Sample size estimation in basic parametric statistical tests

This thesis study examines the importance of sample size estimation and calculation methods in basic parametric statistical tests. Parametric tests, sample size and sampling methods are discussed in detail within the scope of the study. The main purpose of the study is to introduce the methods used to correctly determine the required sample sizes for independent and dependent groups and to evaluate the effects of these methods on various statistical analyses. In particular, it is explained how to calculate sample size for various test types such as independent and dependent two group means test, analysis of variance (ANOVA) for more than two groups, ratio tests and regression-correlation analyses. In addition, within the scope of the thesis, analysis was performed using the Gpower program by taking data from both own samples and different theses and the results were interpreted. It was observed that accurate sample size estimation contributes to obtaining more reliable results in statistical analyses and increases the generalizability of research findings. The research findings show that there is a clear relationship between sample size and statistical power, indicating that higher power levels are associated with the need for larger sample sizes. Specifically, when a power level of 99% was targeted, sample sizes were significantly larger than in studies with 80% power levels. Furthermore, the results show a corresponding decrease in the required sample size as the margin of error increases (especially to 1%, 5%, and 10%). This trend suggests that larger margins of error may allow researchers to justify smaller sample sizes, but may compromise the precision of their estimates.