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Questions and Answers of
Statistics
In studies examining the effect of humor on interpersonal attractions, McGee and Shevlin (2009) found that an individual's sense of humor had a significant effect on how the individual was perceived
A psychologist would like to determine whether there is a relationship between depression and aging. It is known that the general population averages μ = 40 on a standardized depression test. The
Find the estimated standard error for the sample mean for each of the following samples. a. n = 4 with SS = 48 b. n = 6 with SS = 270 c. n = 12 with SS = 132 Discuss.
Explain why t distributions tend to be flatter and more spread out than the normal distribution?
Find the t values that form the boundaries of the critical region for a two-tailed test with α = .05 for each of the following sample sizes: a. n = 6 b. n = 12 c. n = 24
The following sample of n = 6 scores was obtained from a population with unknown parameters. Scores: 7, 1, 6, 3, 6, 7a. Compute the sample mean and standard deviation. (Note that these are
The following sample was obtained from a population with unknown parameters. Scores: 6, 12, 0, 3, 4 a. Compute the sample mean and standard deviation. (Note that these are descriptive values that
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ = 75, and the treatment is administered to the individuals in the sample. After treatment, the sample
To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the
Describe the basic characteristics of an independent measures, or a between-subjects, research study?
For each of the following, assume that the two samples are selected from populations with equal means and calculate how much difference should be expected, on average, between the two sample
For each of the following, calculate the pooled variance and the estimated standard error for the sample mean difference a. The first sample has n = 4 scores and a variance of s2 = 55, and the second
A researcher conducts an independent-measures study comparing two treatments and reports the t statistic as t(30) = 2.085. a. How many individuals participated in the entire study? b. Using a
Hallam, Price, and Katsarou (2002) investigated the influence of background noise on classroom performance for children aged 10 to 12. In one part of the study, calming music led to better
Do you view a chocolate bar as delicious or as fattening? Your attitude may depend on your gender. In a study of American college students, Rozin, Bauer, and Catanese (2003) examined the importance
In a study examining overweight and obese college football players, Mathews and Wagner (2008) found that on average both offensive and defensive linemen exceeded the at-risk criterion for body mass
Functional foods are those containing nutritional supplements in addition to natural nutrients. Examples include orange juice with calcium and eggs with omega-3. Kolodinsky, et al. (2008) examined
In 1974, Loftus and Palmer conducted a classic study demonstrating how the language used to ask a question can influence eyewitness memory. In the study, college students watched a film of an
Numerous studies have found that males report higher self-esteem than females, especially for adolescents (Kling, Hyde, Showers, & Buswell, 1999). Typical results show a mean self-esteem score of M =
A researcher is comparing the effectiveness of two sets of instructions for assembling a child's bike. A sample of eight fathers is obtained. Half of the fathers are given one set of instructions and
Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic?
When people learn a new task, their performance usually improves when they are tested the next day, but only if they get at least 6 hours of sleep (Stickgold, Whidbee, Schirmer, Patel, & Hobson,
Steven Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were given a mix of humorous and non-humorous sentences and significantly
Downs and Abwender (2002) evaluated soccer players and swimmers to determine whether the routine blows to the head experienced by soccer players produced long-term neurological deficits. In the
Research has shown that people are more likely to show dishonest and self-interested behaviors in darkness than in a well-lit environment (Zhong, Bohns, & Gino, 2010). In one experiment, participants
If other factors are held constant, explain how each of the following influences the value of the independent-measures t statistic and the likelihood of rejecting the null hypothesis: a. Increasing
Describe the homogeneity of variance assumption and explain why it is important for the independent measures t test?
One sample has SS = 48 and a second sample has SS = 32. a. If n = 5 for both samples, find each of the sample variances and compute the pooled variance. Because the samples are the same size, you
One sample has SS = 70 and a second sample has SS = 42. a. If n = 8 for both samples, find each of the sample variances, and calculate the pooled variance. Because the samples are the same size, you
As noted on page 320, when the two population means are equal, the estimated standard error for the independent-measures t test provides a measure of how much difference to expect between two sample
Two separate samples, each with n = 12 individuals, receive two different treatments. After treatment, the first sample has SS = 1740 and the second has SS = 1560. a. Find the pooled variance for the
Two separate samples receive two different treatments. The first sample has n = 9 with SS = 710, and the second has n = 6 with SS = 460. a. Compute the pooled variance for the two samples. b.
For the following studies, indicate whether a repeated measures t test is the appropriate analysis. Explain your answers. a. A researcher is comparing the amount of time spent playing video games
Research has shown that losing even one night's sleep can have a significant effect on performance of complex tasks such as problem solving (Linde & Bergstroem, 1992). To demonstrate this
Strack, Martin, and Stepper (1988) reported that people rate cartoons as funnier when holding a pen in their teeth (which forced them to smile) than when holding a pen in their lips (which forced
How would you react to doing much worse on an exam than you expected? There is some evidence to suggest that most individuals believe that they can cope with this kind of problem better than their
Research results indicate that physically attractive people are also perceived as being more intelligent (Eagly, Ashmore, Makhijani, & Longo, 1991). As a demonstration of this phenomenon, a
Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggest that the antioxidants in foods such as blueberries may reduce
The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of n = 4 participants before and after they receive the treatment.a. Calculate the
A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained and each participant ate a fixed diet without any oatmeal for 30
A variety of research results suggest that visual images interfere with visual perception. In one study, Segal and Fusella (1970) had participants watch a screen, looking for brief presentations of a
One of the primary advantages of a repeated-measures design, compared to independent measures, is that it reduces the overall variability by removing variance caused by individual differences. The
The previous problem demonstrates that removing individual differences can substantially reduce variance and lower the standard error. However, this benefit only occurs if the individual differences
Participants enter a research study with unique characteristics that produce different scores from one person to another. For an independent-measures study, these individual differences can cause
A researcher uses a matched-subjects design to investigate whether single people who own pets are generally happier than singles without pets. A mood inventory questionnaire is administered to a
There is some evidence suggesting that you are likely to improve your test score if you rethink and change answers on a multiple-choice exam (Johnston, 1975).To examine this phenomenon, a teacher
The teacher from the previous problem also tried a different approach to answering the question of whether changing answers helps or hurts exam grades. In a separate class, students were encouraged
At the Olympic level of competition, even the smallest factors can make the difference between winning and losing. For example, Pelton (1983) has shown that Olympic marksmen shoot much better if they
The Preview section of this chapter presented a repeated-measures research study demonstrating that swearing can help reduce pain (Stephens, Atkins, & Kingston, 2009).In the study, each
Explain the difference between a matched-subjects design and a repeated-measures design. Discuss.
A researcher conducts an experiment comparing two treatment conditions and obtains data with 10 scores for each treatment condition. a. If the researcher used an independent-measures design, how
A sample of n = 9 individuals participates in a repeated measures study that produces a sample mean difference of MD = 6.5 with SS = 200 for the difference scores. a. Calculate the standard deviation
a. A repeated-measures study with a sample of n = 25 participants produces a mean difference of MD = 3 with a standard deviation of s = 4. Based on the mean and standard deviation, you should be able
a. A repeated-measures study with a sample of n = 9 participants produces a mean difference of MD = 3 with a standard deviation of s = 6. Based on the mean and standard deviation, you should be able
A sample of difference scores from a repeated-measures experiment has a mean of MD = 4 with a standard deviation of s = 6.a. If n = 4, is this sample sufficient to reject the null hypothesis using a
As mentioned in Chapters 2 and 3 (pp. 38 and 81), Steven Schmidt (1994) reported a series of studies examining the effect of humor on memory. In one part of the study, participants were presented
People tend to evaluate the quality of their lives relative to others around them. In a demonstration of this phenomenon, Frieswijk, Buunk, Steverink, and Slaets (2004) conducted interviews with
In the problems at the end of Chapter 8, we presented a study indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman,
The stimulant Ritalin has been shown to increase attention span and improve academic performance in children with ADHD (Evans, Pelham, Smith, et al. 2001). To demonstrate the effectiveness of the
Explain why the F-ratio is expected to be near 1.00 when the null hypothesis is true. Discuss.
For the preceding problem you should find that there are significant differences among the three treatments. One reason for the significance is that the sample variances are relatively small. To
Binge drinking on college campuses has been a hot topic in the popular media and in scholarly research. Flett, Goldstein, Wall, Hewitt, Wekerle, and Azzi (2008) report the results of a study relating
A researcher reports an F-ratio with df = 3, 36 from an independent-measures research study. a. How many treatment conditions were compared in the study? b. What was the total number of participants
A research report from an independent-measures study states that there are significant differences between treatments, F(2, 54) = 3.58, p < .05. a. How many treatment conditions were compared in the
There is some evidence that high school students justify cheating in class on the basis of poor teacher skills or low levels of teacher caring (Murdock, Miller, and Kohlhardt, 2004). Students appear
The following summary table presents the results from an ANOVA comparing three treatment conditions with n = 8 participants in each condition. Complete all missing values. (Hint: Start with the df
A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, two samples of rats are selected with n = 20 in each sample. The rats in the first sample receive
A developmental psychologist is examining the development of language skills from age 2 to age 4. Three different groups of children are obtained, one for each age, with n = 16 children in each
The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with α = .05 to determine whether there are any significant mean
The following values summarize the results from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with α = .05 to determine whether there is a
Describe the similarities between an F-ratio and a t statistic.
The following data represent the results from an independent-measures study comparing two treatment conditions.a. Use an independent-measures t test with α = .05 to determine whether there is a
One possible explanation for why some birds migrate and others maintain year round residency in a single location is intelligence. Specifically, birds with small brains, relative to their body size,
There is some research indicating that college students who use Facebook while studying tend to have lower grades than non-users (Kirschner & Karpinski, 2010). A representative study surveys
New research suggests that watching television, especially medical shows such as Grey's Anatomy and House can result in more concern about personal health (Ye, 2010). Surveys administered to college
Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of the
Why should you use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions? Discuss.
Posttests are done after an ANOVA. a. What is the purpose of posttests? b. Explain why you do not need posttests if the analysis is comparing only two treatments. c. Explain why you do not need
An independent-measures research study compares three treatment conditions with a sample of n = 10 in each condition. The sample means are M1 = 2, M2 = 3,and M3 = 7. a. Compute SS for the set of 3
The following data summarize the results from an independent-measures study comparing three treatment conditions.a. Use an ANOVA with α = .05 to determine whether there are any significant
For the preceding problem you should find that there are significant differences among the three treatments. The primary reason for the significance is that the mean for treatment I is substantially
The following data summarize the results from an independent-measures study comparing three treatment conditions.a. Calculate the sample variance for each of the three samples.b. Use an ANOVA with
How does the denominator of the F-ratio (the error term) differ for a repeated-measures ANOVA compared to an independent-measures ANOVA? Discuss.
For the data in problem 9,a. Compute SStotal and SS between treatments.b. Eliminate the mean differences between treatments by adding 2 points to each score in treatment I, adding 1 point to each
The following data were obtained from a repeated measures study comparing three treatment conditions.Use a repeated-measures ANOVA with α = .05 to determine whether these data are sufficient to
In Problem 11 the data show large and consistent differences between subjects. For example, subject A has the largest score in every treatment and subject D always has the smallest score. In the
One of the primary advantages of a repeated-measures design, compared to an independent-measures design, is that it reduces the overall variability by removing variance caused by individual
The following data are from an experiment comparing three different treatment conditions:a. If the experiment uses an independent-measures design, can the researcher conclude that the treatments are
A researcher is evaluating customer satisfaction with the service and coverage of two phone carriers. Each individual in a sample of n = 25 uses one carrier for two weeks and then switches to the
The following summary table presents the results from a repeated-measures ANOVA comparing three treatment conditions with a sample of n = 11 subjects. Fill in the missing values in the table. (Hint:
The following summary table presents the results from a repeated-measures ANOVA comparing four treatment conditions, each with a sample of n = 12 participants. Fill in the missing values in the
A recent study indicates that simply giving college students a pedometer can result in increased walking (Jackson & Howton, 2008). Students were given pedometers for a 12 week period, and asked
A repeated-measures experiment comparing only two treatments can be evaluated with either a t statistic or an ANOVA. As we found with the independent measures design, the t test and the ANOVA produce
The repeated-measures ANOVA can be viewed as a two-stage process. What is the purpose of the second stage? Discuss.
For either independent-measures or repeated-measures designs comparing two treatments, the mean difference can be evaluated with either a t test or an ANOVA. The two tests are related by the equation
In the Preview section for this chapter, we presented an example of a delayed discounting study in which people are willing to settle for a smaller reward today in exchange for a larger reward in the
The endorphins released by the brain act as natural painkillers. For example, Gintzler (1970) monitored endorphin activity and pain thresholds in pregnant rats during the days before they gave birth.
A researcher conducts an experiment comparing three treatment conditions with n = 10 scores in each condition. a. If the researcher uses an independent-measures design, how many individuals are
A researcher conducts a repeated-measures experiment using a sample of n = 8 subjects to evaluate the differences among four treatment conditions. If the results are examined with an ANOVA, what are
A researcher uses a repeated-measures ANOVA to evaluate the results from a research study and reports an F-ratio with df = 2, 30. a. How many treatment conditions were compared in the study? b. How
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