- Introduction- This exercise discusses various ways through which the two types of errors are committed. The importance of power and sample size in avoiding wrongfully rejecting or failure to reject the null hypothesis is emphasized.
- Body- Three examples of researches are given to expound on the various ways of committing errors in research. In the third example, more detail is given on analysis of the results using SPSS and the corrective measures that could be taken to avoid discrepancies on the results.
- Conclusion- The power is usually increased with increase in sample size. A larger sample size also reduces the estimation error. Therefore, power and sample size determines the increase or decrease of error in a research. For the results to be adequately precise, samples are supposed to be sufficiently large (Sillurian, 2008).

## Introduction

In public health, as is the case with various institutions, wrongfully rejecting a null hypothesis could have very negative effects on policies and programs which the research was intended to benefit. Shintani (2008) notes that while using a small sample size (he terms this as insufficient power) to test a drug effectiveness could result in a clinically important observed difference, the null hypothesis may not be rejected leading to a conclusion that the drug effectiveness may not be as high as it is thought to be. In addition, he notes that, using a very large sample could lead to a rejection of the null hypothesis even when the observed difference is actually not clinically important. Lenth (2001) outlines the elements involved in a power approach to include:

- Specification of the hypothesis test required on a particular parameter.
- Specifying of the test’s significance level.
- Specifying of the effect size that embodies an alternative of interest in science.
- Obtaining of historical estimates or values of needed parameters in computation of power function of the available test.
- Specifying of a target value of the test.

## Public health research examples in light of type one and type two errors

- Two samples are randomly selected from a population. One sample comprises of alcohol consumers while the second one comprises of non-consumers of alcohol. The two samples are tested for bladder cancer and a 2-sample independent t-test computed on the results to determine whether there is any significance difference in their means. The results show that there is no significance difference between the means of the two samples; the researchers fail to reject the null hypothesis. However, in reality, there is a significant difference between the two means. In this case, the researchers have committed a type two error.
- Students were randomly drawn from two institutions in a state in the U.S. The weights of these students were recorded and a 2-sample independent t-test computed on the weights to test whether there is any significant difference in their means. A significant difference between the means was obtained and the null hypothesis rejected. A critical analysis of the results indicated that a type one error was committed for rejecting the null hypothesis when it was actually true.

## A brief summary of one example

A sample of 15 male and 15 female students were drawn from third year nursing students. Their Body Mass Index (BMI) was recorded and a 2-sample independent t-test computed using SPSS to determine whether a significant difference exists between their means. The results of the analysis are summarized in table 1 below.

Generally, the results indicate that no significant difference between the means of the two samples exists. But the sample size used in this case is too small. According to Ingram (1998), researchers should always be concerned about the sample size to ensure generalization and at the same time detection of significant effects in case they exist (power). Type 2 error in this case is worse than type one error.

The advantage of having a larger sample size is that the power significantly increases while the estimation error decreases (VanVoorhis &. Morgan, 2007). Lachin (1981) gives a specific equation which needs to be solved for effective sample size determination.

*Independent Samples Test.*

## References

Ingram, R. (1998). *Power Analysis and Sample Size Estimation*. NTresearch 3 (2), 132-140. Web.

Lachin, J.M. (1981). *Introduction to Sample Size Determination and Power Analysis for Clinical Trials*. Controlled Clinical Trials, 2, 93-113. Web.

Lenth, R.V. (2001). *Some Practical Guidelines for Effective Sample Size Determination*. The American Statistician, 55 (3), 187-193. Web.

Shintani, A. (2008). *Sample Size Estimation and Power Analysis*. VICC Biostatistics Seminar Series. Web.

Sillurian, L.M. (2008). *Essentials of Biostatistics in Public Health*. Sudbury, MA. Jones and Bartlett Publishers. Web.

VanVoorhis, C.R.W. & Morgan, B.L. (2007). *Understanding Power and Rules of Thumb for Determining Sample Sizes*. Tutorials in Quantitative Methods for Psychology 2007, 3 (2), 43-50. Web.