# Discussion Reply: Comparing Groups

The reply must summarize the

students findings and indicate areas of agreement, disagreement, and improvement.  It must be

supported with scholarly citations in the latest APA format and corresponding list of references

Below is the discussion post you will reply to

D7.9.1

## D7.9.1.a Under what conditions would you use a one-sample t test?

A one-sample t test is best used when a researcher is looking to compare the actual mean of a sample to a sample based on a hypothesis.  This is used if the hypothesis samples mean is significantly different than the actual mean.

## D9.7.1.b Provide another possible example of its use from the HSB data.

Is the mean mosaic patter test score in the modified HSB data set statistically different from the presumed population mean of 30?

Using a one-sample t test to compare the actual mean of the mosaic pattern test it can be determined that the hypothesized mean of 30 is statistically different.  Figure 1 also demonstrates that the upper and lower limits never cross zero, therefore there is always a difference.  t(74) = -2.34, p = .02

Figure 9.1

# D7.9.2 In Output 9.2:

## D7.9.2.a Are the variances equal or significantly different for the three dependent variables?

Question 9.2 asked if there was a significant difference in the math achievement, grades or visualization test score of the fast and regular track students.  The results show that two of the variables are not significantly different.  Both the math achievement test and grades in high school show no significant difference with  the F significance of .47 and .45 respectively the equal variances assumed statistics are used.  The visualization test showed a significant difference in fast and regular track students with an F significance of .01 the equal variances not assumed statistics are used.

## D9.7.2.b List the appropriate t, df, and p (significance level) for each t test as you would in an article.

For the math achievement test, high school grades and visualization test scores question 9.2 ran independent samples t test.  For the math achievement test and high school grades the equal variances assumed statistics should be used.  Math achievement test results are t(73) = 2.70, p = .009, grades in high school test results are t(73) = .90, p = .369.  The visualization test showed a significant difference therefore the equal variances not assumed statistics should be used t(73) = 2.36, = .020.

## D9.7.2.c Which t tests are statistically significant?

Out of the three variables tested two of the three were not statistically significant.  The only test that showed any significant difference was the t test for the visualization test scores.  The F was 6.51 with a significance of .013.

## D9.7.2.d Write sentences interpreting the academic track difference between the means of grades in high school and also visualization.

To determine whether there was a significant difference between fast and regular track students grades in high school and their scores on a visualization test an independent samples t test was conducted.  The results showed that for grades in high school there was no significant difference in the grades in high school between fast and regular track students, t(73) = -.90, p = .369.  There however was a significant difference between the fast and regular track students in regard to the scores on the visualization test t(57.2) = 2.39, p = .020, the and df  were adjusted due to the variances not being equal.

## D9.7.2.e Interpret the 95% confidence interval for these two variables.

The two variables of grades and high school and visualization test as compared between fast and regular track students results show that one is statistically significant and the other isnt.  Students grades in high school are not statistically different between fast and regular track students of the 34 fast track students = 5.50 and 41 regular track students M = 5.83, there was no significant difference.  The 95% confidence interval using the equal variances assumed statistics as directed by no determination of significant difference have a lower limit of 1.056 and an upper limit of .397.  The scores on the visualization test showed a statistically significant difference, therefore the equal variances were not assumed showing a 95% confidence interval lower limit of .348 and an upper limit of 3.981.  The fact that the upper and lower 95% confidence interval limits for both variables have the same sign and does not cross the zero point there is a possibility that there is no difference in fast and regular track grades or visualization scores.

## D9.7.2.f Comment on the effect sizes.

The effect sizes  for these three variables was determined by estimation by dividing the difference between the means of the pooled weighted average of the standard deviation of the means.  The formulas is listed on page 96 of the Morgan et al. (2019) textbook.  For the math achievement test the effect size d is .6 indicating a medium to large effect size, grades in high school have a smaller than typical effect size and visualization test scores have a medium to large effect size of .6 according to Cohen (1988).

# D7.9.3

## D9.7.3.a Compare the results of Outputs 9.2 and 9.3.

The outputs for questions 9.2 and 9.3 are similar both showed a significant difference in the scores on the math achievement test and the visualization test score and there was no statistically significant difference in the grades in high school between fast and regular track students.  These two tests provide similar results.

## D9.7.3.b When would you use the MannWhitney U test?

With the Mann-Whitney U test being similar to an independent sample t test it can be an alternative to parametric tests that are not suitable.  This non-parametric test can be used when the tests assumptions are grossly skewed, not normally distributed, ordinal or the t test assumptions are violated in other ways.

# D7.9.4 In Output 9.4:

## D9.7.4.a What does the paired samples correlation for mothers and fathers education mean?

The paired sample t test is used to compare the results of two variables that are not independent of each other.  This question as about the mothers and fathers education levels.  The test provides both a correlation and a  test result.  With an r = .68 indicating that the men who were more highly educated tended to marry more highly educated women.  The opposite is also true.

## D9.7.4.b Interpret/explain the results for the t test.

The t test compares the education level of the mothers and the fathers.  The results t(72) = 2.40, p = .019, d = .28 shows that the fathers were significantly more educated than the mothers on average.  This difference was significant statistically, but according to Cohen (1988) the effect size was small.

## D9.7.4.c Explain how the correlation and the t test differ in what information they provide.

The correlation and t test provide different information to the researcher.  The correlation in this example is the fathers and mothers education levels are compared to each other and the test compares the average education level of fathers and mothers.  In other words, the correlation tells us who is more educated mothers or fathers, and the t test tells us whether there is a difference in education levels of the pair of a mother and a father.

## D9.7.4.d Describe the results if the r was .90 and the t was zero.

With an = .90 the correlation would be similar to what is in the original question, highly educated men tend to marry highly educated women, with the reverse also being true.  A t of zero indicates that there is not enough evidence to determine if there is a significant difference in the education level of the fathers and mothers.

## D9.7.4.e What if r was zero and t was 5.0?

An r of zero would tell us that there is not enough evidence in the data to determine a correlation between the education level of the fathers and mothers that participated in the study.  A of 5.0 indicates that similar to the original numbers fathers are significantly more educated than the mothers.

# D7.9.5

## D9.7.5.a Compare the results of Output 9.4 with Output 9.5.

The outputs of question 9.4 and 9.5 are similar, but the output of 9.5 gives a little more information as it breaks down the means ranks.  This will tell the researcher the comparison numbers of mothers and fathers education levels.  Output 9.4 stated that the fathers were more educated than the mothers, but output 9.5 says that 27 fathers are more educated than their wives and 21 mothers were more educated than their husbands.

## D9.7.5.b When would you use the Wilcoxon test?

Like questions 9.2 and 9.3 compare parametric and nonparametric tests and when to use them, 9.4 and 9.5 also compare parametric and nonparametric tests.  In the case of question 9.5 the nonparametric test is the Wilcoxon test.  This test should be used when the variables being studied are not normally distributed and/or there are other assumptions of the paired t test that are violated.  In the case of this study the mothers education is significantly skewed therefore the Wilcoxon test is the appropriate test to use.

References

Cohen, J. (1988) Statistical power and analysis for the behavioral sciences (2nd ed.). Hillsdale,

NJ: Lawrence Erlbaum Associates

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2019). IBM SPSS for Introductory Statistics: Use and Interpretation, Sixth Edition (6th ed.). Routledge.

#### What Students Are Saying About Us

.......... Customer ID: 12*** | Rating: ⭐⭐⭐⭐⭐
"Honestly, I was afraid to send my paper to you, but you proved you are a trustworthy service. My essay was done in less than a day, and I received a brilliant piece. I didn’t even believe it was my essay at first 🙂 Great job, thank you!"

.......... Customer ID: 11***| Rating: ⭐⭐⭐⭐⭐
"This company is the best there is. They saved me so many times, I cannot even keep count. Now I recommend it to all my friends, and none of them have complained about it. The writers here are excellent."