1 Million+ Step-by-step solutions

Distinguish between descriptive and inferential statistics.

What is the difference between data and a raw score?

Describing the scales of measurement. Landry (2015) stated, “[Scaled] data can be validly treated as interval”. Explain why data on a rating scale are often treated as interval scale data in the behavioral sciences.

Below is the number of times a commercial was shown displaying high fat, high sugar foods during children’s programming over each of 20 days.

21, 8, 11, 9, 12, 10, 10, 5, 9, 18, 17, 3, 6, 14, 18, 16, 19, 3, 22, 7

1. Create a simple frequency distribution for these grouped data with four intervals.

2. Which interval had the largest frequency?

Using the data given in Question 31, what is the percentile point for the 50th percentile for the college readiness assessment data in a population-based study with college students?

**Data From Problem 31**

Women serving in the armed forces. In February 2016, a CNN poll asked a sample of 1,001 adults nationwide if they think women in the armed services should get combat assignments on the same terms as men (reported at http://www.pollingreport.com). The opinions of adults nationwide were as follows: 36%, on the same terms as men; 51%, only if they want to; 12%, never; and 1%, unsure.

1. What type of distribution is this?

2. Is this a summary for grouped or ungrouped data? Explain.

Perceptions of same-sex marriage. In June 2016, a CBS News poll asked a sample of adults worldwide whether it should be legal or not legal for same-sex couples to marry (reported at http://www.pollingreport.com). The opinions of adults worldwide were as follows: 58%, legal; 33%, not legal; and 9%, unsure/no answer.

1. What type of distribution is this?

2. Knowing that 1,280 adults were polled nationwide, how many Americans polled felt that same-sex couples should be allowed to legally marry?

Which type of central tendency is always located at the center or in the middle of a distribution?

Based on the scale of measurement for each variable listed below, which measure of central tendency is most appropriate for describing the data?

1. The distance in miles that a group of athletes run to train for a marathon

2. The rankings of college undergraduate academic programs

3. The blood type (e.g., Type A, B, AB, O) of a group of participants

The convenience of eating. Privitera and Zuraikat (2014) conducted a study to test whether the proximity of food influences consumption. They placed a bowl of popcorn or apple slices in a container on a table (near) or 2 meters from a participant (far). Do the data in the following figure support their hypothesis that the more proximate the food, the more participants will eat of it? Explain.

You read a claim that variability is negative. Is this possible? Explain.

A researcher measures the time (in seconds) it takes a sample of five participants to complete a memory task. It takes four of the participants 5, 6, 6, and 7 seconds. If M = 7, then what must be the fifth time recorded?

An expert reviews a sample of 10 scientific articles (n = 10) and records the following number of errors in each article: 2, 9, 2, 8, 2, 3, 1, 0, 5, and 7. Compute the SS, variance, and standard deviation for this sample using the definitional and computational formula.

A school administrator has students rate the quality of their education on a scale from 1 (poor) to 7 (exceptional). She claims that 99.7% of students rated the quality of their education between 3.5 and 6.5. If the mean rating is 5.0, then what is the standard deviation, assuming the data are normally distributed?

Conscientious responders. Marjanovic, Holden, Struthers, Cribbie, and Greenglass (2015) tested an index to discriminate between conscientious and random responders to surveys. As part of their study, they had participants complete the Conscientious Responders Scale (CRS; Marjanovic, Struthers, Cribbie, & Greenglass, 2014). The mean score for conscientious responders was 4.58 and the standard deviation was 1.16. Assuming the data are normally distributed in this example, would a score above 5.0 be unlikely? Explain.

The probability that a particular treatment will be effective is p = .31. The probability that a particular treatment will not be effective is q = .69.

1. What type of relationship do these probabilities have?

2. What is the probability that the treatment will be or will not be effective?

A psychologist states that there is a 5% chance (p = .05) that his decision will be wrong. Assuming complementary outcomes, what is the probability that his decision will be correct?

The following is an incomplete probability distribution for a given random variable, x. What is the probability for the blank cell?

The normal distribution is symmetrical. What does this mean?

What type of distribution is most commonly applied to behavioral research?

A normal distribution has a mean of 0 and a standard deviation of -1.0. Is this possible? Explain.

A normal distribution has a standard deviation equal to 10. What is the mean of this normal distribution if the probability of scoring below x = 10 is .5000?

Ruxton, Wilkinson, and Neuhäuser (2015) stated that “researchers will frequently be required to consider whether a sample of data appears to have been drawn from a normal distribution”. Based on the empirical rule, why is it informative to know whether a data set is normally distributed?

Yang and Montgomery (2013) studied how teachers and prospective teachers perceive diversity in an educational environment. In their study, participants responded with their level of agreement to many statements regarding diversity on a scale from -5 (most unlike me) to +5 (most like me); the median value, 0, indicated a neutral rating. One item stated, “Some cultural groups are not prepared enough to achieve in America” (Yang & Montgomery, 2013). The researchers ranked the responses to each item and found that the response to this item was associated with a z score of -0.76. In this example, find the proportion of area to the right of -0.76

The standard error is the standard deviation for what type of distribution?

Landry (2015) stated, “[Scaled] data can be validly treated as interval” (p. 1348). Explain why data on a rating scale are often treated as interval scale data in the behavioral sciences.

Toll, Kroesbergen, and Van Luit (2016) tested their hypothesis regarding real math difficulties among children. In their study, the authors concluded: “Our hypothesis [regarding math difficulties] was confirmed”. In this example, what decision did the authors make: Retain or reject the null hypothesis?

How does our estimate of the population variance change as the sample size increases? Explain.

What test is used as an alternative to the z test when the population variance is unknown?

What measure of effect size is most often reported with the t test?

Rietveld and van Hout (2015) explained that skewness is an important feature of the data as it relates to “assumptions of t tests”. Which assumption does skewness relate to? Explain.

How are related samples different from independent samples?

Which type of repeated measures design can only be used with 2 groups?

Son and Lee (2015) used a “within-subjects repeated measures design” (p. 2277) to evaluate the effect of the amount of rice carbohydrates consumed during mealtime on blood pressure in older people with hypo-tension. Explain what the researchers mean by a within-subjects repeated measures design.

What type of estimation uses a sample mean to estimate a population mean?

Researchers report a 95% CI = 1.56 to 5.77. What would the decision be for a hypothesis test if the null hypothesis were:

a. µ = 1.6?

b. µ = 3?

c. µ = 6?

How many factors are observed in a one-way between-subjects ANOVA?

A researcher records the following data for each of three groups. What is the value of the F statistic? Explain your answer.

An educator wants to evaluate four different methods aimed at reducing the time children spend â€œoff taskâ€ in the classroom. To test these methods, she implements one method in each of four similar classrooms and records the time spent off task (in minutes) in each classroom. The results are given in the table.

a. Complete the F table.

b. Is it necessary to compute a post hoc test? Explain.

Peng and Chen (2014) evaluated effect size estimates for various tests. In their paper, they stated that “The [two] popular effect size indices were found to be . . . Cohen’s d, and η^{2}”. Which effect size measure is reported with an ANOVA?

A within-subjects ANOVA is computed when the same or different participants are observed in each group?

Researchers in mental health fields are often interested in evaluating the effectiveness of using food images to enhance positive mood. Adapting a typical design from such studies, suppose we have participants rate their mood change on a standard self-report affect scale after viewing images of â€œcomfortâ€ foods, fruits/vegetables (F/V), and random non-food images (used as a control group). The results are given in the table at right for this hypothetical study.

a. Complete the F table.

b. Compute a Bonferroni procedure and interpret the results.

a. Complete the F table.

b. Compute a Bonferroni procedure and interpret the results.

Rouder, Morey, Verhagen, Swagman, and Wagenmakers (2016) evaluated the nature of various ANOVA designs. In their analysis they stated,

If a factor is manipulated in a [A] manner, then each participant observes one level of the factor. Conversely, if a factor is manipulated in a [B] manner, then each participant observes all levels of the factor.

Fill in the blank for [A] and [B] using the following two choices: between-subjects or within-subjects.

Explain why the critical value can be different for each hypothesis test computed using the two-way between-subjects ANOVA.

Which effect (main effect or interaction) is unique to the factorial design, compared to the one-way ANOVA designs?

An educator evaluates the effects of small, medium, and large class sizes on academic performance among male and female students. Identify each factor and the levels of each factor in this example.

For each of the following, state whether F = 0 for a main effect, the A × B interaction, or both.

a. Cell means are equal.

b. Row totals are equal.

c. Column totals are equal.

In an effort to promote a new product, a marketing firm asks participants to rate the effectiveness of ads that varied by length (short, long) and by type of technology (static, interactive). Higher ratings indicated greater effectiveness.

a. Complete the F table and make a decision to retain or reject the null hypothesis for each hypothesis test.

b. Based on the results you obtained, what is the next step?

Evidence suggests that those with an optimistic world view tend to be happier than those with a pessimistic world view. One potential explanation for this is that optimists tend to ignore negative events and outcomes more so than pessimists. To test this explanation, participants were assessed and categorized into groups based on whether they were optimistic and pessimistic and whether they had reported more positive or negative life events in the previous week. All participants were then asked to rate theiroverall life happiness (i.e., the dependent variable). The results from this hypothetical study are given in the table.

a. Complete the F table and make a decision to retain or reject the null hypothesis for each hypothesis test.

b. Compute simple main effect tests for the life events factor at each level of the world view factor. State your conclusions using APA format.

Otterbring (2016) tested an individual’s intuitions regarding how restricting versus encouraging touching a product during an in-store product demonstration should influence the number of products purchased and the amount of money spent. A summary for one finding reported in Otterbring’s study is graphically presented below. Is a main effect, interaction, or both depicted in the graph? Explain.

Name the correlation coefficient used for ordinal data.

A researcher measures the relationship between the number of interruptions during a class and time spent â€œon taskâ€ (in minutes). Answer the following questions based on the results provided.

a. Compute the Pearson correlation coefficient.

b. Multiply each measurement of interruptions by 3 and recalculate the correlation coefficient.

c. Divide each measurement in half for time spent â€œon taskâ€ and recalculate the correlation coefficient.

d. True or false: Multiplying or dividing a positive constant by one set of scores (X or Y) does not change the correlation coefficient. Note: Use your answers in (a) to (c) to answer true or false.

A researcher records data to analyze the correlation between scores on two surveys that are supposed to measure the same construct. Using the hypothetical data given in the following table, compute the Pearson correlation coefficient. Are these surveys related?

Danitz, Suvak, and Orsillo (2016) examined the association between change in acceptance, mindfulness practice, and academic values on other outcomes in a first-year undergraduate experience course that in tegrated an acceptance-based behavioral program. The researchers reported,

An examination of correlation indicated that changes in acceptance were negatively associated with changes in depression, r = -.33 (n = 213), p < .001

a. What was the sample size in this study?

b. What was the value of the correlation coefficient? Was the correlation significant at a .05 level of significance? Explain.

Define the following terms:

a. Slope

b. y-intercept

Does residual variation describe variation related to or not related to changes in X?

Chen, Dai, and Dong (2008) measured the relationship between scores on a revised version of the Aitken Procrastination Inventory (API) and actual procrastination among college students. Higher scores on the API indicate greater procrastination. They found that procrastination (Y) among college students could be predicted by API scores (X) using the following regression equation: Ŷ = 0.146X - 2.922. Estimate procrastination when:

a. X = 30

b. X = 40

c. X = 50

A chi-square test is used when we compare frequencies for data on what scale of measurement?

How many factors are observed using a chi-square goodness-of-fit test?

Which non-parametric test can be used as an alternative to both the one-sample t test and the related-samples t test?

What are the degrees of freedom for the Kruskal-Wallis H test and the Friedman test?

What level of confidence is associated with a two-tailed hypothesis test at a .05 level of significance?

Privitera and Freeman (2012) constructed a scale to measure or estimate the daily fat intake of participants; the scale was called the estimated daily intake scale for fat (EDIS-F). To validate the assertion that the EDIS-F could indeed estimate daily intake of fat, the researchers tested the extent to which scores on the scale could predict liking for a high-fat food (as would be expected if the scale were measuring daily fat intake). Liking was recorded such that higher scores indicated greater liking for the food. The researchers found that liking for the high-fat food (Y) could be predicted by scores on the EDIS-F (X) using the following regression equation: Ŷ = 1.01X + 4.71. Using this regression equation:

a. Is the correlation positive or negative? Explain.

b. If a participant scores 40 on the EDIS-F, then what is the expected liking rating for the high-fat food?

Which type of estimation (point or interval estimation) is more

precise?

~~As the level of confidence increases, what happens to the certainty of an interval estimate? ~~

Forest bathing, also called Shinrin-yoku, is the practice of taking short, leisurely walks in a forest to enhance positive health. To test the usefulness of this practice, the time forest bathing per day was recorded among eight patients with depression who subsequently showed a marked reduction in their symptoms over the last week. The data are given in the table.

a. Find the confidence limits at a 95% CI for this sample.

b. Suppose the null hypothesis states that the average time spent forest bathing among patients is 3.5 hours per day. What would the decision be for a two-tailed hypothesis test at a .05 level of significance?

The mean of an exam is 57.3 and the standard deviation is 9.6. What will happen to the standard deviation of these scores if the instructor

(a) Adds 5 points to each score?

(b) Subtracts 4 points from each score?

(c) Multiplies each score by 2?

(d) Divides each score by 3?

Recalculate σ^{2}, σ, s^{2}, and s for Dupre Hall using the definitional formulas, and compare them to the corresponding results from the previous exercise. Which type of formula (computing or definitional) usually leads to greater error due to rounding off before the final result?

Insert the sums you found for Exercise 3 of Chapter 1 into the computing formulas given in this chapter to find σ^{2}, σ, s^{2}, and s for the four dorms. (We highly recommend that you also learn to obtain these results directly with a handheld calculator.)

Compute the median and mean for Distribution 6 in Table 3.2. Why can't you find the mode of this distribution?

**Table 3.2**

Compute the median of Turck Hall from the grouped frequency distribution you created for that dorm when solving the second exercise of Chapter 2.

Repeat the previous exercise with the data in the following table. Note that the marginal frequencies have not changed, so you do not have to recompute the expected frequencies.

a. Now can you reject the null hypothesis that students' attitudes on this question are not at all related to their academic areas?

b. Calculate the appropriate measure for the strength of relationship between the two variables, regardless of your decision in part (a). How strong does the relationship appear to be?

Suppose that students majoring in the natural sciences, social sciences, and humanities were asked whether they were in favor of having greater student participation in academic decisions at their college. The data from the survey appear in the following table.

a. Compute the two-way chi-square test for these data. Can you reject the null hypothesis that students' attitudes on this question are not at all related to their academic areas? What critical value did you use to make your decision?

b. Calculate the appropriate measure for the strength of relationship between the two variables, regardless of your decision in part (a). How strong does the relationship appear to be?

A bond issue is to be put before the voters in a forthcoming election. An opinion poll company obtains a random sample of 200 registered voters and asks them what party they belong to and how they intend to vote on the bond issue. The results are as follows:

a. Test the null hypothesis that political party and prospective vote on the bond issue are independent. What is your conclusion?

b. Calculate CramÃ©r's Ï• for these data. Does it look like there's a strong association between party affiliation and attitude toward this particular bond issue?

psychologist wants to test the hypothesis that college women will do better on a particular type of problemsolving task than will college men. He obtains the following results:

a. Test the null hypothesis that sex and success on the problem-solving task are independent. Does this mean the same as a statement about whether the percent success differs between males and females?

b. Calculate the phi coefficient for these data. Does it look like the psychologist is dealing with a small, medium, or large effect?

Repeat the previous exercise, except that this time there are 79 toddlers choosing among toys that come in a total of four different colors. The number of toddlers preferring each color is as follows:

a. 21 chose red, 14 chose blue, 26 chose yellow, 18 chose green.

b. The same toddlers were tested a year later with the following results: 28 chose red, 20 chose blue, 9 chose yellow, 22 chose green.

**Data from previous exercise**

A developmental researcher has observed that in a random sample of 60 toddlers, 27 preferred blue toys, 19 preferred red toys, and 14 preferred green toys. Perform a chi-square test of the null hypothesis that, in the entire population of toddlers, the preference for these three colors is equally divided.

At Bigbrain University, the typical grade distribution is A, 15%; B, 25%; C, 45%; D, 10%; F, 5%. The grades given by two professors are shown here. For each one (separately), test the null hypothesis that the professor is a typical grader, using a one-variable chi-square analysis.

Out of 100 psychiatric patients given a new form of treatment, 60 improved, while 40 got worse.

a. Use a chi-square test to decide whether you can reject the null hypothesis that the treatment is totally ineffective (i.e., that patients are equally likely to improve or get worse).

b. Redo the significance test in part (a) using the z score formula (i.e., normal approximation) for the binomial test. Explain the relationship between the z score you calculated in this part and the χ2 value you calculated in part (a).

Suppose that after 6 months of a new form of treatment for chronic schizophrenia, 18 patients exhibited some improvement, 4 did not change, and 6 patients actually got worse.

a. Using the sign test, can you reject the null hypothesis (that the new treatment has no effect) at the .05 level? (Show the z score and p value that you used to answer this question.)

b. A more conservative way to conduct the binomial test is to assign half of the tied cases arbitrarily to each category (one pair is discarded if there is an odd number of ties). Redo part (a) after applying this approach to tied cases.

Apply the sign test to the data from Exercise 8 in Chapter 7, using one of the normal approximation formulas. Explain the difference in results between this exercise and the one in Chapter 7.

**Data from exercise 8 (chapter 7)**

For the following set of data, assume that the X score represents the participant's performance in the experimental condition and that the Y score represents the same person's performance in the control condition. (Thus, each participant serves as his or her own control.) Compute the matched t test for these data. Also compute the 95% CI for the mean of the difference scores.

Imagine that you want to test whether a particular coin is biased or fair by flipping the coin four times and counting the number of times it comes up heads.

a. How many different sequences can be produced by flipping the coin four times? How many different values can X (the number of heads) take on?

b. Graph the binomial distribution for N = 4 and P = .5 so that the height of each bar represents the probability that corresponds to each value of X.

c. If the coin were to land on tails four times in a row, could you reject the null hypothesis that the coin is fair? Explain.

Slips of paper are placed in a large hat and thoroughly mixed. Ten slips bear the number 1, 20 slips bear the number 2, 30 slips bear the number 3, and 5 slips bear the number 4. What is the probability of drawing

a. A 1?

b. A 2?

c. A 3?

d. A 4?

e. A 1 or a 4?

f. A 1 or a 2 or a 3 or a 4?

g. A 5?

h. A 2 and then a 3? (The number drawn first is replaced prior to the second draw.)

One hundred slips of paper bearing the numbers from 1 to 100, inclusive, are placed in a large hat and thoroughly mixed. What is the probability of drawing

a. The number 17?

b. The number 92?

c. Either a 2 or a 4?

d. A number from 7 to 11, inclusive?

e. A number in the 20s?

f. An even number?

g. An even number, and then a number from 3 to 19, inclusive? (The number drawn first is replaced prior to the second draw.)

h. A number from 96 to 100, inclusive, or a number from 70 to 97, inclusive?

The following questions refer to the throw of one fair, six-sided die.

a. What is the probability of obtaining an odd number on one throw?

b. What is the probability of obtaining seven odd numbers in seven throws?

In the following problems, cards are drawn from a standard 52-card deck. Before a second draw, the first card drawn is replaced and the deck is thoroughly shuffled. Compute each of the following probabilities.

a. The probability of drawing a 10 on the first draw.

b. The probability of drawing either a deuce, a 3, a 4, a 5, a heart, or a diamond on the first draw.

c. The probability of drawing the ace of spades twice in a row.

d. The probability of drawing either a jack, a 10, a 7 of clubs, or a spade on the first draw and then drawing either the ace of diamonds or 9 of hearts on the second draw.

e. Recompute the probabilities asked for in parts (c) and (d) assuming that the first card drawn is not replaced.

Suppose that participants are asked to memorize a list of words that range from very abstract to very concrete. The number of words recalled of each type for each participant are shown in the following table.

a. Compute the one-way RM ANOVA for these data. Test the F ratio for significance at the .05 level. How many pairwise comparisons could be tested if your ANOVA was significant? What alpha would you use to test each of these comparisons, if you used a Bonferroni adjustment to keep the experimentwise alpha at .05?

b. Reanalyze the data as a mixed-design ANOVA, assuming that the first four participants were selected for their high scores on a spatial ability test, whereas the second group of four participants were chosen for their poor performance in spatial ability. Test each F ratio for significance at the .05 level.

c. Graph the cell means of the two-way mixed-design ANOVA, as described in part (b). Explain how the pattern of the cell means is consistent with the results you obtained in part (b).

Suppose that, prior to performing the clerical tasks in the experiment of Exercise 3, the first six participants took pills they thought to be caffeine but that were actually placebos; the remaining six participants ingested real caffeine pills.

a. Reanalyze the data in Exercise 3 as a mixed-design ANOVA, adding drug condition (placebo versus caffeine) as the between-groups variable. Test each F ratio for significance at the .05 level.

b. Compare the SS components you found as part of your analysis in part (a) to the SS components you found in Exercise 3. Which SS components are the same, and which combinations of SSs in part (a) add up to one of the SS components in Exercise 3?

c. Compute separate one-way RM ANOVAs for the placebo and the caffeine participants, and test these simple main effects for significance at the .05 level. How do these tests relate to your analysis in part (a)?

d. If this design was completely counterbalanced for each of the two drug groups, how many participants would have been assigned to each possible treatment order within each group?

The following data come from an experiment in which each participant has been measured under three different levels of distraction (the DV is the number of errors committed on a clerical task during a 5-minute period). Compute the one-way RM ANOVA for these data. Is the F ratio significant at the .01 level, assuming sphericity? Would this F ratio be significant at the .05 level, assuming a total lack of sphericity?

The following group means come from Exercise 4 in Chapter 12. Compute the one-way RM ANOVA for these data, assuming that there are a total of 15 blocks of (matched) participants and that SSerror = 5, 40. Is the F ratio significant at the .05 level, based on the unadjusted df (i.e., assuming sphericity)? Would this F ratio be significant at the .05 level, given the worst-case adjustment of the df (i.e., assuming a maximum violation of sphericity)?

Redo Exercise 7 from Chapter 7 as a one-way RM ANOVA. What is the relationship between the F ratio you calculated for this exercise and the t value you calculated for that exercise?

**Data from exercise 7 (chapter 7)**

An educational psychologist has developed a new textbook based on programmed instruction techniques and wishes to know if it is superior to the conventional kind of textbook. He therefore obtains participants who have had no prior exposure to the material and forms two groups: an experimental group, which learns via the programmed text, and a control group, which learns via the old-fashioned textbook. The psychologist is afraid, however, that differences among participants in overall intelligence will lead to large error terms. Therefore, he matches his participants on intelligence and forms 10 pairs such that each pair is made up of two people roughly equal in intelligence test scores. After both groups have learned the material, the psychologist measures the amount of learning by means of a 10-item quiz. The results are as follows:

For each of the following experiments, perform a two-way ANOVA and then the follow-up tests that are appropriate for your results. Use a graph of the cell means to explain the results you obtained.

a. Experiment 1

b. Experiment 2

c. Experiment 3

Suppose that a 2 Ã— 2 factorial design is conducted to determine the effects of caffeine and sex on scores on a 20-item English test. The cell means are given in the following table.

a. Given that n = 7 and MSW = 2.0, compute the appropriate F ratios, and test each for significance at the .05 level.

b. Graph the cell means for these data. What type of interaction do you see: ordinal or disordinal?

c. Test all of the simple main effects. What specific conclusions can you draw from these tests?

An industrial psychologist wishes to determine the effects of satisfaction with pay and satisfaction with job security on overall job satisfaction. He obtains measures of each variable for a total group of 20 employees, and the results are shown in the following table. (Cell entries represent overall job satisfaction, where 7 = very satisfied and 1 = very dissatisfied.)

a. Perform a two-way ANOVA on these data. Using an alpha of .05, what can the psychologist conclude?

b. Compute partial eta squared for each of the main effects. Comment on the size of each effect.

c. Graph the cell means for these data. What type of interaction do you see: ordinal or disordinal?

d. Test all of the simple main effects. What specific conclusions can you draw from these tests?

The following table contains the statistics quiz scores for 18 students as a function of their phobia level and gender.

a. Compute the two-way ANOVA for these data, and present your results in the form of an ANOVA summary table (see Table 14.2).

b. Conduct the appropriate follow-up tests to determine which phobic levels differ significantly from other levels. Are these follow-up tests justified by your results in part (a)? Explain.

**Table 14.2**

In Exercise 7 of the previous chapter, the means for the negative feedback, positive feedback, and no feedback groups were X̅_{neg} = 11.1, X̅_{pos} = 14.7, and X̅_{no} = 12.4, and the F ratio for the one-way ANOVA was equal to 3.69. Given that the ANOVA was significant at the .05 level and that there were 20 participants in each group:

(a) Find the value of LSD for this study.

(b) Which pair(s) of means differ significantly, according to the LSD test?

For this exercise, we will use Table 13.4, reprinted here, for the sample means. This time, however, imagine that the size of each sample (n) is 7 and that you do not know MSW. Fortunately, you are given the results of the ANOVA: F(4, 30) = 5.53.

Table 13.4 Means for the Music Experiment Data in Table 12.1B

**Table 12.1B**

a. Find the error term for the ANOVA and use it to calculate Tukey's HSD.

b. Which types of music differ significantly from which other types, according to Tukey's HSD test?

A study using five samples finds that the mean of each sample is as follows: Sample 1 = 6.7; Sample 2 = 14.2; Sample 3 = 13.8; Sample 4 = 10.4; Sample 5 = 15.8. Suppose that HSD (with q based on α = .05) for this study is 5.3.

(a) Which population means should be regarded as different from each other at the .05 level?

(b) Find the 95% CIs for comparing Sample 5 to each of the others.

For your convenience, the data from Exercise 4 from the previous chapter are reprinted in the following table:

a. Using the harmonic mean of all the sample sizes as your value for n, calculate HSD for these data, and determine which pairs of groups differ significantly.

b. Recalculate HSD according to the rules of the Fisher-Hayter test. Would the use of the F-H test be justified in this case? Assuming the F-H test is justified, what conclusions can be drawn from this test? Use the values for HSD in this part and part (a) to compare the power of Tukey's test with the modified LSD test.

Calculate both LSD and HSD for the two experiments in Exercise 3 of the previous chapter, using the harmonic mean of the three sample sizes as your value for n. What conclusions can you draw for each experiment? Use your values for LSD and HSD to compare the relative statistical power of these two procedures.

**Data from Exercise 3(previous chapter)**

For each of the following two experiments, calculate the means and variances for each group first, and then use those statistics to perform the ANOVA.

a. Can you reject the null hypothesis for Experiment 1? Display your results in an ANOVA summary table, and state the significance of your F ratio in a sentence, using the proper format. Include the value for eta squared.

b. Can you reject the null hypothesis for Experiment 2? Display your results in an ANOVA summary table, and state the significance of your F ratio in a sentence, using the proper format. Include an estimate of omega squared.

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