FerrellJEDR8201-5

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FerrellJEDR8201-5 1 Determine the Standard Error of the Mean, Confidence Intervals, and Parametric Assumptions Joyce E. Ferrell School of Education, National University EDR-8201: Statistics I Dr. McKenna December 3, 2023
FerrellJEDR8201-5 2 Determine the Standard Error of the Mean, Confidence Intervals, and Parametric Assumptions Part I: Inferential Statistics and Assumptions 1. What is the standard error of measurement? The standard error of measurement specifies the error amount in a test score or measurement. It is unrelated to the accuracy of scoring. In education, all test results are subject to the standard error of measurement. The difference between your actual score and your highest and lowest hypothetical score is known as the standard error of measurement (Lloyd, 2021). 2. What is the standard error of the mean? The standard error of the mean is the method that determines the differences between more than one sample. It differs from the population mean. The formula for measuring the standard error of the mean is SEM = SD/√N (Lloyd, 2021). 3. Please discuss the term confidence interval. The term confidence interval is an interval estimate providing evidence about the uncertainty. It indicates that the probability of a population parameter will range between a set of values for a particular proportion of times. 4. What are the four main assumptions for parametric statistics? (State the name of the assumption and explain the assumption in your own words) Independence, linearity, normality, and homogeneity of variance are the four main assumptions for parametric statistics. Independence: The data is independent of each other. This assumption suggests that one observation’s value does not affect another’s.
FerrellJEDR8201-5 3 Linearity: The data is known to have a linear relationship where the outcome variable is related to the independent variable. Normality: The data follows a normal distribution. The p-values and significant testing are essential, especially for a low sample in a data set. Homogeneity of variance: Variances among the groups being compared are approximately equal. Similarity and variance are needed throughout the data. 5. Why is it important to test the assumptions before conducting the parametric statistical analysis? Testing the assumptions before conducting the parametric statistical analysis is vital because it could lead to inaccurate or misleading results. Failing to meet the assumptions could compromise the validity of the analysis and the reliability of the conclusions determined from the data. Part II: Standard Error of the Mean and Confidence Intervals 1. Calculate the standard error of the mean (SEM). (Note. SEM is calculated by dividing the standard deviation by the square root of the sample size). Sample size – 36; therefore, you take the square root of the sample size, which is 6. Standard deviation = 12 Sample size = 36 Square root of sample size = 6 SEM = 12/6 = 2 2. Why is it better to use a 99% CI than a 95% CI? Using a 99% confidence interval instead of a 95% CI is better because it increases the range of values acceptable for the population parameter. A wider interval requires more data and might make it more challenging to detect actual effects. Part III: Testing for Parametric Assumptions
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