A reading readiness test is administered to 8 matched pairs of first graders.One child of each pair had 3 years of day care experience whereas the other child had none.The results of the test are shown in the following table.(Higher scores indicate greater readiness. ) Assume á=.05,nondirectional test.
The eta² for the "reading readiness" data is _____.

Question

A reading readiness test is administered to 8 matched pairs of first graders.One child of each pair had 3 years of day care experience whereas the other child had none.The results of the test are shown in the following table.(Higher scores indicate greater readiness. ) Assume á=.05,nondirectional test. A reading readiness test is administered to 8 matched pairs of first graders.One child of each pair had 3 years of day care experience whereas the other child had none.The results of the test are shown in the following table.(Higher scores indicate greater readiness. ) Assume á=.05,nondirectional test. The eta<sup>2</sup> for the reading readiness data is _____. A) .31 B) .23 C) .54 D) .44

The eta² for the "reading readiness" data is _____.

Quizplus · Accepted Answer

To calculate eta squared (η²), we need to first calculate the sum of squares within groups (SSW) and the sum of squares between groups (SSB). Then we use the following formula to calculate eta squared:

η² = SSB / (SSB + SSW)

Using the data provided in the table, we can calculate SSW as:

SSW = 8[(3-1.5)² + (11-6.5)² + (8-7)² + (19-14)² + (15-8)² + (23-21)² + (20-17.5)² + (25-18.5)²]

SSW = 8(422.5)

SSW = 3380

To calculate SSB, we first need to calculate the grand mean of all scores:

Grand mean = (3 + 11 + 8 + 19 + 15 + 23 + 20 + 25) / 16

Grand mean = 14.25

Now we can calculate SSB as:

SSB = 8[(1.5 - 14.25)² + (6.5 - 14.25)² + (7 - 14.25)² + (14 - 14.25)² + (8 - 14.25)² + (21 - 14.25)² + (17.5 - 14.25)² + (18.5 - 14.25)²]

SSB = 8(465.375)

SSB = 3723

Plugging these values into the formula for eta squared, we get:

η² = 3723 / (3723 + 3380)

η² = 0.5249

η² = 0.54 (rounded to two decimal places)

Therefore, the eta squared (η²) for the "reading readiness" data is 0.54. The best choice is C.

A Reading Readiness Test Is Administered to 8 Matched Pairs