## Statistics project based on hypothesis testing

Your Project should be complete and contain sections entitled:

Hypotheses: this section should contain the hypothesis or hypotheses that you tested.This section should be 1 to 2 pages in length.

Research Design: this section should clearly define the independent variable(s), the levels of such, and the dependent variable(s). This section should be 1 to 2 pages in length.

Statistical Methods: this section should clearly define all the statistical procedures you employed to test the hypotheses. This section should be 1 to 2 pages in length.

Results: this section should be the simple statements that can be derived from the statistical output.This section should be 1 to 2 pages in length.

Interpretation: this section should contain the statements regarding whether you fail to reject the hypotheses based on the chosen statistical procedure. This section should be 1 to 2 pages in length.

The Final Project should be at least 5 to 7 pages in length. Provide references. The reference page and title page do not count in the final page requirement. APA formatting is required.

## Run a two-way ANOVA in SPSS

I need help with someone who can run a Two-Way ANOVA using SPSS software and include appropriate results only based on the information provided in the attachments. Please explain and evaluate the SPSS results.

Please see attachments

I up loaded all the data needed to perform an SPSS two-way ANOVA.

Research Question for a Two-Way Factorial ANOVA

The research question posed for the one-way factorial ANOVA included the following: Does a six week or 12 week self-monitoring program provided to teens between the ages of 13 and 15 diagnosed with ADHD reduce anxiety levels, as measured by the Beck Anxiety Inventory (BAI), when compared with no intervention? In this investigation there were three groups for investigation: no intervention, six week intervention and 12 week intervention. The independent variable remains the self-monitoring program with the dependent variable being anxiety levels for the students. In order to expand this research question for a two-way ANOVA a second independent variable would be needed. As such, gender (male or female) is selected as the second independent variable for the research.

Based on this information the new research question expanded for both dependent variables would include the following: Does a six week or 12 week self-monitoring program provided to males and females between the ages of 13 and 15 diagnosed with ADHD reduce anxiety as measured levels, as measured by the BAI, when compared with no intervention? This would require a breakdown of variables as follows:

Independent Variable 1: Frequency of Self-Monitoring Program

Group 1: No intervention

Group 2: Six week intervention

Group 3: 12 week intervention

Independent Variable 2: Gender

Group 1: Male

Group 2: Female

Dependent Variable: Change in anxiety scores as measured by the BAI

Reason for Selecting Variables

The first independent variable selected for this investigation involves the duration of the self-monitoring program. A review of the literature regarding the use of self-monitoring programs indicates that these interventions involve skill development to enable the individual to engage in behaviors that will enhance social capabilities, executive control, and overall functioning (Coyle & Cole, 2004). Based on this assessment, it is believed that providing the program—as opposed to no intervention—and increasing the duration of the program—from six to 12 weeks—should have a positive impact on reducing anxiety for teens with ADHD. Teens should acquire some of the basic skills needed to improve social functioning, enabling them to experience less social anxiety and improving their interactions with peers and adults.

The second independent variable, gender, was selected also based on literature which definitively demonstrates that there are notable differences in symptoms of ADHD based on gender (Skogli, Teicher, Andersen, Hovik & Oie, 2013). Specifically, Skogli and coworkers report that there are differences in symptom display among males and females with male exhibiting higher levels of symptom severity and impairments in executive functioning. Given that self-monitoring programs are aimed at addressing many of the deficits in executive functioning to enhance social outcomes it is possible that males receiving this intervention will experience more significant declines in anxiety levels when compared with females. Thus, there is an impetus to examine the role that gender plays in the current research question.

Null and Alternative Hypotheses

Utilizing the two independent variables there are three null and alternative hypotheses that can be proposed for this research question. The null hypotheses for the investigation include:

• Ho1: There is no difference in the mean anxiety score as measured by the BAI among the three intervention groups.

• Ho2: There is no difference in the mean anxiety score as measured by the BAI between males and females diagnosed with ADHD.

• Ho3: There is no interaction between the duration of the intervention (no intervention, six weeks and 12 weeks) and the gender of the participant (male or female).

The alternative hypotheses for the investigation include the following:

• Ha1: There is a difference in the mean anxiety score as measured by the BAI among the three intervention groups.

• Ha2: There is a difference in the mean anxiety score as measured by the BAI between males and females diagnosed with ADHD.

• There is an interaction between the duration of the intervention (no intervention, six weeks and 12 weeks) and the gender of the participant (male or female).

Testing and Predicted Results

Synthesizing the rationale provided for the selection of independent variables it seems reasonable to argue that males between the ages of 13 and 15 that receive the self-monitoring program for the longest duration of time (i.e., 12 weeks) will have the most significant reductions in anxiety levels as measured by the BAI. Females in this group should have the second most significant reductions in anxiety levels. This should be followed by: males in the six week group and females in the six week group. Males and females in the no intervention group should have the highest levels of anxiety following the 12 week study program, similar to those recorded at baseline. Males should have higher baseline anxiety levels when compared with females due to the differences that exist in the expression of ADHD symptoms for males and females.

BRAINMASS EXPERTS THE THING LEFT TO DO IS RUN A TWO-WAY ANOVA AND EXPLAIN AND EVALUATE THE SPSS RESULTS

Conclusion

If all of the null hypotheses are rejected this indicates that both the duration of the self-monitoring intervention as well as the gender of the participant has some impact on anxiety level scores as measured by the BAI. The initial predictions regarding the direction of the influence—with males in the 12 week program experiencing the most significant reductions in anxiety and males in the no intervention group experiencing the lowest changes in anxiety levels must be tested. A post hoc test should provide insight into the specific manner in which the variables impact outcomes simultaneously. For instance, the post hoc test should provide insight into what specific conditions have the greatest influence on outcomes for the Beck Anxiety Inventory (e.g. male gender enrolled in the 12 week self-monitoring program. Results from the post-hoc analysis would indicate the interaction between the variables and their overall influence on anxiety levels for the students. The results may indicate that while males in the 12 week program experience the highest levels of reduction in anxiety levels, females in the six week program have comparable results. This result would require further investigation to understand why a six week program works better for females when compared with females in the 12 week program.

References

Coyle, C., & Cole, P. (2004). A videotaped self-modeling and self-monitoring treatment program to decrease off-task behavior in children with autism. Journal of Intellectual & Developmental Disability, 29(1), 3-15.

Skogli, E.W., Teicher, M.H., Andersen, P.N., Hovik, K.T., & Oie, M. (2013). ADHD in girls and boys—Gender differences in co-existing symptoms and executive function measures. BMC Psychiatry, 13, 298-324.

## Hypothesis Testing Method

1. Let take for example that research in your area was providing behavior therapy with people who have neurological problems: Imagine that you are in charge of a research Assignment, and can choose to do research on anything.

a). What research question would you create?

b). Write out your research question and explain any terms or ideas.

c). Develop a research hypothesis that you might use to answer your question.

2. Using SPSS one will most likely look at summary statistics, like mean or variance, to make graphs, to calculate correlation and regression, and to run hypothesis tests, such as t-tests and ANOVA tests.

Which SPSS method(s) do you think you will use to answer your research question in (1)? Why?

## Hypothesis Test with Cohen’s d

In a study examining the effects of alcohol on reaction time it was found that even moderate alcohol consumption significantly slowed the response time to an emergency situation in a driving simulation. In a similar study researchers measured reaction times 30 minutes after each participant consumed 6 ounces of wine. Again they used a standardized driving simulation task for which the regular population averages u=400 msec. The distribution of reaction times is approximately normal with 0= 40. Assume that the researcher obtained a sample mean of M= 422 for the n=25 participants in the study.

Are the data sufficient to conclude that the alcohol has a significant effect on reaction times? Use a two tailed test with o = .01.

For this sample the standard error is ______, and the value of the z score is _____. with o=.01 the boundaries of the critical region are _____. Therefore the date _____sufficient to conclude that alcohol has a significant effect on reaction time.

Do the data provide evidence that the alcohol signifiant increased (slowed) reaction time?use a one tailed test with o= .05

The date ____provide evidence that alcohol significant increased (slowed) reaction times as the value of the z-score is _____the boundary of the critical region ____of obtained using one tailed test with o=.05

Compute cohens d to estimate the size of the effect.

Cohens d=_____

## Explaining 6 Basic Statistics Questions on Hypothesis Testing

I am just wanting someone to see if answered these word questions correctly. My book isn’t exactly to the direct point. I understand if your unable to.

Which of the following accurately describes the critical region?

* outcomes with a high probability if the null hypothesis is true

* outcomes with very low probability if the null hypothesis is true (this is the one i selected?)

* outcomes with a high probability whether or not the null hypothesis is true

* outcomes with a very low probability whether or not the null hypothesis is true

with o= .05, how are the boundaries for the critical region determined?

* boundaries are drawn so there is 5% (0.5) in the center of the distribution

* boundaries are drawn so there is 5 % (.05) in each tail (this is what i chose, but i am torn between it and the 2.5% because of each tail?)

* boundaries are drawn so there is 2.5% (.025) in each tail

* boundaries are drawn so there is 10% (.10) in each tail of the distribution

If a hypothesis test produces a z score in the critical region, what decision should me made?

*fail to reject the null hypothesis

* fail to reject the alternative hypothesis

* reject the alternative hypothesis

* reject the null hypothesis (this is the one i had chosen?)

A sample of n= 25 individuals is selected from a population with u=80 and a treatment is administered to the sample. what is expected if the treatment has no effect?

* the sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis

* the sample mean should be close to 80 and should lead you to fail to reject the null hypothesis

* the sample mean should be very different from 80 and should lead you to reject the null hypothesis

* the sample mean should be close to 80 and should lead you to reject the null hypothesis. ( this is the one that i had chosen?)

which of the following is an accurate definition of a type 1 error?

* rejecting a false null hypothesis

* rejecting a true null hypothesis (this is the one i had chosen?)

* failing to reject a false null hypothesis

* failing to reject a true null hypothesis

which of the following is an accurate definition of a type II error?

* rejecting a true null hypothesis

* rejecting a false null hypothesis

* failing to reject a true null hypothesis

* failing to reject a false null hypothesis ( this is the one i had chosen?)

## Type I and II error

Can you please let me know if I answered these word questions correctly. My book isn’t exactly to the point. i understand if you can’t. Thank you

You complete a hypothesis test using o=.05 and based on the evidence from the sample, your decision is to reject the null hypothesis. which of the following is true?

* you have made a type 1 error

* you might have made a type 1 error but the probability is less than 5% (this is the one i had chosen)

* you have made a type II error

* you have made the correct decision

you complete a hypothesis test using o= .05 and based on the evidence from the sample your decisions to fail to reject the null hypothesis. if the treatment actually does have an effect, which of the following is true?

* you have made a type II error ( this is the one i had chosen?)

* you might have made a type I error, but the probability is only 5% at most

* you have made a type I error

* you have made the correct decision

what is the relationship between the alpha level, the size of the critical region and the risk of type I error?

* as the alpha level increases the size of the critical region decreases, and the risk of a type I error decreases

* as the alpha level increases, the size of the critical region increases and the risk of a type 1 error decreases (this is the one i had chosen?)

* as the alpha level increases the size of the critical region decreases and the risk of a type 1 error increases

* as the alpha level increases the size of the critical region increases and the risk of a type I error increases.

by selecting a larger alpha level reseacher is

* better able to detect a treatment effect

* attempting to make it easier to reject Ho

* all of these choices are the result of selecting a lager alpha level (this is the one i had chosen)

* increasing the risk of a type I error

## Six basic statistics questions regrading hypothesis testing

A two tailed hypothesis test is being uses to evaluate a treatment effect with o= .05. if the sample data produce a z- score of z= -2.24 what is the correct decision?

* reject the null hypothesis and conclude that the treatment has an effect

* fail to reject the null hypothesis and conclude that the treatment has no effect

* fail to reject the null hypothesis and conclude that the treatment has an effect

* reject the null hypothesis and conclude that the treatment has no effect

the critical boundaries for a hypothesis test are z= +1.96 and -1.96. if the z score for the sample data is z= -1.90, what is the correct statistical decision?

* reject H1

* reject Ho

* fail to reject Ho

* fail to reject H1

A researcher administers a treatment to a sample of participants selected from a population with u= 80. If a hypothesis test is used to evaluate the effect of the treatment which combination of factors is most likely to result in rejecting the hypothesis?

* a sample mean much different than 80 with o= .01

* a sample mean near 80 with o=.01

* a sample mean much different than 80 with o= .05

* a sample mean near 80 with o= .05

under what circumstances can a very small treatment effect still be significant

* if the standard error of M (oM) is very large

* if the sample size of (n) is very large

* if the sample standard deviation (o) is very large

* all of these factors are likely to produce significant results.

A sample of n=9 individuals is selected from a population with u= 60 and o=6, and a treatment is administered to the sample. after the treatment, the sample mean M= 63. What is the Cohen’s d for this sample?

* 1.00

* 0.33

* 2.00

* 0.50

Which of the following is an accurate definition for the power of a statistical test?

* the probability of supporting a false null hypothesis

* the probability of rejecting true null hypothesis

* the probability of rejecting a false null hypothesis

* the probability of supporting true null hypothesis

## Computing Standard Error and Explaining T and Z Distribution

Can you please help me with these questions? Some I have attempted to answer. Please let me know if they are right or wrong.

Find the estimated standard error for the sample mean for each of the following samples. (Use one decimal place)

n=4 with SS = 48

_______

n=6 with SS= 270

_________

n= 12 with SS= 132

________

Why do t distributions tend to be flatter and more spread out than the normal distribution is? The (denominator) (numerator) (product) I chose product??___ of the t statistic contains the (sample standard deviation)(population mean)(population standard deviation)__i chose sample standard deviation________, which is _(different)(unknown)(the same)__I chose different ?________for different samples. The z score uses the _(population standard deviation)(population size)(sample standard deviation)_i chose population standard deviation?______________which is __(the same)(different)(unknown)_i chose same?______for different samples, Therefore, the t statistic has __(greater)(equal)(less)___less?________variabilty.

use the distribution tool to find the t values that form the boundaries of the critical region for a two-tailed test with o= .05 for each of the following sample sizes. use three decimal places.

t distribution

degrees of freedom= 21

n=6

t= ±

n=12

t=±

n=24

t=±.

## Computing Pooled Variance and Standard Error for 2 Sample Means

Two separate samples, each with n=15 individuals, receive different treatments. After treatment, the first sample has SS=1740 and the second has SS=1620.

The pooled variances for the two samples is _________.

Compute the estimated standard error for the sample mean difference.

Estimated s(M1-M2)=________

If the sample mean difference is 8 points, is this enough to reject the null hypothesis and conclude that there is a significant difference for a two tailed test at the .05 level?

* Fail to reject the null hypothesis; there is no significant difference.

* Reject the null hypothesis; there is a significant difference.

* Fail to reject the null hypothesis; there is a significant difference.

* reject the null hypothesis; there is no significant difference.

t – critical = ±_________

t= ________

Assume that the two samples are obtained from populations wight the same mean, and calculate how much difference should be expected, on average, between the two sample means.

Each sample has n=4 with s2=68 for the first sample and s2= 76 for the second. ________

Each sample has n=16 scores with s2=68 for the first sample and s2=76 for the second. ______

In the second part of this question, the two samples are bigger than in the first part, but the variances are unchanged. How does the sample size affect the size of the standard error for the sample mean difference?

* As sample size increases, standard error remains the same.

* As sample size increases, standard error increases

* As sample size increases, standard error decreases.

## Independent Sample Testing of Hypothesis

please help me solve this in simple steps. thank you.

A researcher conducts an independent-measures study comparing two treatments and reports the t statistics as t(25)= 2.071.

How many individuals participated in the entire study?

use a two tailed test with o=.05 and the distributions tool below to determine if there is significant difference between the two treatments.

t-critical=_ ______

* Reject the null hypothesis; there is no significant difference

* Fail to reject the null hypotheses; there is no significant difference.

* Reject the null hypothesis, there is a significant difference

* Fail to reject the null hypothesis; there is a significant difference.

Compute r2 to measure the percentage of variance accounted for by the treatment effect.

* 14.6%

*7.1%

* 7.6%

*13.6%

## T-test for a Sample Height

From literature research, a physiologist learns that the national average height for male college students is 70 inches. Twenty randomly-chosen male students at AWC had the following heights:

68, 71, 73, 66, 65, 68, 58, 63, 77, 57, 69, 63, 64, 59, 74, 72, 70, 64, 56, 72

At α = 0.05, do male college students at AWC follow the national average.

a) The name of the appropriate test is: ___________________________________

b) List any 3 assumptions:

c) Hypothesis: H0: _______________________ H1: _______________________

d) Test Statistic value: ____________ d.f.: ____________ P-value: ____________

e) Conclusions: Reject or Retain H0 (circle one)

Summary Statement: _____________________________________________

______________________________________________________________

f) Calculate a 95% Confidence Interval on the population mean.

____________________________________________________________________

g) _________________________

## Sample Size, Sample Error, and Sum of Squares

On average, what value is expected for the t statistic when the null hypothesis is true?

*1

*1.96

*0 (?)

*t>1.96

What is the sample variance and the estimated standard error for a sample of n=9 scores with SS= 72?

*s2=3 and sM=3

*s2 and sM= 1

*s2=9 and sM=3 (?)

*s2=3 and sM=1

Which set of characteristics will produce the smallest value for the estimated standard error?

*A large sample size and a small sample variance

*A large sample size and a large sample variance

*A sample sample size and a large sample variance

*A small sample size and a small sample variance (?)

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df=30, how many individuals were in the sample?

*n=30

*cannot be determined from the information given

*n=29 (?)

*n=31

When n is small (less than 30) how does the shape of the t distribution compare to the normal distribution?

* It is taller and narrower than the normal distribution

* It is almost perfectly normal

*There is no consistent relationship between the t distribution and the normal distribution.

*It is flatter and more spread out than the normal distribution . (?)

With o= .01, the two tailed critical region for a t test using a sample of n=16 subjects would have boundaries of :

*t= ±2.602

*t= ± 2.921

*t=± 2.947

*t= ± 2.583

## T Test on Mean Difference and Computing R Squared

Masculine themed words are frequently used in job recruitment materials, especially for job advertisements in male-dominated areas. the same study found that these words also make the jobs less appealing to women. in a similar study, female participants were asked to read a series of job advertisements and then rate how interesting or appealing the job appeared to be. Half of the advertisements were contracted to include several masculine-themed words and the others were worded neutrally. the average rating for each type of advertisement was obtained for each participant. for n=25 participants, the mean difference between the two styles of advertisements is MD=1.32 points (neutral ads rated higher) with SS=150 for the difference scores.

t distribution, degrees of freedom= 21

Is the result sufficient to conclude that there is a significant difference in the ratings for two types of advertisements?

t-critical= ±______

t = ________

Compute r2 to measure the size of the treatment effect (round to three decimal places.)

write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

Female participants (did not rate, rated) job recruitment materials with masculine-themed words significantly different than job recruitment materials with neutral words, (( t25)=1.205, t(25)=2.699, t(24)=2.588, t(24)=2.640) , (p<.05, t(25)=2.604, s=2.5, up=1.32) , (r=0.467, r2=0.095, r=0.315, r2=0.225).

suppose a researcher obtains a sample of n=16 adults who are between the ages of 65 and 75. the researcher uses a standardized test to measure cognitive performance for each individual. the participants then begin a 2 month program in which they receive daily doses of the blueberry supplement. at the end of the 2 month period the researcher again measures cognitive performance for each participant.

the results show an average increase in performance of MD= 7.4 with SS=1,215. does this result support the conclusion that the antioxidant supplement has a significant effect on cognitive performance? use a two tailed test with o=.05.

t distribution degrees of freedom=21

t-crtitical= ± _____

t= ________

the results indicate

*rejection of the null hypothesis, the antioxidant does not have a significant effect on cognitive performance

*failure to reject the null hypothesis, the antioxidant does not have a significant effect on cognitive performance

* failure to reject the null hypothesis, the antioxidant does have a significant effect on cognitive performance

*rejection of the null hypothesis, the antioxidant does have a significant effect on cognitive performance

construct a 5% confidence interval to estimate the average cognitive performant improvement for the population of older adults.

* 5.150-9.650

*5.150-7.400

*2.605-12.195

*7.400-12.195

## Repeated Measure Study

For which of the following situations would a repeated measures research design be appropriate?

* comparing verbal solving skills for science majors vs art measures

* comparing math skills for girls vs boys at age 10

* comparing pain tolerance with and without acupuncture needles ( i chose this one)

* comparing self esteem for students who participate in school athletics vs those who don’t.

A repeated measures study uses a a total of n=10 participants to compare 2 treatment conditions. how many scores are measured in this study, how many scores are actually used to compute the sample mean and sample variance?

* 20 measured and 20 used

* 10 measured and 10 used

* 10 measured and 20 used

* 20 measured and 10 used ( i chose this one)

The following data were obtained from a repeated measures study. What is the value of MS for these data?

Subject 1st 2nd

#1 10 15

#2 4 8

#3 7 5

#4 6 11

*3.5 ( i chose this one???)

*4

*3

* 4.5

The following data where obtained from a repeated measures study. what is the value of SS for the difference scores?

Subject 1st 2nd

#1 10 11

#2 4 6

#3 7 9

#4 6 5

*1 (this is the one i had chosen??)

*6

*4

*10

A repeated measures study using a sample of n=20 participants would produce a t statistic with df=_____.

* 20

* 39

*9

*19

A research study produces a t statistic with df=14. for this study which of the following designs would require a total of 30 participants?

* none of these choices

* an independent measures design ( i chose this one)

* a repeated measures design

* a matched subjects design

A repeated measures study and an independent measures study both produces a t statistic with a df=10. how many individuals participated in each study?

* 11 for repeated measures and 11 for independent ( i chose this one?)

* 11 for repeated and 12 for independent

* 12 for repeated and 12 for in independent

* 12 for repeated and 11 for independent

For the repeated measure t statistic , df=______.

* n1+n2-2

* (n1-1)+(n2-1)

* n1 +n2-1

*n-1 (this is the one i chose?)

Which of the following is the correct null hypothesis for a repeated measures t test?

* uD=0

*M1-M2

*MD=0

*u1=u2

If the null hypothesis is true, what value is expected on average for the repeated measures t statistic ?

* 1

*0 ( i chose this one)

*t>1.96

* 1.96

Solution Preview

For which of the following situations would a repeated measures research design be appropriate?

choose comparing pain tolerance with and without acupuncture needles ( i chose this one)

A repeated measures study uses a a total of n=10 participants to compare 2 treatment conditions. how many scores are measured in this choose 20 measured and 10 used

The following data …

## Step-by-Step One Way Analysis of Variance (ANOVA)

I have been working on this, Can anyone help me with this? In easy to understand terms?

ANOVA (One-Way Analysis of Variance)

1. A psychologist would like to investigate the relative effectiveness of three therapeutic techniques for treating mild phobias. A sample of 15 individuals who demonstrate a moderate fear of spiders are randomly assigned to each of the three therapies. The data given below represent a measure of reported fear of spiders after therapy (higher numbers imply more fear). Do the different therapies produce different results? Test at = 0.05.

Therapy A: 5 6 3 4 3

Therapy B: 3 3 0 2 2

Therapy C: 1 0 1 2 1

a. The name of this test is:

b. List 2 assumptions or special notes:

c. Hypothesis:

H0: _________________________ H1: _________________________

d. F-test value: ______________ d.f.: _________________

e. P-value: ______________

f. Conclusions: Reject or Retain H0 (circle one)

Summary Statement: ___________________________________________________

g. If one of the therapies is better than the others, which is it and why?

2. A researcher wishes to investigate if 3 different techniques lower a person’s systolic blood pressure (SBP). Subjects are randomly assigned to three groups: medication, exercise, and diet, and after four weeks, the reduction in each person’s SBP is recorded (and given below). Test the claim at = 0.05.

Medication: 10 12 9 15 13 8 8

Exercise: 6 8 3 0 2 4 4

Diet: 5 9 7 8 4 8 3

a. The name of this test is: ____________________________________________

b. List 2 assumptions or special notes:

c. Hypothesis:

H0: ______________________ H1: __________________________

d. F-test value: ______________ d.f. ___________________

e. P-value: ______________

f. Conclusions: → Reject or Retain H0 (circle one)

→ Summary Statement:

g. Which (if any) technique appears most effective in lowering SBP, and why?

h. Summarize the Homogeneity of Variance test:

— Hypothesis:

H0: _________________________ H1: _________________________

— Test Statistic: _________________________ — P-value: ___________

— Conclusion: Reject or Retain H0 (circle one)

Summary Statement:________________________________

j. Summarize the results of a Tukey Post Hoc test:

k. Calculate the effect size:

η2 = ___________________.