will be three groups of the young, middle-aged and old cigarette smokers. The continuous dependent variable will be TB cases among the study participants. The age groups will be measured using a nominal scale. Also, the dependent TB cases variables will be measured using nominal scale.
The study will use one-way ANOVA to assess the differences in TB cases among the cigarette smokers. Tukey’s Post-Hoc Test will be used to give further information regarding the preliminary results obtained using the one-way ANOVA. One-way ANOVA will be appropriate because the research question contains groups of independent variables (age groups of smokers) and one dependent variable (TB cases).
The statistical tests will provide crucial information on the association of TB cases with cigarette smokers’ age groups. The tests will show or dispute statistical significance of the differences in the incidents of TB cases and ages of the smokers. If the statistical tests will show significant differences in the number of TB cases and the ages of the study participants (the young, middle-aged and old smokers), then the null hypothesis will not accepted. Thus, the alternative hypothesis will be adopted for the study.
The one-way ANOVA to be used in this study will assume that the age groups of the cigarette smokers will have normally distributed differences. This assumption might lead to faults in the study results. The one-way ANOVA will also assume that there will be no significant differences in the outliers among the different groups of cigarette smokers. Conclusions on the association of age and onset of TB can be made from the results of the proposed study. If TB cases will be found to increase with the increase in the ages of the study participants, then it will be concluded that age greatly determines the onset of TB among cigarette smokers. However, the results will not give hints on other causative agents of TB. The results will have practical applications in public health because public health professionals will understand the link between TB and age of smokers.
Jackson, S. L. (2012). Research methods and statistics: A critical thinking approach (4th ed.). Belmont, CA: Wadsworth.
Pallant, J. (2005). SPSS Survival Manual. Sydney: Ligare.