Research Statistics

1.  What is the estimated standard error for a sample of  n = 25 scores with SD = 60? (1 point)

2.  A sample of n = 36 scores has a mean of M = 40 and a variance of s² = 144.  What is the estimated standard error for the sample mean (consider the information here carefully, what about it is important and what is not)? (1 point)

3. A sample with a mean of M = 40 and a variance of s² = 44 has an estimated standard error of 2 points.  How many scores are in the sample?  (1 point)

4. Describe in words the steps to solve problem #3 (hint, this is just a backwards algebra problem).  (1 point)

5.  Describe the 2 characteristics that will produce the largest value for the estimated standard error? (2 points)

6.  If other factors are held constant, like the standard deviation and the sample mean and the population mean, and the level of alpha remains the same, what is the effect of decreasing the sample size in terms of rejecting or not rejecting the null hypothesis? (1 point)

7. If alpha remains the same, what is the effect of decreasing the sample variance in terms of rejecting or not rejecting the null hypothesis? (1 point)

8.   A researcher conducts a one sample t test using a sample from an unknown population.  If the t statistic has df = 42, how many individuals were in the sample? (1 point)

9.  With α = .05 and df = 8, the critical values for a two-tailed t test are t = ±2.306.  If all other factors are held constant and we increased to df = 35, what would happen, in general, to the critical values for t?  What would this mean for rejecting the null hypothesis?  If you are unsure how to answer this question, look at the actual T table in the back of your text and see what happens to critical values of t as the df increases.  (1 point)

10.  Two samples from the same population both have M = 74 and s² = 20.

One sample has n = 15 and the other has n = 25 scores.

Both samples are used to test a hypothesis that  μ = 80,  and to compute Cohen’s d.

How will the outcomes for the two samples compare regarding hypothesis testing and effect size?

Think about this CAREFULLY and refer to the formulas for both the T test and Cohen’s D. You don’t have to do a calculation—but it will probably help you if you do, to understand what the question is about, you just have to describe what will happen. (3 pts 1 point for each answer).

1. Regarding hypothesis test: outcome:

1. Regarding effect size: outcome:

1. Explain your logic.

11. A sample of n = 36 scores produces a t statistic of t = 4.00.  If the sample is used to measure

effect size with  η², what value will be obtained? (1 point)

12. Cohen’s D and η² are both measures of effect size.  Cohen’s D can be any value from 0 on up, that is 0 through infinity (theoretically).  η² can only be values between 0 and 1.  Explain why this is. (1 point).

13.  How does the confidence interval relate the sample mean and the standard error to the population mean?    Really think about this.   You may find it helpful to look at the formula for a confidence interval and think about the parts in the formula.  (1 point)

14.  If a researcher conducts a test and finds that the difference between two sample means is 4 points, with a 95% confidence interval of + or – 2 points, what does this mean about the location of the true population mean difference? (1 point)

15.  A researcher is testing the effect of a new cold and flu medication on mental alertness.  A sample of n = 9 college students gets a normal dose of the medicine.  Thirty minutes later, each student  plays a video game that requires careful attention and quick decision making.

The game scores for the sample of nine students are:  6, 6, 10, 6, 7, 13, 5, 5, 3.

The variance of the sample game scores is 16.

Game scores for students in the general, unmedicated population average μ = 10.

Does the medication have a significant effect on mental performance at the .05 level of significance?  (9 points total for this problem)

1. What is the standard error? (1 point)

1. Calculate T –show your work (3 point)

1. Assuming the critical value of T is + or -2.36, Do you reject the null hypothesis or not? (1 point)

1. Compute η², the percentage of variance explained by the treatment effect (1 point). .

1. Write a sentence about the outcome of the hypothesis test and effect size as it would appear in a research report (2 point). You may find it helpful to review your text to see how these statements are made.

Chapter 9.  Please, where asked, try to describe what you did clearly and fully.  28 points

1. Describe the grouping of participants in an independent measures study. (1 point)

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1. An independent-measures study uses two samples, each with n = 13, to compare two treatment conditions.  What is the df value for the t statistic for this study? (1 point)

1. A researcher reports t(24) = 5.30, p < .01 for an independent-measures experiment.  How many individuals participated in the entire experiment? (1 point)

1. A researcher reports an independent-measures t statistic with df = 40.  If the two samples are the same size (n₁ = n₂), then how many individuals are in each sample? (1 point)

1. Calculate and describe in words the steps for finding the pooled variance from the below information

(3 pts: 1 point for correct answer, 2 points for clear description).

Sample 1:  n = 10 and S² = 40          Sample 2:  n = 6 and S² = 50

1. Why do we need to find the pooled standard error? (2 points)

1. Describe in words the steps for finding the standard error from the information you were given in problem 5.  (2 points)

1. An independent-measures study with n = 3 in each sample, produces a sample mean difference of 3 points and a pooled variance of 27.  What is the value for the calculated  t statistic? (2 points)

1. Two samples, each with n = 12 scores, produce an independent-measures t statistic of  t = 3.00.  If the effect size is measured using r², what is the value of  η²?   (2 points)

1. For an independent-measures t statistic, what is the effect of decreasing the number of scores in the samples on the critical value of T? (1 point)

1. Which combination of factors  in sample size and variance size is most likely to produce a significant value for an independent-measures t statistic? (1 point)

1. Why does changing the degrees of freedom influence the critical value of T (hint, look at the T distribution graphs in your book or slides). (2 points)

1. A researcher conducts an independent-measures study on how serotonin is related to aggression.  He believes that serotonin will increase aggression.

One sample of rats is a control group and gets a placebo that does not affect serotonin.

A second sample of rats gets a drug that lowers serotonin.

Then the researcher records the number of aggressive responses each of the rats displays.

Here are the data (9 pts total  this problem)

Control         Low Serotonin

n rats = 10              n rats = 11

Mean aggressive Mean aggressive

displays  = 14   displays = 19

S² = 10             S² = 14

1. What are the null and alternate hypotheses? (1 point)

1. What is the pooled variance? (2 point)

1. What is the pooled standard error?  (2 point)

1. What value of T do you get for your calculation? (2 points)

1. If the critical T for a two tailed alpha at .05, is + or – 2.069, can you reject the null hypothesis? (1 point)

1. Compute Cohen’s D to measure the size of the treatment effect. (1 point)

In the literature (14 points total this section)

T tests are often used in the published literature, and will be described like the below results section from Dhir, Chen and Nieminin, 2015.  Please read the results section and answer the questions.

Independent samples t-tests were utilized to examine the demographic differences between Internet addicts and non-addicts. They revealed that Internet addicts tend to experience higher parental control of Internet use (t = 2.57, p < .01, M (SD) = 2.77 (1.23) compared to non-addicts (M (SD) = 2.46 (.99)). Similarly, Internet addicts have lower academic performance (t = 3.82, p < .01, M (SD) = 2.93 (.75)) than non-addicts (M (SD) = 3.20 (.71). No significant differences between addicts and non-addicts were found in terms of age, monthly family income, or CAP.

1. In the above paragraph, what, exactly, does p<.01 mean?   (3 points)

1. What are the mean and the standard deviation for academic performance among internet addicts? (2 points)

T tests are often presented in tables, as in the below table from Davis et al. (2015).  Look at the table and answer the questions below.  All the information is IN the table.  You don’t need to calculate anything.

1. What is the t for the difference between Mirrors and IS on the measure of WBI work habits? (2 points)

t= 1.90

1. What is the total sample size for this study? (1 point)

Total sample size for this study is 31.

1. Are the two groups significantly different on that measure? What is the p value and what does that value mean, in words?  (3 points)

1. Quite a number of T values are non significant, but still have rather notable effect sizes of ½ a standard deviation or more difference between the two groups.  Why do you think the finding might be non significant, though the effect size seems meaningful? (3 points)