Activity 5-3

Use statistical software to find the lower and upper bounds for the 95% CI around the effect size (d).

-.11, 1.09

Compute the lower and upper bounds for the 95% CI around the mean difference.

-.16, 1.32

Assuming the null hypothesis is true and that there are no methodological flaws in the study, how likely is it that the observed difference is due to sampling error? You should be able to provide a numerical value.

.11

For this study, what is the two-tailed probability that you would obtain a t greater than 1.74 or less than -1.74, assuming the null hypothesis is true?

.11

Compute an effect size (d).

.50

What was the observed mean difference?

.58

Compute the test statistic in the following steps or use statistical software to find these values.

1.74

All of the necessary assumptions are met by this study. Match each of the statistical assumptions to the fact that implies the assumption was met. It is unlikely that the sample and population standard deviations will be dramatically different. The IV identifies how the sample is distinct from the population and the DV is measured on an interval ratio scale. The population of driving/phone confidence scores has a normal shape. The driving/phone confidence scores of each participant were collected carefully, one person's scores did not affect anyone else's scores.

B. Homogeneity of variance D. Appropriate measurement of the IV and DV C. Normality A. Independence

Fill in the blanks with the appropriate numbers from the statistical analyses you ran. We computed a single sample t and d to compare participants' ratings of their driving ability while using the phone (M = [a], SD = [b]) to 4 (the value reflecting average confidence), t ([c]) = [d], p = [e] , 95% CI ([f],[g]), (two-tailed), d = [h], ([i]).

Fill in the blanks with the appropriate numbers from the statistical analyses you ran. We computed a single sample t and d to compare participants' ratings of their driving ability while using the phone (M = 4.58, SD = 1.16) to 4 (the value reflecting average confidence), t (11) = 1.74, p = .11 , 95% CI (-.16,1.32), (two-tailed), d = .50, (-.11, 1.09).

Consider the existing scientific literature (to the degree you are able). Are the statistical results consistent with those reported in the scientific literature?

I don't know, there is not enough information in this activity to make this judgment.

Consider the methodological rigor of this study. Which of the following, if it occurred, would suggest the study has methodological problems that would lessen the strength of the statistical evidence?

If several of the participants in the study did not fluently speak/read the language in which the questionnaire was printed and consequently they did not understand the questions they were answering.

If you were to replicate this study with a larger sample, what do you think would happen to the SEM?

It would decrease

Consider the p value. Do you find the evidence against the null to be compelling?

No, the p value is too high to provide compelling evidence against the null hypothesis so I should withhold judgment at this time.

Write a scientific conclusion that includes a discussion of all four pillars of scientific reasoning. The summary should start with the following statement. Note that the numbers are omitted because they would tell the answer to many of the previous questions. We computed a single sample t test to compare the sample's mean driving confidence (M = xx SD = xx to the midpoint of a driving confidence scale with was 4, t (xx) = xx, p = .xx, 95% CI [xx, xx], d = xx, [xx, xx].

People's estimates were .58 higher than the scale midpoint. The t test offered only weak evidence against the null hypothesis. However, the effect size was medium suggesting the observed effect may have practical importance. Given the conflicting results from the p value and effect size this study should be redone with a larger sample size doing so may provide results on which scientific conclusions could be drawn. These results can not support any scientific conclusion, we must withhold judgment on the question of this population being over confidence in their driving ability. The study's methodology seemed sound so using the same methods in a large study would be a good idea. No previous research has been done on this specific population of drivers.

Why would you want the SEM to decrease?

The SEM is a measure of sampling error and we want our samples to be good estimates of the population.

Select the two-tailed null hypothesis.

The average rating will be equal to 4.

What information does the effect size provide that p does not?

The effect size tells you if the results are likely to have practical implications.

Consider the confidence intervals. Do the confidence intervals suggest that the estimates are fairly precise or very rough estimates of the population parameters?

Very rough, the effect size CI suggests that the true effect may be between a very small negative effect to very large positive effect.

Sketch a graph of a t distribution with the obtained t value labeled. This is a two tailed test, so be sure to put the positive and negative t on the graph. Were you able to draw this graph?

Yes

Do you think that the effect is sufficiently large to have practical importance? Explain your reasoning.

Yes, the effect size is moderate and may have practical importance.

Consider the effect size. Does the effect size suggest that the observed effect will have practical importance?

Yes, the observed effect is medium, large enough to have practical importance; given that the p value provided only weak evidence against the null hypothesis, though, this study should probably be redone before drawing any conclusion.

A student wonders if people are overly optimistic when judging their ability to drive safely while using a phone. To test this, the student recruits 12 drivers and asks them to rate their driving ability using three different questions, such as: My ability to drive while talking on the phone is: 1 2 3 4 5 6 7 Below average Average Above average The answers to the questions were averaged to create a single number for each participant. Previous research indicates that scores on the scale are normally distributed. The average scores for each participant were: 4, 3, 4, 5, 4, 5, 3, 5, 6, 5, 7, 4. If people are unbiased in their reports, the mean should be 4 (the midpoint on the scale). The reason being, some individuals are certainly above average and others are certainly below average but, as a whole, a group of people should be average. However, if a sample of people exhibit the above average effect, their mean would be higher than four, the scale score representing "average". Use a two-tailed test to determine the probability that the mean difference between the sample mean (M = 4.58, SD = 1.17) and the scale's midpont (4) occurred due to sampling error. Next, find and interpret the effect size. And, finally, construct an appropriate scientific conclusion. Why should you use a two-tailed hypothesis test for this research scenario?

You recognize both over confidence and under confidence are interesting results with important implications for the drivers.

A point and whisker plot of the data is provided below. Is the mean response above or below 4?

above

Describe the size of the effect as small, small-medium, medium, medium-large, or large.

medium

If the sample used in the study represented the population well the population mean difference and population d is probably close to the

middle of the appropriate CI.

Based on the results of the single sample t test (and assuming there are no methodological flaws in the study), there is ___________ evidence that the population of drivers exhibit the above average effect with respect to their ability to drive while using the phone.

only weak