Question

A group of researchers want to determine if marital satisfaction among women declines following the birth of a first child. To test this hypothesis, they collected data on marital satisfaction from 22 women at two time points: 6 months after marriage and 1 month after the first child was born. They observed that the average marital satisfaction among women at time 1 was 7.0 and the average marital satisfaction among women at time 2 was 5.8. The sum of squares for the difference scores (SS_D) was 200. Use the critical-value approach for a dependent samples t-test (where α = .05) to determine if there is a significant decline in marital satisfaction among women following childbirth.

                                                                                                              

      1.      Identify the alternative hypothesis

      2.      List your degrees of freedom

      3.      List your estimated standard error

      4.      List your t test statistic (where: Time 2 – Time 1)

      5.      List your critical t value(s)

      6.      Is the decline in marital satisfaction among women following childbirth statistically significant? (Yes/No)

      7.      Calculate Cohen’s d for the difference in marital satisfaction

Answer 1

(1) Ha: d-bar < 0

(2) df = 22 - 1 = 21

(3) Variance = SSD/(n - 1) = 200/21 = 9.5238, so s = √variance = 3.0861

Standard error SE = s/√n = 3.0861/√22 = 0.658

(4) d-bar = 5.8 - 7 = -1.2

t = d-bar/SE = -1.2/0.658 = -1.8238

(5) Critical value for a lower-tailed test at α = 0.05 and df = 21 is -1.7207

(6) Since -1.8238 < -1.7207, we reject Ho and conclude that the decline in marital satisfaction among women following childbirth statistically significant

(7) Cohen's d = d-bar/s = -1.2/3.0861 = -0.3888

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