Stats Test #3

When a sample size is relatively small (e.g., n = 15), how does the shape of the t distribution compare to the normal distribution?

It is symmetrical but more spread out than the normal distribution.

One of the major concern of repeated-measure study design is that the first assessment (i.e., pre-test) may influence participants' performance on the second assessment (i.e., post-test). What is this problem called?

Order effect.

For a dependent samples t-test, what is the t critical for α = .05 2 tails test conducted on a sample of n = 15 participants?

t = ±2.145

For which of the following research problems would t-test for related samples be appropriate?

Comparing a patients' back pain before and after 6 weeks of physical therapy. Comparing anxiety level of clients before and after therapy session.

For which of the following research problems would a t-test for a single sample be appropriate?

Comparing a mean age of a sample of Texans to the mean age of entire population of Texans.

For which of the following research problems would a t-test for 2 independent samples be appropriate?

Comparing an average blood pressure of adults on a low sodium diet to a control sample of adults on a regular diet. Comparing an average approval ratings of a presidential candidate in a sample of rural voters to average ratings in a sample of urban voters.

In a repeated-measures study conducted with a sample of n = 16 participants, the difference scores have a mean of MD = 3.25 and the standard deviation, s = 7. What is the estimated standard error sMD in this study?

1.75

The results of a hypothesis test with the t-test for a single sample are reported as follows: t(32) = 2.83 p < .05, two-tails test. Based on this report, how many individuals were in the sample?

33

A t-test for independent samples computed by a researcher on the data from his experiment about the effect of distraction on memory is reported as t(30) = 2.0 p < .05 1 tail test. Based on this information, what is the effect size evaluated by r2 in this study? (Note: the numerical answers are rounded to 2 decimal places.)

r2 = 4/34 = 0.12

If a researcher wants to test hypothesis using p < 0.01 1-tail test, what are the critical t values for a single sample t-test computed on a sample of n = 30 participants?

t = ±2.462

If a researcher wants to test hypothesis using p < 0.05 2-tails test, what are the critical t values for a single sample t-test computed on a sample of n = 25 participants?

t =±2.064

Which of the following is the correct reporting format of a single sample t-test conducted on a sample n = 40 with Cohen's d effect size, according to APA style?

t(39) = 2.28 , p < .05 1-tail test, estimated Cohen's d = 0.25,

A researcher reports t(26) = -2.36, p < .05 2-tails test for the outcome of a repeated-measures t-test. How many individuals participated in the study?

n = 27

In a t-test for a single sample, which of the following will increase chances of rejecting a null hypothesis H0 (i.e., will result in a computed t that has a better chance to fall into a rejection area)?

a large difference between a sample mean and a population mean. a small estimated standard error.

What is the mean difference MD for the following data from a repeated-measures study? Participant Before Training AfterTraining #1 10 12 #2 7 8 #3 5 4 #4 6 10 #5 2 6

MD = 2.0

A researcher used a repeated-measures experiment to examine the effectiveness of motivational workshop on work productivity. The data collected in a sample of n = 25 employees produced the dependent sample t-test, t (24) = 2.29. Which of the following is the correct decisions regarding the null hypothesis, H0 for the 2-tails tests based on this outcome?

Reject H0 with p < .05 but fail to reject with p < .01.

A single sample t-test conducted on a sample of n = 29 participants produces a t statistic of t = 2.87. For a two-tails test, what is the correct decision about the outcome of the test?

The researcher can reject the null hypothesis with both, α = .05 and α = .01.

A researcher tested the effectiveness of new medication on a sample of n = 24 patients. What is the outcome of the study, if the computed t-test for a single sample is t = 2.02 and the researcher uses p < 0.05, 1-tail test for hypothesis testing?

The researcher should reject the null hypothesis and conclude that the new medication is effective.

A team of physical therapists conducted a repeated measure study to examine effectiveness of hydrotherapy on reducing knee pain. The experiment was conducted on a sample of n=15 patients suffering from a chronic knee pain. All participants rated their knee pain before and after receiving a hydrotherapy. If the researchers plans to use a t-test for dependent samples with p < .05 1-tails test to analyze the data collected in the study, which of the following is the correct alternative hypothesis, H1?

There is a significant reduction of chronic knee pain after hydrotherapy.

Which of the following is the correct null hypothesis for an independent samples t-test (assume 2-tails test)?

There is no significant difference between populations represented by two samples (i.e., μ1 = μ2).

A researcher wants to examine the effect of new medication on mental alertness. A sample of n = 16 college students is selected to the study. Each participant is given a normal dose of the medicine and thirty minutes later, each student's alertness is measured on a video game that requires careful attention and quick decision making. The results show that the sample mean alertness score is M = 84 with the standard deviation s = 15. Assuming that in a college student population the mean alertness score is µ = 75, are the data sufficient to conclude that the new medication has a significant effect on mental alertness?

H0: Fail to reject H0 H1: There is a significant effect, µ ≠ 75 Computed estimated standard error SM= 3.75 Computed t= 2.4 Degrees of freedom, df= 15 Critical t-value= 2.947 Decision: Reject the null H0 Estimated Cohen's d= NA Conclusion: There is no significant effect of new medication on mental alertness, t(15) = 2.4, p > .01, 2-tails test.

A clinical psychologist wanted to examine effect of relaxing music on anxiety. She selected two samples of patients and randomly assigned them to one of two conditions (i.e No Music or Relaxing Music). One sample was asked to complete the anxiety test in a quiet room (i.e., without music) and the second sample completed the same anxiety test while relaxing music was playing in the room. The partially computed data collected in the study are shown below: No Music: Relaxing Music: n1 = 10 n2 = 8 M1 = 43 M2 = 38 SS1 = 105 SS2 = 95 Based on these results, is there a significant effect of relaxing on anxiety? Use a t-test for independent samples with p < .05, 2-tails to answer this research question.

H0: Reject the null H1: µ1 ≠ µ2 Computed pooled variance = 12.5 Estimated standard = 1.68 Computed t statistic = 2.98 Critical t-value = 2.12 Decision: fail to reject the null hypothesis Cohen's d: d = 1.41 Conclusion: There was a significantly lower anxiety after listening to relaxing music compare to no music , t(16) = 2.98, p < .05, 2-tails test, the estimated Cohen's d= 1.41.

A researcher would like to determine if art therapy is effective in increasing well-being of nursing home residents. A sample of n = 25 nursing home residents was asked to rate their well-being before and after an art therapy session. The data showed that the average change in participants' well-being was MD = 5.9 with the standard deviation of D scores s = 14. Are the data sufficient to conclude that there is a significant effect of art therapy on well-being of nursing home residents? Use the repeated-measures t-test with α = .05 2-tails to answer this question.

H0: μD=0 H1= μD≠0 Estimated standard error: SM= 14/√25 = 2.8 Computed t statistic: t=5.9/2.8 = 2.11 df= 24 Critical t-value: -2.064, 2.064 Decision: Reject the null hypothesis Estimated Cohen's d: d=5.9/14= 0.42 Conclusion: There is a significant increase effect of art therapy on well-being, t(24)= 2.064, p<.05 2-tails, estimated Cohen's d= 2.8

A team of physical therapists conducted a repeated measure study to examine effectiveness of hydrotherapy on reducing knee pain. The experiment was conducted on a sample of n=15 patients suffering from a chronic knee pain. All participants rated their knee pain before and after receiving a hydrotherapy. If the researchers plans to use a t-test for dependent samples with p < .01 2-tails test to analyze the data collected in the study, which of the following is the correct null hypothesis, H0?

There is no significant effect of hydrotherapy on chronic knee pain.

The estimated standard error in the denominator of the dependent samples t statistic measures how much difference, in average, could be expected between pre- and post measurement by chance (i.e., if a sample is just measured twice without any treatment between the two measurements).

True