The results of the analysis are as shown below. Using the priori function on GPower, the sample size based on the factors above was determined. The factors given for calculating the sample size are as follows: ANOVA (fixed effects, omnibus, one-way) Calculate the sample size needed given these factors: In addition, in research that involves human subjects a large sample may be considered unethical (Nayak, 2010). This makes the use of a smaller sample size desirable because it is cheaper and requires fewer resources to collect data. Furthermore, larger samples are resource and time intensive for a researcher to collect data sufficiently. Therefore, a researcher does not need a large sample. The author points out that in some studies smaller samples sufficiently answer the research questions. The main advantage the article suggests is that large samples can be a waste of resources. According to Nayak (2010), a small sample is desirable in answering some research questions due to its advantages. Acheson (2010) points out that selecting the right sample size is critical in any research study. The study is worth doing using a smaller sample size due to a number of reasons. In turn, this ration ensures that the study is neither underpowered nor overpowered (Faul, Erdfelder, Lang, & Buchner, 2007). This is achieved by ensuring the right balance between Type I and Type II errors. The main reason for selecting this ratio is to ensure a high statistical power. The β/α ratio used in the power analysis above equals to four. This indicates that as the sample size decreases the β err prob increases and in turn decreases the power of the study. This value of β err prob provides a power of 0.653 for the study. The results of the analysis carried out indicate that for half the sample size and a β/α ratio equal to four, α err prob is equal to 0.086 while the β err prob equal to 0.3461. Output: Noncentrality parameter δ =đ.7606817 T tests - Means: Difference between two independent means (two groups) Analysis:Ĝompromise: Compute implied α & power Output: Noncentrality parameter δ =Ē.4899799Īctual power = 0.8002178 Using the compromise function: T tests - Means: Difference between two independent means (two groups) Analysis:Ě priori: Compute required sample size Power = 1 – beta = 1 – 0.2 = 0.8 Using the priori function: One-tailed t-test with two independent groups of equal size Calculate the sample size needed given these factors: The factors given for calculating the sample size are as follows:
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