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In-Class Learning Activity 8: Standard Error of Measurement SPED 5021/6021 T...

Sep 24, 2024

In-Class Learning Activity 8: Standard Error of Measurement SPED 5021/6021 Test: Peabody Picture Vocabulary Test Student Name Test Score Standard Error of Measurement Student A 85 3 Student B 70 3 Student C 95 3 Instructions: 1.For each of the students listed in the table, calculate their confidence intervals at the 68% and 95% levels 2.Interpret the Confidence Intervals a.What do the confidence intervals tells you about each student’s true score? b.How does the SEM affect the range of possible scores for each student? 3.How would you communicate these results to the student’s parents?

Solution by Steps

step 1

To calculate the confidence intervals for each student, we use the formula for the confidence interval (CI) given by:

CI = \text{Score} \pm z \times \text{SEM}

where

z

is the z-score corresponding to the desired confidence level. For 68%,

z \approx 1

and for 95%,

z \approx 1.96

step 2

For Student A (Score = 85, SEM = 3): - 68% CI:

85 \pm 1 \times 3 = (82, 88)

- 95% CI:

85 \pm 1.96 \times 3 \approx (78.12, 91.88)

step 3

For Student B (Score = 70, SEM = 3): - 68% CI:

70 \pm 1 \times 3 = (67, 73)

- 95% CI:

70 \pm 1.96 \times 3 \approx (63.12, 76.88)

step 4

For Student C (Score = 95, SEM = 3): - 68% CI:

95 \pm 1 \times 3 = (92, 98)

- 95% CI:

95 \pm 1.96 \times 3 \approx (88.12, 101.88)

step 5

The confidence intervals indicate the range in which we expect the true score of each student to lie. For example, for Student A, we are 68% confident that their true score is between 82 and 88, and 95% confident it is between 78.12 and 91.88

step 6

The Standard Error of Measurement (SEM) affects the range of possible scores by determining how much variability we expect in the test scores. A smaller SEM would result in narrower confidence intervals, indicating more precision in the estimated true score

step 7

To communicate these results to the students' parents, I would explain that the confidence intervals provide a range of scores that reflect the student's performance, emphasizing that these intervals give an estimate of where the true ability level likely falls

Answer

The confidence intervals for each student indicate the range of their true scores based on their test performance and the SEM.

Key Concept

Confidence intervals provide a range of values that likely contain the true score of a student based on their test score and the SEM.

Explanation

The calculated confidence intervals help in understanding the reliability of the test scores and the potential variability in the students' true abilities.