WK 5: Questions and Answers

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WK 5: Questions and Answers

Part I. Inferential Statistics Concepts and Assumptions & Concepts

1. What is the standard error of measurement?

The standard error of measurement (SEm) is a measure that depicts how repeated measures of an individual score tend to be distributed around a true score. The true score is at all times unknown because no measure can be developed to accurately reflect the true score. Hence, the SEm is useful since it is a function of both the standard deviation of experiential scores and the dependability of the test. The test is perfectly dependable when SEm equals 0. On the other hand, the test is undependable when SEm is at its maximum and equals the standard deviation of the experiential scores (Furlan & Sterr, 2018). The main benefit of this measurement is that it serves a complementary role to the reliability coefficient, which ranges from 0 to 1.

2. What is the standard error of the mean?

The standard error of the mean is a measure used to evaluate the variances between more than one sample of data. It is used to help one examine how well the sample data epitomizes the whole population by assessing the precision with which the sample data denotes a population using standard deviation. The standard error of the mean is usually denoted as (SE ). In practice, an unbiased estimate of the standard error of a mean is calculated by dividing the sample standard deviation (s) by the square root of the number of what was observed in the sample (Kitchenham & Madeyski, 2020). Thus, the magnitude of SE depends on both the inconsistency of the observations and the number of observations. In other words, the higher the inconsistency, the greater the standard error, while the higher the number of observations, the smaller the standard error will be. Increasing the sample size is considered the best alternative to decrease the standard error.

3. Please discuss the term confidence interval

Confidence interval (CI) is the probability that a population value will fall between a set of limits for a certain proportion of times. It is used to measure the level of unlikelihood in a sampling method using statistical methods like t-tests. CI has probability limits, with the common being a 95% or 99% confidence level. A 95% CI depicts that when 100 different samples are obtained to calculate a 95% CI for each sample, then about 95 out of the 100 CI will have the true mean value (). This will be similar to the 99% limit. It is important to note that the CI does not reflect the unpredictability in the unknown. Rather, it shows the amount of random error in the sample and offers a range of values that are expected to include the unknown limit (Wang, 2022).

4. What are four main assumptions for parametric statistics?

Normality

Equal Variance

Independence

No Outliers

5. Please discuss and explain in your own words each of the four main assumptions.

In statistics, parametric tests are tests that make assumptions concerning the core spreading of data. Common parametric tests used include One sample test, Two-sample test, and One-way ANOVA. Therefore, the following assumptions must be met for the parametric assumption to be valid.

First, normality should be met to ensure that the data in each group are normally distributed. Various tests can be used to examine normality. For instance, when the sample sizes of every group are small, a can be used to examine whether each sample is normally distributed. Similarly, when the p-value of the test is less than the recommended significance level, the data is likely not normally distributed. In cases where the sample sizes could be large, utilizing a Q-Q plot will be essential to visually examine whether the data is normally distributed.

Second, homogeneity of variance must be met to ensure that the data collected from different groups have the same variance. Creating side-by-side boxplots for each group can be recommended to ensure this is accurately achieved. Further, the following rule of thumb can help assume whether the variances are approximately similar and can use the two-sample t-test.

Third, the data obtained must be independent. The easiest approach to examine this assumption is to confirm that the data was collected using a probability sampling method. This is an approach where every member of a population has an equal chance of being selected to be in the sample. Common sampling methods used include simple random sampling, systematic random sampling, cluster random sampling, and stratified random sampling.

Lastly, there should be no extreme outliers. The easiest way to examine whether this assumption is met is by creating boxplots for each group to examine whether there are any clear outliers greater than the rest of the other observations in the group. Similarly, Grubbs Test can be used to examine the outliers.

6. Why is it important to discuss or test the assumptions before conducting parametric statistical analyses?

Since one cannot conduct parametric analyses without proving that the data follows the rule of the analyses, there are various benefits accompanied by this. Assumptions testing before conducting a parametric test can help one decide whether the conclusions are accurately drawn from the analysis results. This can help determine which requirements must be fulfilled before performing the analysis.

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.).

.

District-wide freshmen standard deviation = 12

36 selected freshman test mean score is 85

SEM = M =/N

M =12/36

M = 2

2.Why is it better to use a 99% CI then a 95% CI?

Usually, the most used confidence level is 95%. However, when seeking to obtain a higher degree of confidence that the interval will have the true population value, then increasing CI from 95% to 99% is necessary. This is because an increase in confidence level offers a high opportunity for the population to fall within the range.

3. Explain a 95% CI and give an example or apply the meaning in a real-world situation

A 95% confidence interval means that 95% of the population mean will fall within the provided interval and 5% out of the interval. For instance, when ABZ News conducted a poll by contacting 1,014 adults in April, the results indicated that 56% would elect person X while 39% would elect person Y. The results had a margin of error of +/-3.5 Percentage points. This would mean a 95% probability that between 35.5% and 42.5% of voters would elect person Y (39 percent plus or minus 3.5 percent). Conversely, the results would reveal a 5% probability that less than 35.5% or 42.5% of voters would vote for person Y.

4. Explain a 99% CI and give an example or apply the meaning in a real-world situation

A 99% confidence interval means that 99% of the population mean will fall within the provided interval and 1% out of the interval. Using the same example above (question 3), there is a 99% probability that between 35.5% and 42.5% of voters would elect person Y (39 percent plus or minus 3.5 percent). Equally, the results would reveal a 1% probability that less than 35.5% or 42.5% of voters would vote for person Y.

Part III. Testing for Parametric Assumptions

Conduct the required analyses to test for the assumptions of normality (Shapiro-Wilks or Kolmogorov-Smirnov) and homogeneity of the variance (Levenes) for the two films from the data in themoviedata file.

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

. Statistic df Sig.

Name_of_film .338 40 .000 .637 40 .000

a. Lilliefors Significance Correction

Test of Homogeneity of Variances

Name_Film

Levene Statistic df1 df2 Sig.

7.841 11 15 .000

2. Please write a few sentences describing the assumptions required in this exercise and whether or not they were met. Please include information from the output to support your answers.

The assumption of homogeneity of variance requires that all comparison groups have similar variance and are normally distributed. In this exercise, the normality assumption was met by using the . On the other hand, an equal variance was assessed using Levenes test, which uses an F-test to test the null hypothesis that the variance is equal across groups. The output revealed that the assumption was met since the variance is equal across groups.

References

Furlan, L., & Sterr, A. (2018). The applicability of standard error of measurement and minimal detectable change to motor learning researcha behavioral study.Frontiers in human neuroscience,12, 95. https://doi.org/10.3389/fnhum.2018.00095

Kitchenham, B., & Madeyski, L. (2020). Inconsistencies with formulas for the standard error of the standardized mean difference of repeated measures experiments.Statistics in medicine,39(27), 41014104. https://doi.org/10.1002/sim.8669

Wang, G. (2022). The 95% Confidence Interval for .Journal of Surveying Engineering,148(1), 04021030.

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