Introductory Statistics For The Behavioral Sciences 7th Edition Joan Welkowitz, Barry H. Cohen, R. Brooke Lea - Solutions

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Convert each of the following statistically significant values of t, obtained from the t test for the difference between two independent means, to rpb.
A good many statistical functions can be performed in Excel. As a first step, use the Sum function to add up the scores for each of the quantitative variables in the Excel file of Ihno's data.
Why would it be a bad idea to create a grouped frequency distribution for the Doty Hall data from Chapter 1?
Repeat Exercise 1 for the variables Math Courses and Math Phobia. Would it make sense to request a histogram instead of a bar chart for Math Phobia? Discuss.
Why is it not necessary to know the exact number of cases in the population being studied in order to use the procedures described in this chapter?
The area below a z score of 3.1.Use your statistical package to find the indicated areas under the normal curve (your answer should include six digits past the decimal point):
The area above a z score of 3.3.Use your statistical package to find the indicated areas under the normal curve (your answer should include six digits past the decimal point):
The area below a z score of −3.7.Use your statistical package to find the indicated areas under the normal curve (your answer should include six digits past the decimal point):
The area between the mean and a z score of .542.Use your statistical package to find the indicated areas under the normal curve (your answer should include six digits past the decimal point):
The area between the mean and a z score of −1.125.Use your statistical package to find the indicated areas under the normal curve (your answer should include six digits past the decimal point):
Use your statistical package to compute the Pearson r between gender and baseline anxiety for Ihno's students; calculate the t value for testing r, using Formula 10.7, and compare it to the t value you obtained for Computer Exercise 1 of Chapter 7.
Suppose that Ihno is planning to compare the men with the women in her class. Use the noncentral t distribution function in your statistical package to answer the following questions. Assume that alpha is .05 and that each test is two-tailed.a. Use the t value you computed for the gender difference
the results of a one-way ANOVA are statistically significant, why is it desirable to compute a measure of effect size?
4.a. Use the Kruskal-Wallis procedure to test whether the different quiz conditions (last question easy, moderate, difficult, or impossible) had a significant effect on postquiz anxiety scores. Regardless of the significance of your test, perform all of the possible pairwise comparisons as rank-sum
In this exercise you will be testing the (two-valued) grouping variable you created from a median split of the phobia scores for the computer exercises in Chapter 14. Perform a binomial test for P = .5 separately for each gender. Explain the relationship between the tests of the two genders.
Read Ihno's data into your statistical software package. For those not using the Statistical Package for the Social Sciences (SPSS), we have provided the data in two convenient formats: a tab-delimited text file and an Excel spreadsheet (Microsoft Office 2007). For the convenience of SPSS users, we
Repeat Exercise 1 for baseline heart rate (compare to Chapter 7, Computer Exercise 2). How can you interpret the sign of the correlation for this and the previous exercise?Data from exercise 1Use your statistical package to perform a linear regression predicting the statistics quiz score from the
In Exercise 7 of the regular (not Computer) exercises in the previous chapter, you were asked to calculate the Wilcoxon matched-pairs test to determine whether a training method improved exam scores for 12 poorly performing students. For this exercise, compute the Spearman correlation between the
Perform a matched-pairs t test to determine whether there is a significant increase in heart rate from baseline to the prequiz measurement. Also, test the difference between the pre- and postquiz measurements. (Advanced exercise: Repeat these paired t tests separately for men and women.)
Use your statistical package to find the mode for each of the categorical (i.e., qualitative variables) in Ihno's data set.
Request the following percentiles for the variables Baseline Heart Rate and Prequiz Heart Rate for all students: 15, 30, 42.5, 81, and 96.
Create a grouping variable that equals 1 if a student has taken no more than one college math course prior to registering for statistics and 2 if the student has taken two or more math courses. Test whether taking more than one prior math course is independent of a student's major. Request a
Conduct a two-way chi-square analysis of Ihno's data to test the null hypothesis that the (two-valued) grouping variable you previously created from a median split of the phobia scores is independent of gender. Request the phi coefficient for this relationship. Use your software to compute the
(a) When using chi square for a two-variable problem, why is it desirable to compute either the ϕ or Cramér's ϕ when statistically significant results are obtained?(b) When should each of the coefficients in part (a) be used?
Conduct a two-way chi-square analysis of Ihno's data to test the null hypothesis that the proportion of females is the same for each of the five represented majors in the entire university population. Request a statistic to describe the strength of the relationship between gender and major.
Suppose that the same researcher asks the 139 students to vote yes or no as to whether they like each of the three types of television shows and obtains the following results: for sitcoms, 92 yes and 47 no; for sports, 61 yes and 78 no; for reality shows, 74 yes and 65 no. What type of chi square
Suppose that Ihno obtains registration information from her university and finds that the numbers of undergraduates who have declared each of the five majors are as follows: psychology, 400; pre-med, 310; biology, 270; sociology, 140; economics, 240. Can you reject the null hypothesis that Ihno's
The same researcher wants to test the relationship between gender differences and preference for the three television shows. For the data in Question 1, she finds the following: Of the 57 students who prefer sitcoms, 29 are female and 28 are male. Of the 44 who prefer sports, 9 are female and 35
a. Perform a one-way chi-square test to determine whether you can reject the null hypothesis that, at Ihno's university, there are the same number of students majoring in each of the five areas represented in Ihno's class, if you assume that her students represent a random sample with respect to
A researcher wants to test the null hypothesis that three types of television programming are preferred equally by college students. She obtains a sample of 139 college students and finds that 57 prefer sitcoms, 44 prefer sports, and 38 prefer reality shows. What statistical procedure should be
At a small rural college, incoming students are arranged into 320 pairs by the administration based on their high school credentials. (The students do not know this). One member of each pair is chosen randomly to participate in an enriched orientation program. At the end of the first semester, it
Repeat Exercise 5 for the baseline and prequiz anxiety scores. (If your software does not have the sign test, repeat Exercise 4 for the anxiety variable.)Data from exercise 5If your software has the capability, request a sign test of the baseline versus the prequiz heart rates, and compare the
If your software has the capability, request a sign test of the baseline versus the prequiz heart rates, and compare the results to those from the binomial test in the previous exercise.
If you have not already done this for a previous exercise, create a variable that is the difference between baseline and prequiz heart rate. Then recode this new variable so that negative difference scores are assigned a numeric score of 1, positive difference scores are assigned a score of 2, and
A researcher wishes to determine if a particular form of psychotherapy will improve the mental health of patients who suffer from depression. If the researcher cannot obtain a quantitative measure of mental health but can conclude whether it has improved, stayed the same, or become worse for each
When should the normal distribution be used as an approximation to the binomial distribution?
Redo the binomial test on gender (with P = .5, only) separately for each college major.
You want to determine if a coin is biased in favor of falling heads up or tails up.(a) You flip the coin three times and obtain three heads. What should you decide?(b) Why is the informal experiment in part (a) badly designed?(c) Which error is more likely to result from the experiment in part (a),
For Ihno's data, perform a binomial test on the gender variable, with P = .5. Can you reject the null hypothesis that Ihno's statistics class is a random sample from a population in which both genders are equally represented? Use the binomial test to compare the proportion of women in the class
Give an example of a psychological research study where the variables can be expressed only as categories, and not in any quantitative way.
Redo Exercise 4 using heart rate as the dependent variable instead of anxiety.Data from exercise 4Add the experimental factor (i.e., difficulty of the 11th quiz question) to the analysis in Exercise 1, and compute the mixed-design ANOVA. Request a plot of the cell means, and explain your ANOVA
Add the experimental factor (i.e., difficulty of the 11th quiz question) to the analysis in Exercise 1, and compute the mixed-design ANOVA. Request a plot of the cell means, and explain your ANOVA results in terms of the pattern in your graph. Follow the mixed-design ANOVA with separate one-way
Add gender to the analysis in Exercise 1, and compute the mixed-design ANOVA. Request a plot of the cell means, and explain your ANOVA results in terms of the pattern in your graph. Regardless of whether the interaction is significant, follow the mixed-design ANOVA with separate one-way RM ANOVAs
Give an example for which each of the following is appropriate:(a) Repeated-measures ANOVA.(b) The randomized blocks design.(c) The two-way mixed design.(d) The before-and-after form of the two way mixed design.(e) One-way repeated-measures design with counterbalancing.
Redo Exercise 1 for heart rate.Data from exercise 1Perform an RM ANOVA to test for a significant change in anxiety level in all subjects over time (baseline, prequiz, and postquiz). Regardless of whether or not the ANOVA is significant, follow it with matched t tests (or two-level RM ANOVAs) for
What is the sphericity assumption in behavioral science research? Give an example of when it might be violated.
Perform an RM ANOVA to test for a significant change in anxiety level in all subjects over time (baseline, prequiz, and postquiz). Regardless of whether or not the ANOVA is significant, follow it with matched t tests (or two-level RM ANOVAs) for each pair of levels of the time factor.
(a) What advantage does repeated-measures ANOVA have over ANOVA without repeated measures (where every score is derived from a different participant)?(b) Why might a researcher decide not to use repeated-measures ANOVA in spite of this advantage, and what alternatives would be considered?
(a) What is a simple main effect?(b) When should a researcher test simple main effects, and what procedure should the researcher use?
Give an example of how a large interaction in a two-way ANOVA could cause the main effects to be misleading.
Redo the two-way ANOVA in Exercise 3 using postquiz anxiety as your dependent variable.a. Request a graph of the cell means, and refer to the graph to explain the results of the two-way ANOVA.b. Regardless of your ANOVA results, test the simple main effect of quiz condition for each phobic group,
Create a grouping variable based on an approximate “median split” of the phobia scores so that one group contains the students with the 55 lowest phobia scores, and the other has the 45 highest phobia scores. Then perform a two-way ANOVA on postquiz heart rate, using the new phobia grouping
A researcher conducts a two-way ANOVA. One factor is sex: male or female. The other factor is drug level: whether participants receive a pill designed to treat obsessive-compulsive disorder or a placebo that looks and tastes the same but contains no medicine. Describe some of the interactions that
Redo Exercise 1, replacing the college-major factor with the grouping variable you created in Computer Exercise 3 of Chapter 12 (from the number of math courses taken).Data from exercise 1Using college major and sex as your independent variables, perform a two-way ANOVA on the math background quiz.
Complete the following table by stating what sums of squares, mean squares, and F tests are computed in both one-way ANOVA and two-way ANOVA, and what sums of squares, mean squares, and F tests are computed in a two-way ANOVA but not in a one-way ANOVA. Computed in both one-way and
Using college major and sex as your independent variables, perform a two-way ANOVA on the math background quiz. Request descriptive statistics. Use the cell means to explain your results. (Advanced exercise: Redo the two-way ANOVA without the psychology majors.)
(a) What is a factorial design?(b) What is the difference in purpose between a two-way ANOVA and a oneway ANOVA?
Give an example of when the Bonferroni correction should be used.
(a) What is the difference between post hoc comparisons and a priori comparisons?(b) What advantage results from using a priori comparisons?
What are the advantages of using the Fisher-Hayter modified LSD test? When should this test be used?
Redo the one-way ANOVAs requested in Computer Exercise 3 of the previous chapter, selecting LSD as your MCP. Also, use your statistical software to perform ordinary t tests for each pair of math groups for each dependent variable. Explain the differences between the LSD test and ordinary t tests as
(a) When should you use Tukey's HSD test rather than Fisher's protected t tests?(b) When should you use Fisher's protected t tests rather than Tukey's HSD test?
Redo the one-way ANOVAs requested in Computer Exercise 2 of the previous chapter, selecting both Tukey and Bonferroni from the list of post hoc tests in each case. What is the problem with using HSD to make comparisons between groups in this exercise? Use the results for this exercise to compare
If a multiple comparisons procedure involves the use of t tests, why is it that a researcher cannot skip the ANOVA and just do these t tests?
Redo the one-way ANOVAs requested in Computer Exercise 1 of the previous chapter, selecting both LSD and Tukey from the list of post hoc tests in each case. For postquiz anxiety, which pairs of quiz conditions (last question easy, moderate, difficult, or impossible) differ significantly from each
An F test from an ANOVA using five samples is statistically significant. The researcher now wishes to determine which pairs of the five population means differ significantly from each other. Why are multiple comparisons procedures necessary rather than just performing all of the possible t tests?
Repeat Exercise 2 using the Kruskal-Wallis H test, and compare these results to the corresponding ANOVA results.Data from exercise 2Using the means and standard deviations you have already calculated for the data from the four dormitories (i.e., Turck, Dirk, Dupre, and Doty Halls), perform an
Give an example of when the Kruskal-Wallis H test should be used instead of an ordinary one-way ANOVA.
Create a grouping variable from the number of math courses taken (Group 1 = none; Group 2 = one or two; Group 3 = three or more), and perform one-way ANOVAs on both the math background quiz and the statistics quiz. In each case, explain your results in terms of the means of the three groups.
Using college major as the independent variable, perform one-way ANOVAs to test for significant differences in both the math background quiz and the statistics quiz. Request descriptive statistics and a homogeneity of variance (HOV) test. Use the sample means to explain the results of each ANOVA.
If there are only two groups (i.e., the researcher wishes to test the hypothesis that the means of two populations are different), will a one way ANOVA yield the same results as the t test for two independent sample means? Explain.
Perform one-way ANOVAs to test whether the different quiz conditions (last question is easy, moderate, difficult, or impossible) had a significant effect on postquiz anxiety and postquiz heart rate. Request descriptive statistics and draw a graph of the sample means, with the levels of the
A researcher wishes to test the hypothesis that the means of five populations are different. Why would it be a bad idea to test the researcher's hypothesis by computing 10 separate t tests (first test population 1 versus population 2, then test population 1 versus population 3, then test population
In the following table, decide which of the numbered statements belongs in each box: 1. You are studying an effect that is likely to be quite large. 2. Caution is indicated because you are studying an effect that may be quite small. 3. Power is likely to be so low, and the probability of a Type
A researcher argues as follows: “I performed a correlational study with a very large sample. Because my sample was so large, I obtained a correlation of r = .07 that was statistically significant. But this correlation is too small to be of any practical value, as there is very little (linear)
Solve this problem using the same methods and assumptions that you used for Exercise 1.a. Use the t value you computed to compare the students in the “impossible to solve” condition with those in the “easy to solve” condition in terms of postquiz heart rates (see Computer Exercise 3 of
“Using the .05 criterion of significance, the probability of a Type I error is .05. Using the .001 criterion of significance, the probability of a Type I error is .001 (much smaller). Therefore, researchers should always use the .001 criterion of significance.” Use the concept of statistical
What is the power of a statistical test? Why is it important when planning a research study?
Create a new variable whose value is 1 for psychology majors and 2 for all other majors. Compute Pearson's r between this new variable and the math background quiz score. Interpret both the sign and the magnitude of this correlation.
When using the Pearson r correlation coefficient (and virtually all other statistical procedures), it is important to pay attention to the sign of a coefficient (plus or minus). Why, then, do we ignore the sign when interpreting a point-biserial correlation coefficient?
(a) How do the variables in a research study that uses the ordinary Pearson r correlation coefficient differ from the variables in a study that uses the point-biserial correlation coefficient?(b) Is the procedure for computing a point-biserial correlation coefficient different from the procedure
Explain why each of the following statements is true:(a) The data from any research study that uses the t test for the difference between two independent sample means can also be analyzed by computing a point-biserial correlation coefficient.(b) Any researcher using the t test for the difference
Perform a linear regression to predict the statistics quiz score from the student's self-reported math phobia level, and write out the raw-score regression formula. Use a scatter plot to help you interpret this result. Repeat the linear regression and scatter plot using math phobia to predict
When using linear regression, does the researcher want the standard error of estimate to be small or large? Why?(a) If the standard error of estimate is large, what does this imply about the variability of scores on Y for any given value of X? Why does this make predicting scores on Y from scores
Use your statistical package to perform a linear regression predicting the statistics quiz score from the math background quiz score. Write out the formula for the raw-score regression line. What statistics quiz score would be predicted for a student who obtained a score of 20 on the math
In a research study using a sample of 30 participants, the Pearson r correlation between X and Y is .09 and is not statistically significant. Should linear regression be used to predict scores on Y given scores on X? Why or why not?
Describe three situations in which you would consider using Spearman correlation instead of Pearson correlation.
(a) What is the difference between the reliability of a measure and the validity of a measure?(b) What is the difference between test-retest reliability and split-half reliability?(c) What is criterion validity?
(a) Separately for male and female students, compute the Spearman correlation coefficient between the baseline and the prequiz heart rates. How do these results relate to those you obtained in part (b) of the first exercise? How do the corresponding p values compare?(b) Compute the Spearman
Using a very large sample of participants, a statistically significant Pearson r correlation of .11 is obtained between X and Y. Does this mean that there is a strong relationship between X and Y? Why or why not?
The SAT is used to predict the success of high school students in college. Suppose that the Pearson r correlation between scores on the SAT and grades at University Z during the freshman year, based on a sample of 500 participants, is + .53. A student complains that a friend of hers did poorly on
Use your statistical package to create a scatter plot of the relation between the math background quiz score and the statistics quiz score for the 85 students who have both scores. Describe the pattern that you see. If possible, use your statistical package to add a linear regression line to the
In a research study using a sample of 30 participants, the Pearson r correlation between X and Y is .09 and is not statistically significant. Should the researcher conclude that there is little or no relationship between X and Y? Why or why not?
Create two new variables: prequiz heart rate minus baseline heart rate and prequiz anxiety minus baseline anxiety. Compute Pearson's r between these two difference scores, and interpret the meaning of this correlation.
In a correlational study, X is the number of hours of violent television programs that participants watch, and Y is the number of violent acts committed by the participants in real life. Suppose that there is a moderately high correlation (say, .48) between X and Y for a sample of 100 American
Compute the Pearson r between baseline heart rate and baseline anxiety for all students; also, find the Pearson r between prequiz heart rate and prequiz anxiety measurements.
A student obtains scores of 72 on Test X and 72 on Test Y. The student therefore concludes that there is a high correlation between Test X and Test Y. Why is this conclusion incorrect?
(a) Use your statistical package to compute the Pearson r between baseline and prequiz heart rates for all students; also, find the Pearson r between the pre- and postquiz heart rate measurements.(b) Recalculate these two r's separately for men and women.
For each of the following, state whether you would expect the Pearson r correlation between X and Y to be positive, zero, or negative. Assume that each correlation is based on a sample of 50 participants who have scores on both X and Y.(a) X = grades in a high school advanced placement psychology
(a) Separately for male and female students, perform the Wilcoxon test to determine whether there is a significant increase in heart rate from baseline to the prequiz measurement. Also, test the difference between the pre- and postquiz measurements. Compare your results to those you obtained in

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Introductory Statistics For The Behavioral Sciences 7th Edition Joan Welkowitz, Barry H. Cohen, R. Brooke Lea - Solutions

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