STATS Final
A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote. The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters. If these data were used for a chi-square test for independence, what is the expected frequency for registered females?
28
A chi-square test for goodness of fit has df = 2. How many categories were used to classify the individuals in the sample?
3
A researcher reports an F-ratio with df = 2, 18 from an independent-measures research study. Based on the df values, how many treatments were compared in the study, and what was the total number of subjects participating in the study?
3 treatments and 21 subjects
A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 9, and Σ X 2 = 94. For this study, what is SStotal?
34
For an analysis of variance comparing four treatments, MSbetween = 12. What is the value of SSbetween?
36
A researcher would like to test the claim that 9 out of 10 doctors prefer Brand X. A sample of 60 doctors is obtained and each is asked to compare Brand X with another leading brand. The data show that 48 of the doctors picked Brand X. If these data are evaluated using a chi-square test for goodness of fit, what is the expected frequency for Brand X?
54
A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 3 categories and the second of which is classified into 4 categories. What is the df value for the chi-square statistic?
6
The following table shows the results of a two-factor analysis of variance with 2 levels of factor A, 3 levels of factor B, and a separate sample of n = 5 participants in each of the treatment conditions. Note that several values are missing in the table. What is the missing value for the sum of squares for the within group effect? Source SS df MS Between 80 xx A 8 xx xx F = xx B xx xx 20 F = xx AxB xx xx xx F = xx Within xx xx xx Total 176 xx
96
In an analysis of variance, differences between participants contribute to which of the following variances?
Both between-treatments variance and within-treatments variance
Assume that in the year 2000 there are four different forms of psychotherapy available for curing phobias. An experimenter arranges for different phobic people to each receive one of the four psychotherapies. (A total of 100 people participate in the study.) At the end of the therapy, each patient is categorized as cured or not cured. What statistic is appropriate for testing the question of whether the form of psychotherapy is related to success in curing phobias?
Chi-square
There is a good test for measuring authoritarian personality. An experimenter decides to see if being an authoritarian person is related to success in a particular profession. To this end, the experimenter selects 100 members of the profession, and on the basis of the test categorizes each of them as authoritarian or non-authoritarian. She then evaluates their individual professional histories, from which she categorizes each of them as being successful or unsuccessful in his or her profession. What statistical test would be useful in answering the question of whether authoritarian personality is related to success in this profession?
Chi-square
Are men more dominant than women? A random sample of 100 men and 200 women is obtained and they are all given a test for dominance which simply classifies each person as either dominant or not dominant. What option would answer the question, "Is dominance a sex-related characteristic?"
Chi-square test
Assume that a new interpretation of the frustration aggression hypothesis says that it is not all people who become aggressive when frustrated, but only those who have been brought up in a home where physical punishment is used become aggressive when frustrated. To test this hypothesis, two groups of children are found. One group is brought up in homes where physical punishment is used as a form of discipline. The other group consists of children whose parents chastise them verbally, or remove privileges, but do not actually hit them. The children are all placed in a situation where they are frustrated in the course of play activity. The play situation includes a doll that the children have in their hands at the time of the frustration experience. The experimenter intends to have judges classify the children as either physically aggressive or not, physically aggressive toward the doll (at the time of frustration). Which statistic would be used?
Chi-square test
If the F-ratio for factor A has df = 1, 40 and the F-ratio for factor B has df = 3, 40, then the F-ratio for the interaction must have df = 2, 40.
False
If you measured hearing acuity and age for a group of people who are 50 to 90 years old, you should obtain a positive correlation between the two variables.
False
The distribution of F-ratios is negatively skewed.
False
The line defined by the equation Y = -3 X + 6 slopes up to the right.
False
The observed frequencies for a chi-square test can be fractions or decimal values.
False
Suppose a teacher wants to know whether being on time or late for class is related to exam performance. He divides the class into two groups: those who are and those who are not late. He then wants to see if there is a relationship between being late to class and exam performance. Which single statistic would then be appropriate?
Independent groups t-test
In a two-factor ANOVA, which of the following is not computed directly but rather is found by subtraction?
SSAxB
In an analysis of variance, which of the following is determined by the size of the sample mean differences?
SSbetween
What is evaluated by the chi-square test for goodness of fit?
The shape or proportions for a population distribution
For a two-factor analysis of variance, the significance of any specific F -ratio is completely independent of the significance of the other F -ratios.
True
For an ANOVA, if SSbetween = 40 and SSwithin = 60, then η2 = 40/100.
True
For an ANOVA, when the null hypothesis is true, the F-ratio is balanced so that the numerator and the denominator are both measuring the same sources of variance.
True
For an independent-measures ANOVA comparing four treatment conditions, dfbetween = 3.
True
If an analysis of variance produces SSbetween treatments = 30 and MSbetween treatments = 10, then the ANOVA is comparing four treatment conditions.
True
If an analysis of variance produces a value of F = 0, then all the samples have the same mean.
True
If other factors are held constant, increasing the sample size for a chi-square test for independence will increase the likelihood of rejecting the null hypothesis.
True
One characteristic of nonparametric tests is that they make few, if any, assumptions about the populations being investigated.
True
Posttests such as Scheffé are not necessary for an analysis of variance comparing only two treatment conditions.
True
The chi-square test for goodness of fit evaluates the distribution for one variable, and the test for independence evaluates the relationship between two variables.
True
The data for a chi-square test are called observed frequencies.
True
The larger the differences among the sample means, the larger the numerator of the F-ratio will be.
True
A scientist wants to examine factors that may be related to cancer. The scientist believes that differences in age at death that will be found when determining what type of smoker a person was (pipe smoker, cigar smoker, cigarette smoker, or nonsmoker) but he also thinks it is important to consider the extent of smog in the person's environment. For this new extended study, the people in the sample are divided up into those who lived in areas with heavy smog and those who lived in areas that were relatively free from smog. Smoking habit remains the other independent variable, and the dependent variable remains age at death. The new question of major interest to the scientist is whether the pattern of differences in age at death attributed to smoking habits would be influenced by whether people lived in smog-filled environments. What is the appropriate statistic?
Two factor ANOVA
If an analysis of variance is used for the following data, what would be the effect of changing the value of SS2 to 100? Sample Data M1 = 15 M2 = 25 SS1 = 90 SS2 = 70
Increase SSwithin and decrease the F-ratio
What is indicated by a positive value for a correlation?
Increases in X tend to be accompanied by increases in Y
A chi-square test for independence is being used to evaluate the relationship between two variables. If the test has df = 2, what can you conclude about the two variables?
One variable consists of 2 categories and the other consists of 3 categories.
For a fixed level of significance, how is the critical value for chi-square related to degrees of freedom?
The critical value increases as df increases.
A researcher measures IQ and weight for a group of college students. What kind of correlation is likely to be obtained for these two variables?
A correlation near zero
In an analysis of variance, differences caused by treatment effects contribute to which of the following variances?
Between-treatments variance but not within-treatments variance
If an analysis of variance is used for the following data, what would be the effect of changing the value of SS1 to 50? Sample Data M1 = 10 M2 = 20 SS1 = 90 SS2 = 70
Decrease SSwithin and increase the size of the F-ratio
In an ANOVA, what is represented by the letter N?
The total number of scores in the entire study
A Pearson correlation of r = -0.90 indicates that the data points are clustered close to a line that slopes down to the right.
True
A set of X and Y scores has MX = 4, MY = 10, SSX = 10, and SP = 5. The regression equation for these scores is Y = 0.5X + 8. Hint: Look CAREFULLY at your formula sheet for the formula for b.
True
An ANOVA is used to determine whether any significant difference exists between treatment means, and posttests are used to determine exactly which treatment means are significantly different.
True
A linear regression equation has b = 3 and a = - 6. What is the predicted value of Y for X = 4?
Ŷ = 6
Which of the following Pearson correlations shows the greatest strength or consistency of relationship?
-0.90
A set of X and Y scores has a regression equation with a slope of b = 4. If the mean for the X values is MX = 2 and the mean for the Y values is MY = 6, what is the Y-intercept value for the regression equation?
-2
An independent-measures experiment with three treatment conditions has a sample of n = 10 scores in each treatment. If all three treatments have the same total, T1 = T2 = T3, what is SSbetween?
0
A researcher obtains a Pearson correlation of r = 0.60 for a sample of n = 6 pairs of X and Y scores. If the researcher tests the significance of the correlation, what value will be obtained for the t statistic?
0.6/0.4 = 1.50
A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 9, and ΣX2 = 94. For this study, what is SSbetween?
10
An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment. For this study, what is dfbetween treatments?
2
The following table shows the results of a two-factor analysis of variance with 2 levels of factor A, 3 levels of factor B, and a separate sample of n = 5 participants in each of the treatment conditions. Note that several values are missing in the table. What is the missing value for the F-ratio for Factor A? Source SS df MS Between 80 xx A 8 xx xx F = xx B xx xx 20 F = xx AxB xx xx xx F = xx Within xx xx xx Total 176 xx
2
An ANOVA is used to evaluate the mean differences among three treatment conditions with a sample of n = 12 participants in each treatment. For this study, what is dfbetween treatments?
2
A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 9, and Σ X 2 = 94. For this study, what is SSwithin?
24
For an independent-measures ANOVA comparing three treatments with a sample of n = 5 in each treatment, what is the critical value for the F -ratio using α = .05?
3.88
For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor A?
30
The following table shows the results of an analysis of variance comparing three treatments. What is the value of η 2 , the percentage of variance accounted for, for these data? Source SS df MS Between. 30 2 15 F = 7.50 Within 60 30 2 Total 90 32
30/90 = .33
A research study comparing three treatments with n = 5 in each treatment produces T1 = 5, T2 = 10, T3 = 15, with SS1 = 6, SS2 = 9, SS3 = 9, and Σ X 2 = 94. For this study, what is SStotal?
34
For an analysis of variance comparing four treatments, MSbetween = 12. What is the value of SSbetween?
36
The following table shows the results of a two-factor analysis of variance with 2 levels of factor A, 3 levels of factor B, and a separate sample of n = 5 participants in each of the treatment conditions. Note that several values are missing in the table. What is the missing value for the sum of squares for Factor B? Source SS df MS Between 80 xx A 8 xx xx F = xx B xx xx 20 F = xx AxB xx xx xx F = xx Within xx xx xx Total 176 xx
40
A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote. The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters. If these data were used for a chi-square test for independence, what is the observed frequency for registered males?
40
An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment. For this study, the three samples have SS 1 = 10, SS 2 = 20, and SS 3 = 15. What value would be obtained for MS within ?
45/12
An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment. For this study, the three samples have SS 1 = 10, SS 2 = 20, and SS 3 = 15. What value would be obtained for MS within ?
45/12
The following data were obtained from a two-factor independent-measures experiment with n = 5 participants in each treatment condition. What is the F-value for Factor B (just type the number)? B1 B2 B3 A1 M = 3 T = 15 SS = 18 M = 6 T = 30 SS = 28 M = 9 T = 45 SS = 26 A2 M = 1 T = 5 SS = 8 M = 4 T = 20 SS = 20 M = 1 T = 5 SS = 20
6
An analysis of variances produces dfbetween = 3 and dfwithin = 24. If each treatment has the same number of participants, then how many participants are in each treatment?
7
A researcher records the age and price for a group of used Hondas. What kind of correlation is likely to be obtained for these two variables?
A negative correlation
A two-factor research study is used to evaluate the effectiveness of a new blood-pressure medication. In this two-factor study, Factor A is medication versus no medication and factor B is male versus female. The medicine is expected to reduce blood pressure for both males and females, but it is expected to have a much greater effect for males. What pattern of results should be obtained if the medication works as predicted?
A significant main effect for factor A and a significant interaction
There is a notion that early discrimination training increases the IQ of children; that is, color discriminations (particularly subtle ones), discriminations among musical tones, etc., if fostered in children, are expected to increase IQ. A group of identical twins is used in an experiment to test this theory. One member of each twin pair gets this early discrimination training, but the other does not. Then, at a later date, their respective IQ scores are obtained. Which statistic would be used to test the hypothesis?
Dependent groups t-test
A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference for three different designs for a new automobile. Each individual in a sample of n = 30 males and n = 30 females selects a favorite design from the three choices. If the researcher obtains a chi-square statistic of χ2 = 4.81, what is the appropriate statistical decision for the test?
Fail to reject the null hypothesis with either α = .05 or α = .01
A research report presents the results of an independent-measures ANOVA as follows: F (3, 28) = 5.36, p < .01. The research study compared three treatments.
False
A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable.
False
A research report presents the results of an independent-measures ANOVA as follows: F (3, 28) = 5.36, p < .01. If all the samples were the same size, then each sample had n = 7 participants.
False
A research report presents the results of an independent-measures ANOVA as follows: F (3, 28) = 5.36, p < .01. The research study used a total of 31 participants.
False
A researcher finds a significant correlation between the amount of time spent watching television and blood pressure for a sample of 40-year-old men. This means that watching more television causes high blood pressure.
False
A researcher uses an independent-measures t test to evaluate the mean difference between two treatments. If the t statistic has df = 12, then an ANOVA evaluating the same data would produce an F-ratio with df = 1, 11.
False
A set of X and Y scores has a Pearson correlation of r = -0.60. For these data, 60% of the variability in the Y scores can be predicted from the relationship with X.
False
A two-factor analysis of variance produces an F-ratio for factor A that has df = 3, 36. This analysis is comparing three different levels of factor A.
False
A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants.
False
An ANOVA comparing two treatment conditions produces SSwithin = 80 and SSbetween = 50. For these data, η 2 = 25/80.
False
For a two-tailed hypothesis test evaluating the significance of a correlation, the null hypothesis states that the sample correlation is zero.
False
For the chi-square test for goodness of fit, the researcher must select a sample with an equal number of individuals in each category.
False
If an analysis of variance produces SS between = 20 and SS within = 40, then η 2 = 0.50.
False
If an analysis of variance produces a value of F = 1.00, then all the samples have the same mean.
False
If an analysis of variance is used for the following data, what would be the effect of changing the value of M2 to 25? Sample Data M1 = 10 M2 = 20 SS1 = 90 SS2 = 70
Increase SSbetween and increase the F-ratio
People living near an airport claim that the jets have hurt their hearing. An audiologist decides to see if their claim is justified. No tests of hearing were made before they moved to the airport vicinity, so he has to use different people for comparisons. He selects people who live in the same town, sufficiently far from the airport so that they cannot hear the planes taking off and landing. He wants to compare the hearing of the two groups to test the claim of the people who live near the airport. Both groups are given hearing tests that yield a score of hearing loss relative to some norms. The test scores range from 0 to 40. Which statistic should be used?
Independent groups t-test
If the mean and variance are computed for each sample in an independent-measures, two-factor experiment, which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA?
Large differences between sample means and small sample variances
On average, what value is expected for the F -ratio if the null hypothesis is false?
Much greater than 1.00
A cancer research organization has data on a large sample of the American population who have died over the past 20 years. They have information indicating the type of smoking done- by each individual (pipe smoker, cigar smoker, cigarette smoker, or nonsmoker). They also have the age at death for each person in their sample. The organization wants to see if their data supports the contention that smoking is related to age at death. Which statistic would they use?
One Factor ANOVA
It is generally recognized that a large proportion of men are interested in football, and that this is less often true for women. It is a simple matter to categorize people as interested or not interested in football. What is wanted is some estimate of the degree of relationship between gender and whether or not a person is interested in football. What is the appropriate statistic to examine?
Phi Coefficient
What would the scatter plot show for data that produce a Pearson correlation of r = +0.88?
Points clustered close to a line that slopes up to the right
Which of the following describes a typical distribution of F-ratios?
Positively skewed with all values greater than or equal to zero
For the regression equation, Ŷ = -2X + 6, if the X value is above the mean (positive deviation), what can be determined about the predicted Y value?
The predicted Y value will be below the mean for the Y scores.
A researcher obtains a negative value for chi-square statistic. What can you conclude because the value is negative?
The researcher made a mistake; the value of chi-square cannot be negative.
If a two-factor analysis of variance produces a statistically significant interaction, what can you conclude about the main effects?
The significance of the main effects is not related to the significance of the interaction
In an ANOVA, what is represented by the letter T?
The sum of the scores in a specific treatment
A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories, and a chi-square test for independence is used to examine the distribution of individuals in a 2×2 matrix of categories. Which test has the larger value for df?
The test for goodness of fit
For an ANOVA comparing three treatment conditions, what is stated by the null hypothesis (H0)?
There are no differences between any of the population means.
Which of the following accurately describes the expected frequencies for a chi-square test?
They can contain fractions or decimal values.
What is the purpose of posttests?
To determine which treatments are significantly different
For a chi-square test, the expected frequencies are calculated values that are intended to produce a sample that is representative of the null hypothesis.
True
For a chi-square test, the observed frequencies are obtained from the sample.
True
When comparing more than two treatment means, why should you use an analysis of variance instead of using multiple t tests?
Using multiple t tests increases the risk of a Type I error.
When comparing more than two treatment means, why should you use an analysis of variance instead of using multiple t tests?
Using multiple t tests increases the risk of a Type I error.
The data for a chi-square test consist of ___________.
frequencies
Given a very simple repetitive task, high-IQ people tend to do poorly. An industrial psychologist wants to get an estimate of the proportion of variance in poor performance at a simple repetitive task that is associated. with 1Q. Poor performance is measured by number of errors (which ranged from 4 to 40 in the sample). Which statistic should be computed?
r-squared or r
A teacher sees students straggling into her class at highly diverse times. She secretly records when each person comes into her class. Everyone in the class at the bell gets a score of zero. Then, as each late person comes in, the number of seconds after the bell that the person arrives is recorded. Number of seconds late, then, is each person's individual score. The scores ranged from 0 to 600 (for people who were 10 minutes late). The teacher also has each person's exam average over the semester. She wants to determine whether a person's lateness and his or her exam scores in her class are related. Which statistic should she use?
t-test for r > 0
A set of n = 5 pairs of X and Y scores has ΣX = 15, ΣY = 5, and ΣXY = 10. For these data, what is the value of SP (the TOP part of the ALTERNATIVE correlation formula on your formula sheet)?
-5
A two-factor ANOVA produces an F -ratio for factor A with df = 1, 36 and an F -ratio for factor B with df = 2, 36. Which of the following describes the experiment producing these F -ratios?
2 levels of factor A and 3 levels of factor B
An analysis of variances produces dftotal = 29 and dfwithin = 27. For this analysis, how many treatment conditions are being compared?
3
A set of n = 15 pairs of scores (X and Y values) has SSX = 4, SSY = 25, and SP = 6. What is the Pearson correlation for these data? Hint: Look VERY carefully at your formula sheet, especially at the alternative definitional formula for r (wow, I can't believe I actually told you that).
6/10
A chi-square test for independence is being used to evaluate the relationship between two variables. If the test has df = 1, what can you conclude about the two variables?
Both variables consist of 2 categories.