Statistics Module 3: Chapters 5-6
The item below is based on the following scenario.A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 37 and a standard deviation of 12. The administrators decide to test the new program in one school of 340 students.What is the predicted mean of the experimental distribution? a) 12 b) 27 c) 37 d) 47
47
If beta equals 70%, then alpha a) equals 30% b) equals 50% c) equals 70% d) cannot be determined from information provided
Cannot be determined from information provided
The comparison distribution for the mean of a sample is the distribution of means because a) comparing the mean of a sample to a distribution of a population of scores of individuals is a mismatch b) the available population parameters are inaccurate and reflect too little variance within the population c) the distribution of means is likely to have more varied scores than would be represented in the population d) the proper comparison is stated in the research hypothesis
Comparing the mean of a sample to a distribution of a population of scores of individuals is a mismatch
The upper and lower ends of a confidence interval are the a) interval estimates b) certainty brackets c) multi-point estimates d) confidence limits
Confidence limits
Effect size is an important tool for making sense of research results because it a) indicates the degree to which a result is statistically significant b) indicates the size of the statistical effect c) limits variance and therefore increases power d) is always smaller than the variance
Indicates the size of the statistical effect
Cohen's (1962) review of power in psychological studies revealed that a) power levels were reasonable for most studies b) most researchers used large samples sizes to compensate for low power c) no study had power greater than 50% d) most studies were not worth repeating
No study had power greater than 50%
Supporters of accepting results that reach only "marginal significance" argue that a) the standard .05 significance level is an arbitrary b) hypothesis testing is an all or nothing decision c) the standard .05 and .01 significance level are overly liberal d) hypothesis testing should use the most conservative criterion possible
The standard .05 significance level is an arbitrary convention
Ing general, the shape of a distribution of means tends to be a) unimodal and symmetrical b) bimodal and symmetrical c) unimodal and skewed d) rectangular and symmetrical
Unimodal and symmetrical
When hypothesis testing with a sample of two or more, the formula for figuring your sample's score on the comparison distribution is a) Z = (M - μ) / σ b) Z = (M - μM) / σM c) Z = (X - μ) / σ d) Z = (X - μM) / σM
Z = (M - μM) / σM
The 99% confidence interval is the region in a group of scores that a) a psychologist can be 99% confident includes the true population mean. b) a psychologist can be 1% confident includes the true population mean c) includes 49% of the scores below the mean and 50% of the scores above the mean. d) includes 50% of the scores below the mean and 49% of the scores above the mean
a psychologist can be 99% confident includes the true population mean
Some psychologists have argued that simple significance tests are misleading, and that a better statistic to evaluate the outcome of an experiment would be the a) effect size b) level of power c) probability of a Type II error d) number of participants divided by the standard deviation
effect size
The probability of rejecting the null hypothesis when in fact it is true is a) a type II error b) the power of rejection c) alpha d) beta
Alpha
If a study conducted at that .05 significance level has 80% power a) alpha = 5%, beta 80% b) alpha = 5%, beta = 20% c) alpha = 95%, beta 80% d) alpha = 95%, beta = 20%
Alpha = 5%, beta 20%
A psychologist conducts a study and finds that d = -.63. This effect size would most likely be described as a) small b) medium c) large d) an error because d cannot be negative
Medium
The statistical method currently used to combine the results of multiple studies is a) meta-analysis b) power analysis c) regression analysis d) retrospective analysis
Meta-analysis
Which of the following would usually be considered "marginally significant"? a) p <.001 b) p <.0 c) p<.05 d) p<.10
P<.10
The degree to which the experimental manipulation separates the two populations of individual scores is a) experimental effectiveness b) power c) the effect size d) the significance level
The effect size
The alpha level is a) usually determined while analyzing experimental data b) the chance of obtaining an inconclusive result when the research hypothesis is true c) the probability of a type I error d) always set at 1%
The probability of a type I error
The mean of a distribution of means is a) the square-root of the original population mean b) the original population mean divided by the sample size c) the same as the original population mean d) the sample mean multiplied by the variance
The same as the original population mean
The conventional levels of a significance of 5% and 1% a) provide maximum protection against type I errors b) provide maximum protection against type II errors c) are a compromise between the risks of making Type I and Type II errors d) are more related to power and sample-size considerations than decision errors
Are a compromise between the risks of making type I and type II errors
The probability of NOT making a type II error is a) the experimental safety region b) power c) alpha d) beta
Power
Which of the following statistics would be the most likely to appear in a research article? a) Z test b) standard error c) 99% confidence interval d) variance of the distribution of means
Standard error
The item below is based on the following scenario.A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 37 and a standard deviation of 12. The administrators decide to test the new program in one school of 340 students.What is the standard deviation of the comparison distribution? a) .42 b) .65 c) 12 d) 144
.65
The item below is based on the following scenario Anxiously-attached individuals in the general population tend to have low levels of satisfaction in their romantic relationships (μ = 10, σ = 5, positively skewed distribution). A therapist interested in increasing relationship satisfaction provides a week-long relaxation seminar to 11 anxious individuals. After completing the seminar, relationship satisfaction in the sample averages 12. What is the corresponding Z score for the sample's mean score on the comparison distribution? a) 0.66 b) 1.32 c) 0.44 d) 1.74
1.32
The item below is based on the following scenario.Anxiously-attached individuals in the general population tend to have low levels of satisfaction in their romantic relationships (μ = 10, σ = 5, positively skewed distribution). A therapist interested in increasing relationship satisfaction provides a week-long relaxation seminar to 11 anxious individuals. After completing the seminar, relationship satisfaction in the sample averages 12.What is the corresponding Z score for the sample's mean score on the comparison distribution? a) 0.66 b) 1.32 c) 0.44 d) 1.74
1.32
The item below is based on the following scenario.An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.What is the μM? a) 8 b) 11 c) 25 d) 64
25
The item below is based on the following scenario.A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 37 and a standard deviation of 12. The administrators decide to test the new program in one school of 340 students.What is the mean of the comparison distribution? a) 12 b) 27 c) 37 d) 47
37
The item below is based on the following scenario A manufacturer who is considering the implementation of a one-week training program for all new employees decides to test the program with the next 100 employees hired, and then compare their productivity rate to the productivity rate of new employees based on past records—a rate that is normally distributed with a mean of 60 and a standard deviation of 8. The new program needs to produce a minimum improvement of 4 to be considered worthwhile. What is the mean of the comparison distribution? a) 52 b) 60 c) 68 d) 100
60
The item below is based on the following scenario. A manufacturer who is considering the implementation of a one-week training program for all new employees decides to test the program with the next 100 employees hired, and then compare their productivity rate to the productivity rate of new employees based on past records - a rate that is normally distributed with a mean of 60 and a standard deviation of 8. The new program needs to produce a minimum improvement of 4 to be considered worthwhile. What is the predicted mean of the experimental distribution? a) 52 b) 60 c) 64 d) 100
64
Rejecting the null hypothesis when the research hypothesis is false is a) effect size b) power c) a type I error d) a type II error
A type I error
Using the .01 level of significance means that, in the long run, a) a type I error occurs 1 time in 20 b) a type I error occurs 1 time in 100 c) a type II error occurs 1 time in 20 d) a type II error occurs 1 time in 100
A type I error occurs 1 time in 100
Failing to reject the null hypothesis when the research hypothesis is true is a) effect size b) power c) a type I error d) a type II error
A type II error
The item below is based on the following scenario. A large school district is considering implementing a program that, is successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 37 and standard deviation of 12. The administrators decide to test the new program in one school of 340 students. What is the shape of the comparison distribution? a) positively skewed b) negatively skewed c) approximately normal d) cannot be determined from the information provided
Approximately normal
As the number of people in a sample gets larger, the distribution of means a) begins to look less and less like a normal curve b) becomes a better approximation of the normal curve c) becomes more positively skewed d) becomes more negatively skewed
Becomes a better approximation of the normal curve
The item below is based on the following scenario.Anxiously-attached individuals in the general population tend to have low levels of satisfaction in their romantic relationships (μ = 10, σ = 5, positively skewed distribution). A therapist interested in increasing relationship satisfaction provides a week-long relaxation seminar to 11 anxious individuals. After completing the seminar, relationship satisfaction in the sample averages 12.What is the shape of the comparison distribution? a) positively skewed b) negatively skewed c) approximately normal d) cannot be determined from the information provided
Cannot be determined from the information provided
While no research hypothesis is ever definitely false, failing to reject the null hypothesis in a study that has a high level of power allows one to a) suspect that the research hypothesis may still be true b) conclude that the research hypothesis is most likely false c) make no statements about the research hypothesis d) reject the notion that the effect size has anything to do with statistical significance
Conclude that the research hypothesis is most likely false
Which of the following statements regarding confidence intervals is FALSE? a) confidence intervals are misused more often than significance tests b) confidence intervals can be used in hypothesis testing c) confidence intervals emphasize numerical estimates d) confidence intervals are sometimes reported in research articles
Confidence intervals are misused more often than significance tests
Cohen proposed effect-size conventions based on the effects observed in psychology research in general because a) experimenters need to assess whether the obtained effect size will allow them to reject the null hypothesis b) determining how large an effect can be expected in a given experiment is difficult c) they follow from the original scales he developed d) they are more accurate than calculating a minimum meaningful difference
Determining how large an effect can be expected in a given experiment is difficult
Standard power tables are useful for a) directly determining the power of an experiment b) determining the predicted score for the group exposed to the experimental manipulation c) determining the predicted effect size of a proposed experiment d) determining the probability of falsely accepting the research hypothesis
Directly determining the power of an experiment
The variance of a distribution of means is smaler than the original population variance because a) it is based on fewer individuals than is the original population b) it is an estimate of the sample parameters rather than of the original population c) extreme scores are less likely to affect the distribution of means d) the mean of a distribution of means is so different than the population mean
Extreme scores are less likely to affect a distribution of means
Power is the probability that a) if the research hypothesis is false, the experiment will support the null hypothesis b) if the research hypothesis is true, the experiment will support it c) a type I error will not be made d) the research hypothesis will not be accepted incorrectly
If the research hypothesis is true, the experiment will support it
A type I error is the result of a) improper measurement techniques on the part of the researcher b) failing to reject the null hypothesis when, in fact, it is true c) incorrectly rejecting the null hypothesis d) incorrectly failing to reject the null hypothesis
Incorrectly rejecting the null hypothesis
A psychologist conducts a study and finds that d = 1.41. This effect size would most likely be described as a) small b) medium c) large d) an error because d cannot be greater than 1
Large
The effect size and the number of participants are two important determinants of a) the minimum significant result b) experimental significance c) power d) alpha
Power
The item below is based on the following scenario.An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.If the mean score of the sample is more extreme than the cutoff score on the comparison distribution, the psychologist will conclude that a) the null hypothesis is that the rats in the sample will learn more is supported b) the wallpaper did not have a significant effect on the rate of learning c) the color of the chamber had a significant effect on the rate of learning d) the results are inconclusive since the null hypothesis cannot be rejected
The color of the chamber had a significant effect on the rate of learning
A 95% confidence interval is figured by finding a) the Z score for the bottom 5% of the distribution b) the Z score for the upper 95% of the distribution c) the cutoff points for the lower 2.5% and the upper 2.5% of the distribution d) the cutoff points for the lower 5% and the upper 5% of the distribution
The cutoff points for the lower 2.5% and the upper 2.5% of the distribution
A cognitive psychologist tests whether memory for abstract ideas improves when the information is presented both verbally and visually. Which of the following scenarios represents a type I error? a) the psychologist concludes that memory does not improve when the true situation is that it does not improve b) the psychologist concludes that memory does not improve when the true situation is that it does improve c) the psychologist concludes that memory does improve when the true situation is that it does improve d) the psychologist concludes that memory does improve when the true situation is that it does not improve
The psychologist concludes that memory does improve when the true situation is that it does not improve.
A child psychologist conducts a study to test whether infants born prematurely begin to walk earlier than do infants in general. Which of the following scenarios represents a Type II error? a) The psychologist concludes that premature infants do walk earlier than infants in general when the true situation is that they actually do not b) The psychologist concludes that premature infants do walk earlier than infants in general when the true situation is that they actually do. c) The psychologist concludes that premature infants do not walk earlier than infants in general when the true situation is that they actually do d) The psychologist concludes that premature infants do not walk earlier than infants in general when the true situation is that they actually do not.
The psychologist concludes that premature infants do not walk earlier than infants in general when the true situation is that they actually do
A child psychologist conducts a study to test whether infants born prematurely begin to walk earlier than do infants in general. Which of the following scenarios represents a type I error? a) the psychologist concludes that premature infants do walk earlier than infants in general when the true situation is that they actually do not b) the psychologist concludes that premature infants do walk earlier than infants in general when the true situation is that they actually do c) the psychologist concludes that premature infants do not walk earlier than infants in general when the true situation is that they actually do d) the psychologist concludes that premature infants do not walk earlier than infants in general when the true situation is that they actually do not
The psychologist concludes that premature infants do walk earlier than infants in general when the true situation is that they actually do not
The item below is based on the following scenario An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11. What is the null hypothesis? a) the rate of learning for the sample of rats tested with colorful wallpaper will be no different than the population of rats tested under ordinary circumstances b) the rate of learning for the sample of rats tested with colorful wallpaper will be faster than the population of rates tested under ordinary circumstances c) the rate of learning for the population of rats tested with colorful wallpaper will be no different than the population of rats tested under ordinary circumstances d) the rate of learning for the population of rates tested with colorful wallpaper will be faster than the population of rats tested under ordinary circumstances
The rate of learning for the population of rats tested with colorful wallpaper will be no different than the population of rats tested under ordinary circumstances
dividing the variance of the population of individuals by the number of individuals in each sample yields a) the standard deviation of the population b) the variance of the distribution of means c) an estimate of the sample's standard deviation d) the average deviation of the distribution of means
The variance of the distribution of means
One important advantage of using effect sizes is that a) they indicate all the relevant parameters of a group of scores b) they directly indicate the statistical significance of the research hypothesis c) they provide the same information as statistical significance, but they permit meta-studies d) they are standardized scores that make comparisons of different studies easier
They are standardized scores that make comparisons of different studies easier
In actual practice, the usual reason for determining power before conducting a study is a) to eliminate the possibility that a mistake may occur b) to ensure that regardless of whether the research hypothesis is true, the experiment will yield a significant result c) to determine the power of participants needed to have a reasonable level of power d) to anticipate the likelihood that the experiment will need to be repeated
To determine the number of participants needed to have a reasonable level of power
Setting the significance level at .20 increases the chance of a) obtaining a nonsignificant result b) failing to reject the null hypothesis c) a type I error d) a type II error
Type I error
James asks his friend Rob for advice on how to increase the power of his experiment. Which of Rob's suggestions is incorrect? a) use a larger sample size b) use a less diverse population c) use a two-tailed test instead of a one-tailed test d) use a more intense experimental manipulation to increase effect size
Use a two-tailed test instead of a one-tailed test
The difference between creating a Z score from a single score and creating one from a sample mean is that a) you use the mean and standard deviation from the distribution of means b) the estimated population variance is used directly c) the difference score is divided by the sample's standard deviation d) only the population's mean is used in the computation
You use the mean and standard deviation from the distribution of means
Setting the significance level cutoff at .10 instead of the more usual .05 increases the likelihood of a) a Type I error b) a Type II error c) failing to reject the null hypothesis d) accepting the null hypothesis when, in fact, it is false
a Type I error
The standard deviation of a distribution of means is sometimes called "the standard error of the mean," or the "standard error," because a) it is an inaccurate estimate of a sample standard deviation and cannot be used to determine the variance b) it is calculated by summing the errors figured by subtracting sample means from the population variance c) it is frequently used as an "error term" when calculating the estimated sample variance d) it represents the degree to which particular sample means are "in error" as estimates of the mean of the population of individual scores
it represents the degree to which particular sample means are "in error" as estimates of the mean of the population of individual scores
If the effect size and the desired level of power are known, the power formula can be used to determine the a) minimum meaningful difference b) number of participants needed c) population distribution d) alpha level of the experiment
number of participants needed
Effect size is a) the amount of statistical importance a particular finding has in psychological practice b) the power of a study divided by the sample size c) the sample size multiplied by 1 - beta d) the degree to which an experimental manipulation separates two populations
the degree to which an experimental manipulation separates two populations
In hypothesis testing, after figuring the Z score for the sample's mean, the next step would be to compare this Z score to a) the parameters of the known population b) an estimated distribution based on earlier research findings c) the distribution of means of all the possible samples in the experimental condition from the research d) the distribution of means that would be found if the null hypothesis were true
the distribution of means that would be found if the null hypothesis were true
If the research hypothesis is true but the study has a low level of power, then a) the probability that the study will have a significant result is high b) the probability that the study will have a significant result is low c) the null hypothesis will almost certainly be rejected d) beta is necessarily low
the probability that the study will have a significant result is low
The standard deviation of a distribution of means is a) figured by subtracting the variance from the sample mean and taking the square root b) the square root of the variance of the distribution of means c) the population variance divided by the N in each sample d) the same as the square root of the sample variance
the square root of the variance of the distribution of means
Type II errors concern psychologist because a) they could mean that good theories or useful practical procedures are not used b) they could mean that experiments must be repeated to confirm positive results c) rejecting the null hypothesis should only occur when the research hypothesis is true d) future research might be based on results mistakenly declared significant
they could mean that good theories or useful practical procedures are not used
In general, the shape of a distribution of means tends to be a) unimodal and symmetrical b) bimodal and symmetrical c) unimodal and skewed d) rectangular and symmetrical
unimodal and symmetrical
The item below is based on the following scenario.An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11.The shape of the distribution of means a) will be rectangular b) will be flatter than a normal curve c) will be approximately normal d) cannot be determined from the information given
will be approximately normal