### Assignment: Analyzing Assessment Data

Assignment: Analyzing Assessment Data

**Analyzing Assessment Data**

*There are a few steps to take when analyzing sample test statistics. The first is to make sure that the data is in a usable format. This means that the data must be organized in a way that allows for easy comparisons. The second step is to determine the shape of the distribution. This can be done by plotting the data and studying its symmetry, center, and spread. The third step is to identify any outliers in the data set and decide whether or not they should be eliminated from further analysis. Finally, various tests can be performed on the data in order to determine factors such as variance and statistical significance. When analyzing sample test statistics, it is important to consider the mean, standard deviation, alpha level, and p-value (Washington et al., 2020). The p-value is especially important, as it allows analyst to determine the statistical significance of the findings. In general, a p-value of less than .05 indicates that the results are statistically significant. The purpose of this assignment is to analyze sample test statistics for the information given in chapter 11 table 11.1.*

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**Explanation of Reliability**

*Reliability in statistical tests refers to the ability of the test to provide consistent results. A reliable test is one that produces similar results each time it is administered, providing accurate information about the population being tested. There are several factors that can affect the reliability of a statistical test, including the design of the test, how well it measures what it purports to measure, and how stable the measurements are over time (Kim & Park, 2019). Researchers must carefully consider all of these factors when designing and interpreting statistical tests.*

*From the sample test statistics given in table 11.1, the test statistics is reliable given a large sample size of 100. The larger the sample, the more likely it is that the statistic will be representative of the population. The Central Limit Theorem is often thought to hold for sample sizes equal to or larger than 30. The fact that the population mean and standard deviation will be equal to the average of the sample means and standard deviations is a crucial component of central limit theorem. A measure is considered to be reliable if it produces similar results under consistent conditions. The larger the sample size, the more reliable the measure. This is because a larger sample size provides more data points, which leads to a more accurate representation of the population. There are several factors that can affect the reliability of a measure, such as method variance and measurement error. Method variance occurs when there are different ways of measuring the same thing.*

**Sample Range**

*The range of the sample is (93-52) which is 41. To calculate the range for a data sample, data analyst first needs to determine the maximum and minimum values in the set. Once they have those numbers, subtracting the minimum from the maximum will lead to a sample range. For example, if your data set contains the numbers 5, 7, 9, 2, 1, then the maximum value is 9 and the minimum value is 1. Therefore, the range is 8 (9-1). The range is important in sample data because it helps to identify the extremes of a data set. This information can be helpful in identifying potential outliers and in understanding the distribution of data. The range can also be used to calculate other statistics, such as the standard deviation. In summary, by calculating the range of a data set, we can determine its extremes (Schmidt & Hollestein, 2018). The range is simply the difference between the largest and smallest values in a set. This can be helpful in identifying outliers (values that are far from the rest of the data) or in understanding the variability of data.*

**The Difference between Standard Deviation and Standard**

**Error of Measurement**

*From table 11.1, the Standard deviation is 7.7 and the Standard error of measurement (SEM) is 3.8. Standard deviation is a statistic that is used to measure the variability of a set of data. It is computed by taking the square root of the variance. The standard error of measurement is a statistic that is used to estimate the standard deviation of a population from a sample. It is computed by taking the square root of the variance of the sample (Andrade, 2020). The instructor can use this information to help students understand how much variability there is in their measurements of performance in tests and to help them determine how much confidence they can have in their measurements.*

*In summary, the standard deviation (SD) is a measure of the variability of the data. The standard error (SE) is a measure of the variability of the sampling distribution. The SD and SE are both used in statistical tests to determine whether the difference between two groups (or samples) is statistically significant. The SD is used to calculate the variance, and the SE is used to calculate the confidence interval. The larger the SD and SE, the more uncertain we are about whether or not there is a statistically significant difference between the groups (or samples). Therefore, we need to use a more conservative test statistic (i.e., a higher p-value) to account for this increased uncertainty.*

*The Process of Analyzing Individual Items Once an Instructor Has *

**Analyzed Basic Concepts of Measurement**

*When it comes to analyzing individual items, there are three key concepts that instructors need to take into account: difficulty, discrimination, and directionality. First, when considering the difficulty of an item, instructors must ask themselves how easy or hard it is to identify the target attribute(s). Second, once an item has been identified as being difficult, instructors must determine whether or not students are able to distinguish between correct and incorrect responses. And finally, in order to gauge the directionality of an item (or test), instructors must ascertain whether or not students are more likely to choose a correct response over an incorrect response.*

*When it comes to data analysis, instructors need to be aware of the three Ds: difficulty, discrimination, and deviation. Difficulty refers to how easy or difficult it is to measure a particular attribute or trait. Discrimination refers to the ability of an instrument to correctly measure what it is supposed to measure. And deviation reflects the amount of variation that exists in a population with respect to a particular characteristic. Ideally, an instructor wants data that is both easy to measure and accurately reflects the differences among individuals. However, this is not always possible. Sometimes we must make do with data that is difficult to obtain or that has high levels of variation. *

**Interpretation of P-value**

*It is not always clear what a p value of 0.100 means, and it’s possible that the question is mislabeled on the exam. However, if it is correctly labeled, then a p value of 0.100 suggests that there is a 10% chance that the results observed were due to chance alone. In other words, there is a 90% chance that the results observed were not due to chance. Given this information, it would not be advisable to eliminate the item from consideration solely on the basis of its p value. However, if other factors (e.g., low item-level validity or test reliability) also suggest that the item should be eliminated, then it would make sense to do so.*

**Questions On the Exam Has a Negative PBI**

*In most cases, it is helpful to know if a question has a negative PBI for the correct option, because it tells one that most of the distractors have a positive PBI. In other words, if an individual see a question like this on the exam, it is likely that most of the distractors are going to be tempting answers that look right but are actually wrong. So, instructors should be extra careful when setting or including such a question in their exams. A negative PBI provides evidence that the distractors are plausible options, and can mislead test-takers into choosing the wrong answer. It is important to note that a high PBI does not always mean that an option is correct, but rather that it is more likely to be correct than the other options (Seekis et al., 2021). So, if a student is struggling with a question, they should try to find the option with the highest PBI and go from there.*

*It is important for instructors to be able to adjust questions with negative PBI in order to ensure that students are correctly receiving the information. There are a few ways that this can be accomplished. One way is to provide additional examples of the concept being taught. This will help students to better understand the material and make more informed choices when answering questions. Another way to adjust questions with negative PBI is to offer specific instructions on how to answer the question. This can be done by providing an example of a correct answer or by offering a step-by-step explanation of the process required to reach the correct answer.*

**References**

*Andrade, C. (2020). Understanding the difference between standard deviation and standard error of the mean, and knowing when to use which. Indian Journal of Psychological Medicine, 42(4), 409-410. https://doi.org/10.1177/0253717620933419*

*Kim, T. K., & Park, J. H. (2019). More about the basic assumptions of t-test: normality and sample size. Korean journal of anesthesiology, 72(4), 331-335. https://synapse.koreamed.org/articles/1156595*

*Schmidt, S. A., Lo, S., & Hollestein, L. M. (2018). Research techniques made simple: sample size estimation and power calculation. Journal of Investigative Dermatology, 138(8), 1678-1682. https://doi.org/10.1016/j.jid.2018.06.165*

*Seekis, V., Bradley, G. L., & Duffy, A. L. (2021). How is trait self-compassion used during appearance-related distress by late adolescents and emerging adults with positive or negative body image? A qualitative study. Journal of Adolescent Research, 07435584211011471. https://doi.org/10.1177/07435584211011471*

*Washington, S., Karlaftis, M., Mannering, F., & Anastasopoulos, P. (2020). Statistical and econometric methods for transportation data analysis. Chapman and Hall/CRC.*

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Data from assessments can be used to determine if learners are meeting course outcomes or learning objectives. Assessments can be utilized in many ways, such as learner practice, learner self-assessment, determining readiness, determining grades, etc. The purpose of this assignment is to analyze sample test statistics to determine if learning has taken place.

To address the questions below in this essay assignment, you will need to use the information from your textbook chapter readings and the data provided in Table 11.1 (“Sample Test Statistics”) in Chapter 11 of The Nurse Educator’s Guide to Assessing Learning Outcomes.

In a 1,000-1,250-word essay, respond to the following questions:

Explain what reliability is and whether this test is reliable based on the information in Table 11.1 (“Sample Test Statistics”). What evidence supports your answer?

What is the range for this sample? What information does the range provide and why is it important?

What is the difference between standard deviation and standard error of measurement? How would the instructor use this information?

Explain the process of analyzing individual items once an instructor has analyzed basic concepts of measurement. Consider the three Ds (difficulty, discrimination, and distractors) in your response.

If one of the questions on the exam had a p value of 0.100, would it be a best practice to eliminate the item? Justify your answer.

If one of the questions on the exam has a negative PBI for the correct option and one or more of the distractors have a positive PBI, what information does this give the instructor? How would you recommend that the instructor adjust this item?

You are required to cite two or three sources to complete this assignment. Sources must be published within the last 5 years and appropriate for the assignment criteria and nursing content.

Prepare this assignment according to the guidelines found in the APA Style Guide, located in the Student Success Center.

This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

You are required to submit this assignment to LopesWrite. A link to the LopesWrite technical support articles is located in the Class Resources if you need assistance.