Psych 311 Exam 4
Give an example of two variables that might be related and that would best be tested with a chi-square test of independence.
(many would be corect - need to be nominal scale variables)
A researcher computes the following phi correlation coefficient: Rø = 0.42. If the sample size was 20, then what is the decision for this correlation test? A) Retain the null hypothesis. B) Reject the null hypothesis. C) There is not enough information to answer this question.
A) Retain the null hypothesis.
A researcher computes a 2 × 4 chi-square test for independence. What are the degrees of freedom for this test? A) 2 B) 3 C) 4 D) 8
B) 3
The correlation coefficient ranges from -1.0 to +1.0, with values closer to ±1.0 indicating A) a more positive relationship between two factors B) a stronger relationship between two factors C) that two factors are less likely to be related D) that the correlation is due to outliers
B) a stronger relationship between two factors
The Wilcoxon signed-ranks T test is used as a nonparametric alternative to which parametric test? A) one-sample t-test B) two-independent sample t-test C) related samples t-test D) both A and C
C) related samples t-test
Outliers can change the _____ of a correlation. A) direction B) strength C) sign (+, -) D) all of the above
D) all of the above
Select the description below that identifies the following correlation: r = .28, p < .01. A) the correlation is positive B) the correlation is statistically significant C) the coefficient of determination is .08 D) all of the above
D) all of the above
(4 pts) Would Pearson r show a strong correlation if the data were not in a linear pattern but instead represented a "U-shaped" function? Explain.
No. Pearson r only assesses a linear relationship between variables.
The sign (+ or -) of a correlation coefficient indicates the________________________________ of a relationship between two factors.
direction
If r = .25, then the coefficient of determination is .= ___________06.
.06 (.0625 without rounding)
A 2 × 2 chi-square test for independence has ___ degrees of freedom.
1
A researcher measures the following correlation: r = -0.21. What is the value of the coefficient of determination? A) 0.04 B) -0.04 C) 0.42 D) -0.42
A) 0.04
If X^2 = 5.32 and n = 40, then what is the value of the coefficient of determination? A) 0.133 B) 0.36 C) 0.64 D) There is not enough information to answer this question.
A) 0.133
A researcher conducts a chi-square goodness-of-fit test in which k = 3 and = 4.32. What is the decision for this test at a .05 level of significance? A) Retain the null hypothesis. B) Reject the null hypothesis. C) There is not enough information to answer this question.
A) Retain the null hypothesis.
A researcher determines that X^2 = 3.76 to test for significance for a phi correlation coefficient. What was the decision for this phi correlation test? A) Retain the null hypothesis. B) Reject the null hypothesis C) There is not enough information to answer this question.
A) Retain the null hypothesis.
A researcher measures the following correlation between cups of coffee consumed daily and daily work schedule. Which description best explains the relationship between these two factors? (graph shows lines going in positive direction, line connecting 3 points) A) The more a person works, the more coffee he or she tends to drink. B) The less a person works, the more coffee he or she tends to drink. C) The more a person works, the less coffee he or she tends to drink. D) No linear pattern is evident.
A) The more a person works, the more coffee he or she tends to drink.
Which of the following is a key assumption for a chi-square goodness-of-fit test? A) The observed frequencies are independently recorded in each cell. B) The variance between groups is equal. C) There is no mean difference between groups. D) The proportion in each cell is equal to zero.
A) The observed frequencies are independently recorded in each cell.
A correlation of r = .38 in a sample of 30 participants is statistically significant for a two-tailed test at a .05 level of significance. A) True B) False
A) True
The coefficient of determination is mathematically equivalent to eta-squared. A) True B) False
A) True
The degrees of freedom for a chi-square goodness-of-fit test are A) k - 1 B) n - 1 C) (k1 - 1)(k2 - 1) D) (k - 1)(n - 1)
A) k - 1
The point-biserial correlation coefficient is a measure of the direction and strength of the linear relationship between two variables, where A) one is continuous, and one is dichotomous B) both variables are on an ordinal scale C) one is at interval level or higher and one is ordinal D) both variables are on a nominal scale
A) one is continuous, and one is dichotomous
A researcher conducts two chi-square tests. The 2 × 2 chi-square was X^2 = 3.92. The 2 × 3 chi-square was X^2 = 5.92. Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance? A) the 2 × 2 chi-square B) the 2 × 3 chi-square C) both chi-square tests results in a decision to reject the null hypothesis D) none; both chi-square tests result in a decision to retain the null hypothesis
A) the 2 x 2 chi-square
The appropriate correlation coefficient for measuring the direction and strength of the linear relationship between two ranked or ordinal variables is A) the Spearman correlation coefficient B) the point-biserial correlation coefficient C) the phi correlation coefficient D) none of the above
A) the Spearman correlation coefficient
A researcher computes a 4 × 6 chi-square test for independence with a sample of 120 participants, with X^2 = 14.79. What is the effect size for this result? A) 0.04 B) 0.20 C) 0.12 D) 0.35
B) 0.20
A researcher measures the correlation between gender and student aptitude scores from 0 to 100 among 20 participants. If Rpv = 0.49, then what is the decision for this correlation test? A) Retain the null hypothesis. B) Reject the null hypothesis. C) There is not enough information to answer this question.
B) Reject the null hypothesis.
Suppose a correlation is computed in each of two samples. If the value of SSxy is the same in each sample, and (square root ofSSxSSy) is larger in Sample 1, then in which sample will the value of the correlation coefficient be larger? A) Sample 1 B) Sample 2 C) None; the correlation coefficient will be the same in both samples. D) There is not enough information to answer this question.
B) Sample 2
One way a researcher can correct for having expected frequencies smaller than five is to increase the levels of the categorical variable such that the number of levels A) is equal to the sample size B) is greater than four C) is less than five D) is minimal
B) is greater than four
A researcher observes a correlation of values from 2 to 10 points and draws conclusions about the full range of values in the population from 0 to 21 points. Which limitation for correctly interpreting a correlation coefficient did the researcher violate? A) reverse causality B) restriction of range C) a confound variable D) homoscedasticity
B) restriction of range
A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected. Hence, the decision was to A) reject the null hypothesis B) retain the null hypothesis C) no decision was made
B) retain the null hypothesis
The most common measure of effect size for the correlation coefficient is called A) the correlation coefficient B) the coefficient of determination C) estimated Cohen's d D) the test statistic
B) the coefficient of determination
As a general rule, the larger the degrees of freedom for a chi-square test, A) the smaller the critical value will be B) the larger the critical value will be C) the smaller the level of significance will be D) the larger the level of significance will be
B) the larger the critical value will be
If the expected frequencies equal to observed frequencies for a chi-square test for independence, what do we conclude? A) the degrees of freedom for the test are equal to 0 B) the test statistic value is equal to 0 C) the frequencies observed fit well with the frequencies expected D) both B and C
B) the test statistic value is equal to 0
The denominator of the correlation coefficient measures the extent to which two variables A) vary together B) vary independently C) covary D) both A and C
B) vary independently
The assumption that there is an equal variance or scatter of data points dispersed along the regression line is referred to as A) Normality B) Linearity C) Homoscedasticity D) restriction of range
C) Homoscedasticity
A researcher asks participants to taste each of three meals and to choose the one they like best. The same foods are in each meal, expect for the calorie total of the meal (which is low, moderate, or high calorie). Based on the observed frequencies given below, what is an appropriate conclusion for this test at a .05 level of significance? Type of Meal Low Calorie Moderate Calorie High Calorie fo 6 7 17 fe 10 10 10 A) Participants liked the high calorie meal more than the low calorie meal. B) Participants liked the low calorie meal less than the moderate calorie meal. C) Participants liked the high calorie meal more than was expected. D) all of the above
C) Participants liked the high calorie meal more than was expected.
Which of the following is a statistical procedure used to test hypotheses about the discrepancy between the observed and expected frequencies in two or more nominal categories? A) one-way ANOVA B) analysis of regression C) chi-square test D) all of the above
C) chi-square test
Which of the following is an example of a nonparametric test? A) analysis of variance B) the t-tests C) chi-square test D) Pearson correlation
C) chi-square test
One way a researcher can correct for having expected frequencies smaller than five is to increase the sample size such that A) it is equal to the number of cells B) it is three times larger than the number of cells C) it is five times larger than the number of cells D) it is seven times smaller than the number of cells
C) it is five times larger than the number of cells
The Kruskal-Wallis H test is used as a nonparametric alternative to which parametric test? A) related samples t-test B) two-independent sample t-test C) one-way between-subjects ANOVA D) one-way within-subjects ANOVA
C) one-way between-subjects ANOVA
Which of the following indicates the strongest correlation? A) r = -0.57 B) r = +0.78 C) r = -0.90 D) r = +0.88
C) r = -0.90
To compute the expected frequencies for a chi-square test for independence, we use which of the following formulas? A) k - 1 B) p(n) C) (row total + column total)/grand total D) (row total × column total)/grand total
D) (row total x column total)/grand total
A researcher reports the following results for a chi-square test: X^2(1) = 5.386, p < .05 (V = 0.224). If this test were a test for independence, then how many groups were observed? A) 1 B) 2 C) 3 D) 4
D) 4
A researcher compares the frequency of participants who sleep primarily on their stomach, back, or side during the night. What is the critical value for a chi-square goodness-of-fit test at a .05 level of significance? A) 2 B) 3 C) 3.84 D) 5.99
D) 5.99
A chi-square goodness-of-fit test leads to a decision to retain the null hypothesis. Which of the following correctly explains this decision? A) frequencies observed were significantly different from frequencies expected at each level of the categorical variable B) frequencies observed were significantly different from frequencies expected across the levels of the categorical variable C) frequencies observed were significantly different from frequencies expected within and between expected frequencies D) Frequencies observed were statistically similar to the frequencies expected at each level of the categorical variable
D) Frequencies observed were statistically similar to the frequencies expected at each level of the categorical variable
The normality assumption states that the population of X and Y scores form a bivariate ("two variable") normal distribution, such that A) the population of X and Y scores are normally distributed B) for each X score, the distribution of Y scores is normally distributed C) for each Y score, the distribution of X scores is normally distributed D) all of the above
D) all of the above
The observed frequencies can be summarized, A) in a table B) in a figure C) in the main text D) all of the above
D) all of the above
To summarize correlations, we report: A) the strength of the correlation B) the direction of the correlation C) the p value D) all of the above
D) all of the above
Which of the following is an example of a parametric test? A) analysis of variance B) one-sample t-test C) Pearson correlation D) all of the above
D) all of the above
A researcher can correct for having expected frequencies smaller than five by A) increasing the number of cells B) increasing the sample size C) decreasing the observed frequency D) both A and B
D) both A and B
The numerator of the correlation coefficient measures the extent to which two variables A) vary together B) vary independently C) Covary D) both A and C
D) both A and C
The sign test is used as a nonparametric alternative to which parametric test? A) one-sample t-test B) two-independent sample t-test C) related samples t-test D) both A and C
D) both A and C
A researcher conducts two chi-square tests. The 2 × 2 chi-square was X^2 = 3.82. The 2 × 3 chi-square was X^2 = 5.02. Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance? A) the 2 × 2 chi-square B) the 2 × 3 chi-square C) both chi-square tests results in a decision to reject the null hypothesis D) none; both chi-square tests result in a decision to retain the null hypothesis
D) none; both chi-square tests result in a decision to retain the null hypothesis
The Friedman test is used as a nonparametric alternative to which parametric test? A) related samples t-test B) two-independent sample t-test C) one-way between-subjects ANOVA D) one-way within-subjects ANOVA
D) one-way within-subjects ANOVA
Give the definition for a "third variable" or confound in correlational research.
It is an unanticipated variable not accounted for in the study that could be causing or correlating with observed changes in one or more other variables.
In a chi-square test, one assumption that must be met concerns the expected frequencies for any give cell. What is this assumption?
It must be at least 5.
(5 pts). Can a chi-square test ever be used to support a hypothesis about a causal relationship? Explain.
Yes. If the levels of one factor were randomly assigned (e.g., low or high cognitive load) and the other factor could be affected by that first factor (e.g., making an error on a computer task or not), then you could conclude that factor 1 caused the different outcome in factor 2.
5 pts. Imagine you are a journal editor. A researcher reports means and standard deviations for groups for a study that required running a chi-square test. Is there a problem? What is the problem?
Yes. It's not meaningful to calculate means and SDs for chi-square data because the data represent frequency counts and they are measured on a nominal scale.
The test statistic (i.e., the formula) is the same for a chi-square goodness-of-fit test and which other test?
chi square test for independence
One nonparametric statistical test is the chi-square test. Name three others.
e.g., sign test, Mann-Whitney U test, Wilcoxen signed ranks T test, Kruskal-Wallis H test, Friedman test
When at least one categorical variable has more than two levels, Cramer's V is used to estimate ______________________________ for a chi-square test for independence.
effect size
The formula for the chi-square test measures the size of the discrepancy between observed and _____________________________frequencies.
expected
When finding the critical value in a chi-square distribution, how many tails do you look in for the cutoff?
one tail
The Spearman correlation coefficient is used to measure the correlation between two variables that are measured on a(n) _______________________ scale.
ordinal
To summarize the chi-square test for independence, report the test statistic, degrees of freedom, observed frequencies (or percentages), effect size, and the___________________________________value.
p
The ______________________ correlation coefficient is used to measure the correlation between two dichotomous variables
phi
A major weakness in using a nonparametric test like chi square when a parametric test could validly be used is that the nonparametric test is lower on __________________________________.
power
When the chi-square test for independence is significant, this indicates that two variables are____________________________.
related (or dependent or correlated)
The formula for the Spearman correlation coefficient was derived from the formula for___________________________________________________________
the Pearson correlation coefficient (or just "Pearson r")
When the chi-square test for independence is significant, this indicates that there is significant variability between groups. A) True B) False
B) False
(8 pts). Name the correlation coefficient used to test the relationship between these for sets of variables (So, state the four answers, in order): 1. height and weight 2. retirement status (yes or no) and blood pressure 3. retirement status and death penalty view (pro vs. con) 4. rankings of runners on place (1st-8th) and birth order (1st-8th).
1. Pearson r 2. Point biserial 3. phi 4. Spearman
A researcher measures the correlation between self-esteem (high, low) and physical fitness scores among school athletes. In the study, 12 participants reported high self-esteem and 12 reported low self-esteem. If Sy = 9.06 and My1 - My2 = 11, then what is the value of the correlation coefficient? A) 0.61 B) 0.30 C) 0.39 D) There is not enough information to answer this question.
A) 0.61
A researcher selects a sample of 80 people and records the frequency of participants choosing a low, moderate, or high calorie dessert in a buffet. What are the degrees of freedom for this chi-square goodness-of-fit test? A) 2 B) 3 C) 79 D) 80
A) 2
A researcher tests whether levels of education and income levels are related. In this study, he observes the following frequencies. If he computes a chi-square test for independence at a .05 level of significance, then what is the decision for this test? Education Level High School Bachelor's Graduate Low Income 22 8 5 High Income 8 12 28 A) Education and income level are related. B) Education and income level are not related. C) Education and income level are independent. D) Both B and C are appropriate.
A) Education and income level are related.
What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement? A) Parametric tests are used for interval and ratio data, whereas nonparametric tests are used for nominal and ordinal data. B) Parametric tests are used for ordinal and nominal data, whereas nonparametric tests are used for interval and ratio data. C) Parametric tests are used for ordinal or interval data, whereas nonparametric tests are used for nominal data only. D) There is no distinction; both types of tests are used to analyze data on any scale of measurement.
A) Parametric tests are used for interval and ratio data, whereas nonparametric tests are used for nominal and ordinal data.
A researcher measures the correlation between the frequency of self-esteem (high, low) and health status (lean/healthy, overweight/obese). Based on the frequencies for each nominal category given below, what is the value of the phi correlation coefficient? Health Status Lean/Healthy Overweight/Obese Self-Esteem Low 18 32 High 32 18 A) 0.08 B) 0.28 C) 0.52 D) 0.56
B) 0.28
A researcher selects a sample of 110 participants and computes the following phi correlation coefficient: Rø = 0.31. What is the value of X^2? A) 3.84 B) 10.57 C) 34.10 D) There is not enough information to answer this question.
B) 10.57
A researcher computes a 2 × 3 chi-square test for independence. What is the critical value for this test at a .05 level of significance? A) 3.84 B) 5.99 C) 7.81 D) 12.59
B) 5.99
A researcher records the frequency of participants selecting one of four new slogans for an advertising campaign. If it was expected that among 200 people polled there would be no preference for any one slogan, then what was the expected frequency for each slogan. A) 25 people B) 50 people C) 100 people D) 200 people
B) 50 people
The following graphs display the data points for two linear correlations. Based on the information provided in these graphs, ____________ displays a negative correlation and _____________displays a stronger correlation. (Graph A has a scatter plot going in a positive direction with a line not quite touching points.) (Graph B has a scatter plot going in a negative direction with a line toing through one point.) A) Graph A; Graph B B) Graph B; Graph A C) Graph A; Graph A D) Graph B; Graph B
B) Graph B; Graph A
What is the key assumption for a chi-square goodness-of-fit test? A) The population is normally distributed. B) Observed frequencies are independently recorded in each cell. C) Expected frequencies are homogeneous. D) all of the above
B) Observed frequencies are independently recorded in each cell.
A local ice cream shop wants to see if they should promote a new swizzleberry swirl or creamsicle flavored drink. In order to determine which one to promote, they took a sample of 80 patrons and asked them to choose which they preferred. The one that is significantly preferred over the other (at a .05 level of significance) will be promoted. It is expected that an equal number of patrons will choose each flavor. Based on the observed frequencies given below, what is the decision for this test? Flavored Drinks Swizzleberry Swirl Creamsicle Flavored Flavored Observed Results 28 52 A) Promote the swizzleberry swirl flavored drink. B) Promote the creamsicle flavored drink. C) Do not promote any flavored drinks. D) There is not enough information to answer this question.
B) Promote the creamsicle flavored drink.
A researcher measures the correlation of the time it take participants to complete two tasks purported to measure the same cognitive skill. Participant times are converted to ranks from fastest to slowest. If (sum of D^2) = 165 and n = 20, then what is the decision for this correlation test? A) Retain the null hypothesis. B) Reject the null hypothesis. C) There is not enough information to answer this question.
B) Reject the null hypothesis.
Which of the following is the assumption that the best way to describe the pattern of data is using a straight line? A) normality B) linearity C) homoscedasticity D) restriction of range
B) linearity
The Spearman rank-order correlation coefficient is a measure of the direction and strength of the linear relationship between two ________ variables. A) nominal B) ordinal C) interval D) ratio
B) ordinal
We compute the frequency expected in each category using known ________ stated in the null hypothesis. A) hypothesis tests B) proportions C) variances D) effect sizes
B) proportions
The Mann-Whitney U test is used as a nonparametric alternative to which parametric test? A) one-sample t-test B) two-independent sample t-test C) related samples t-test D) both A and C
B) two-independent sample t-test
The degrees of freedom for a chi-square test for independence test are A) k - 1 B) n - 1 C) (k1 - 1)(k2 - 1) D) (k - 1)(n - 1)
C) (k1 - 1)(k2 - 1)
The correlation coefficient ranges between ____ and ____. A) 0; +1 B) -1; 0 C) -1; +1 D) -(infinity); +(infinity)
C) -1; +1
A researcher measures the following correlation between number of years of education and life satisfaction: r = +0.08. What is the value of the coefficient of determination? A) 0.08 B) 0.16 C) 0.01 D) 0.11
C) 0.01
A researcher measures the relationship between two variables, X and Y. If SSxy = 340 and SSxSSy = 320,000, then what is the value of the correlation coefficient? A) 0.32 B) 0.34 C) 0.60 D) almost a zero correlation
C) 0.60
A researcher measures the correlation in rankings for a sample of restaurants and consumers' rankings of their favorite restaurants. If (sum of D^2) = 96 and n = 12, then what is the value of the correlation coefficient? A) 0.07 B) 0.34 C) 0.66 D) 0.94
C) 0.66
A researcher measures the relationship between narcissism and willingness to help. If SSxy = 240, SSx = 320, and SSy = 410, then what is the value of the correlation coefficient? A) 0.002 B) 0.02 C) 0.66 D) 0.69
C) 0.66
Which of the following measures of effect size can be reported with a 3 × 4 chi-square test for independence? A) proportion of variance B) the phi coefficient C) Cramer's V D) all of the above
C) Cramer's V
A researcher tests whether job security and life satisfaction are related. In this study, he observes the following frequencies. If he computes a test for independence at a .05 level of significance, then what is the decision for this test? Life Satisfaction Yes No Job Security Yes 14 10 No 12 9 A) Job security and job satisfaction are related. B) Job security and job satisfaction are dependent. C) Job security and job satisfaction are independent. D) Both A and B are appropriate.
C) Job security and job satisfaction are independent.
An unanticipated variable not accounted for in a research study that could be causing or associated with observed changes in one or more measured variables is called A) reverse causality B) restriction of range C) a confound variable D) homoscedasticity
C) a confound variable
A statistical procedure used to describe the strength and direction of the linear relationship between two factors is called A) effect size B) power C) a correlation D) coincidence A statistical procedure used to describe the strength and direction of the linear relationship between two factors is called A) effect size B) power C) a correlation D) coincidence
C) a correlation
Which of the following is the assumption that there is an equal variance of data points dispersed along the regression line? A) normality B) linearity C) homoscedasticity D) restriction of range
C) homoscedasticity
A researcher computes a 4 × 4 chi-square test for independence and estimates the following effect size: V = 0.36. This effect size is A) small B) medium C) large
C) large
We convert r to a t statistic for which of the following correlation tests? A) Pearson B) Spearman C) point-biserial D) phi
C) point-biserial
Which of the following would not be reported for a correlation? A) the sample size B) the coefficient of determination C) the critical values for each test D) the strength and direction of the correlation
C) the critical values for each test
The appropriate correlation coefficient for measuring for the direction and strength of the linear relationship between two dichotomous variables is A) the Spearman rank-order correlation coefficient B) the point-biserial correlation coefficient C) the phi correlation coefficient D) none of the above
C) the phi correlation coefficient
To summarize the chi-square goodness-of-fit test, which of the following is reported? A) test statistic B) p value C) degrees of freedom D) all of the above
D) all of the above
Which of the following is a limitation for interpreting a correlation? A) Correlations do not demonstrate cause-and-effect. B) Outliers can change the direction and/or strength of the correlation. C) Conclusions should not be drawn beyond the range of scores measured. D) all of the above
D) all of the above
Which of the following is an appropriate measure of effect size for a 2 × 2 chi-square test for independence? A) proportion of variance B) the phi coefficient C) Cramer's V D) all of the above
D) all of the above
Many nonparametric tests are called ________ because they make no assumptions regarding the shape of the distribution in the population. A) parametric tests B) skewed-distribution tests C) significance-free tests D) distribution-free tests
D) distribution-free tests
When computing a chi-square goodness-of-fit test, the frequency expected in a given cell should never be less than A) the sample size B) the number of cells C) the frequency observed D) five
D) five
The correlation coefficient is used to measure the ________ and ________ of the linear relationship between two factors. A) date; time B) mean; variance C) significance; effect size D) strength; direction
D) strength; direction
