This is a question I have to answer for a University of Phoenix class, If any one could help and explain to me (in a stistics for dummies explanation:)I would appreciate it. Here goes:
Six months after a divorce, the former wife, and husband each take a test that measures divorce adjustment. The wife's score is 63, and the husband's score is 59. Overall, the mean score for divorced women on the test is 60(SD=6);the mean score for divorced men is 55(SD=4). Which of the two has adjusted better to the divorce in relation to other divorced people of their own gender? Explain your answer.
Help!!!
The woman's score was 63, with a mean of 60 and a standard deviation of 6.
So she scored within 1/2 of a SD.
The man's score was 59 with a mean of 55 and a SD of 4, so he was within 1 SD of the mean.
If a score closer to the mean implies better adjustment, then clearly the woman according to this test adjusted better.
I would tend to disagree with Reiny. Better adjustment would most likely be indicated by the higher scores, rather than closer to the mean (assuming that low scores indicate bad adjustment while higher ones indicate good adjustment).
Each score needs to be judged in terms of its own standardization group (men or women). A SD of +.5 = the about the 70th percentile. In other words, the woman scores equal to or above 70% of all women. In contrast, the man's SD of +1 = about the 84th percentile, scoring equal to or above 84% of all men.
I hope this helps a little more. Thanks for asking.
To determine which of the two, the wife or the husband, has adjusted better to the divorce in relation to other divorced people of their gender, we can analyze their scores in relation to the mean scores and standard deviations of their respective gender groups.
1. Calculate the z-scores:
The z-score measures how many standard deviations an individual's score is from the mean. We'll calculate the z-scores for the wife and the husband separately.
For the wife:
z-score = (wife's score - mean score for divorced women) / standard deviation for divorced women
z-score = (63 - 60) / 6
For the husband:
z-score = (husband's score - mean score for divorced men) / standard deviation for divorced men
z-score = (59 - 55) / 4
2. Interpret the z-scores:
The z-scores tell us the number of standard deviations the individuals' scores are above or below the mean for their gender group. A positive z-score indicates a score above the mean, and a negative z-score indicates a score below the mean.
A higher positive z-score suggests better adjustment compared to others of the same gender, while a lower negative z-score suggests poorer adjustment.
3. Compare the z-scores:
Compare the z-scores for the wife and the husband to determine who has adjusted better relative to others of the same gender.
If the wife's z-score is higher than the husband's z-score, it suggests she has adjusted better compared to other divorced women. Conversely, if the husband's z-score is higher, it suggests he has adjusted better compared to other divorced men.
4. Determine the result:
After comparing the z-scores, we can conclude which of the two individuals has adjusted better in relation to other divorced people of their own gender.
Note: If you need a specific result, please provide the actual values for the mean and standard deviation of divorced women and divorced men, as the values mentioned in the question may not be accurate.
To determine which of the two individuals has adjusted better to the divorce in relation to others of their own gender, we need to compare their scores to the mean scores of divorced women and divorced men, respectively. We can do this by calculating z-scores for each individual's test scores.
A z-score measures how far away a particular score is from the mean, in terms of standard deviations. It allows us to compare scores from different distributions.
For the former wife:
The mean score for divorced women is 60, with a standard deviation of 6. We can calculate her z-score using the formula:
z = (x - mean) / standard deviation
z = (63 - 60) / 6
z = 3 / 6
z = 0.5
So, her z-score is 0.5.
For the former husband:
The mean score for divorced men is 55, with a standard deviation of 4. We can calculate his z-score using the same formula:
z = (x - mean) / standard deviation
z = (59 - 55) / 4
z = 4 / 4
z = 1
So, his z-score is 1.
Interpreting z-scores:
A positive z-score means the individual's score is above the mean, while a negative z-score means the individual's score is below the mean. The larger the absolute value of the z-score, the farther away it is from the mean.
In this case, the former wife's z-score of 0.5 indicates that her test score is 0.5 standard deviations above the mean score of divorced women. On the other hand, the former husband's z-score of 1 means his test score is 1 standard deviation above the mean score of divorced men.
Since the husband's z-score is larger, it suggests that he has adjusted better to the divorce in relation to other divorced men, compared to how the wife has adjusted in relation to other divorced women.