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Introduction
This paper is aimed at the identification of the research question and hypotheses concerning the study of tooth decay conducted earlier. The research question is the following: What is the connection between the percentage of untreated tooth decay in the US among different ages, ethnicity, gender, and income groups?
Null Hypothesis
A null hypothesis of the research states that there is no difference in the percentage of untreated tooth decay between several identified groups. It should be noted that there is one sample of tooth decay and such variables as age, ethnicity, gender, and income that were determined to examine the topic. Precisely speaking, the research involves six age groups, are, 6-11, 12-19, 20-44, 45-64, 65-74, and 75+, Non-Hispanic White, Non-Hispanic Black, and Mexican-American, poor, near-poor, and non-poor as well as male and female participants. The diversity of variables allows representing the situation from different angles.
Alternative Hypothesis
An alternative hypothesis claims that there are considerable differences between identified groups with different variables. In particular, cases of untreated tooth decay are higher in the age group 20-44 while the age group 12-19 has the least cases of untreated tooth decay; the poor Mexican-American males had the highest proportion of untreated tooth decay. Therefore, the alternative hypothesis is the statement of the logical negation of the null hypothesis. It means the connection between the studied variables.
Type I and Type II errors
To examine the hypothesis, it seems appropriate to set a practical alpha level that is also called a practical significance. Such a level of significance is more relevant for one sample than statistical significance. As a result of the validation of the null hypothesis, errors of two types might occur. The Type I error consists in the fact that the correct null hypothesis is rejected (Stufflebeam & Shinkfield, 2011). The level of significance is the probability of the Type I error in the decision, in other words, the likelihood of false rejection of the null hypothesis.
To avoid the Type I error, it is necessary to determine the level of the alpha before the data are collected. As a rule, they choose the conditional value of 0.05, although one could choose a more restrictive value such as 0.01 (Rosenthal & Rosenthal, 2011). The chance to make a mistake of Type I would never exceed the chosen significance level as the null hypothesis is rejected only if p-values <0,05. Consequently, the interval value would be 95 percent, and errors of Type I would not appear.
In its turn, the Type II error states the adoption of the incorrect hypothesis. This type of error does not reject the null hypothesis when it is false and concludes that there is no effect, whereas it exists (Stufflebeam & Shinkfield, 2011). In the case of the conducted study, a false conclusion such as disregard of some important aspects might occur. The reduction of the probability of the Type II error is considerably more difficult than of these of Type I. Generally, it could be reduced by increasing the number of variables under analysis. For example, previous dentist illnesses or related diseases might be added to increase the validity of the research and avoid Type II errors.
Conclusion
In conclusion, it should be emphasized that the paper analyzes and evaluates statistical variables, states the research question along with hypotheses, and reveals the notion of Type I and Type II errors.
References
Rosenthal, J. A., & Rosenthal, G. (2011). Statistics and data interpretation for social work. New York, NY: Springer.
Stufflebeam, D. L., & Shinkfield, C. L. (2011). Evaluation theory, models, and applications (2nd ed.). San Francisco, CA: Jossey-Bass.
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