Exam 4, 311

The degrees of freedom for a chi-square test for independence test are

(k(1) - 1)(k(2) - 1)

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 correct--need to be nominal scale variables)

To compute the expected frequencies for a chi-square test for independence, we use which of the following formulas?

(row total × column total)/grand total

The correlation coefficient ranges between ____ and _____

-1; +1

A researcher measures the following correlation: r = -0.21. What is the value of the coefficient of determination?

0.04

A researcher computes a 4 × 6 chi-square test for independence with a sample of 120 participants, with X(squared) = 14.79. What is the effect size for this result?

0.20

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

0.28

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 M(y1) - M(y2) = 11, then what is the value of the correlation coefficient?

0.61

A 2 × 2 chi-square test for independence has ___ degrees of freedom

1

Which of the following measures of effect size can be reported with a 3 × 4 chi-square test for independence?

Cramer's V

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 Degree Graduate Degree Low Income 22 8 5 High Income 8 12 28

Education and income level are related.

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 in Word Doc.)

Graph B; Graph A

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

Job security and job satisfaction are independent.

(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

What is the key assumption for a chi-square goodness-of-fit test?

Observed frequencies are independently recorded in each cell.

What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement?

Parametric tests are used for interval and ratio data, whereas nonparametric tests are used for nominal and ordinal data.

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 f(o) 6 7 17 f(e) 10 10 10

Participants liked the high calorie meal more than was expected.

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 Flavored Creamsicle Flavored Observed Results 28 52

Promote the creamsicle flavored drink.

A researcher measures the correlation between gender and student aptitude scores from 0 to 100 among 20 participants. If r (pb) = 0.49, then what is the decision for this correlation test?

Reject the null hypothesis

Suppose a correlation is computed in each of two samples. If the value of SS(xy) is the same in each sample, and sqrt. SS(x)SS(y) is larger in Sample 1, then in which sample will the value of the correlation coefficient be larger?

Sample 2

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 in Word Doc.)

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

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.

True

The coefficient of determination is mathematically equivalent to eta-squared.

True

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.

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 confound variable

A statistical procedure used to describe the strength and direction of the linear relationship between two factors is called

a correlation

The correlation coefficient ranges from -1.0 to +1.0, with values closer to ±1.0 indicating

a stronger relationship between two factors

Which of the following is an example of a parametric test?

analysis of variance one-sample t-test Pearson correlation all of the above

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

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?

chi-square test

Which of the following is an example of a nonparametric test?

chi-square test

The sign (+ or -) of a correlation coefficient indicates the________________________________ of a relationship between two factors.

direction

Many nonparametric tests are called ________ because they make no assumptions regarding the shape of the distribution in the population.

distribution-free tests

(4 pts) Draw a scatterplot showing a positive correlation between age and # of emotion-focused goals.

draw one

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

When computing a chi-square goodness-of-fit test, the frequency expected in a given cell should never be less than

five

The assumption that there is an equal variance or scatter of data points dispersed along the regression line is referred to as

homoscedasticity

The degrees of freedom for a chi-square goodness-of-fit test are

k -1

A researcher computes a 4 × 4 chi-square test for independence and estimates the following effect size: V = 0.36. This effect size is

large

The point-biserial correlation coefficient is a measure of the direction and strength of the linear relationship between two variables, where

one is continuous, and one is dichotomous

The Friedman test is used as a nonparametric alternative to which parametric test?

one-way within-subjects ANOVA

The ______________________ correlation coefficient is used to measure the correlation between two dichotomous variables

phi

We convert r to a t statistic for which of the following correlation tests?

point-biserial

Which of the following indicates the strongest correlation?

r = -0.90

When the chi-square test for independence is significant, this indicates that two variables are_______________________

related (or dependent or correlated)

The correlation coefficient is used to measure the ________ and ________ of the linear relationship between two factors

strength; direction

Which of the following would not be reported for a correlation?

the critical values for each test

As a general rule, the larger the degrees of freedom for a chi-square test,

the larger the critical value will be

The appropriate correlation coefficient for measuring for the direction and strength of the linear relationship between two dichotomous variables is

the phi correlation coefficient

The Mann-Whitney U test is used as a nonparametric alternative to which parametric test?

two-independent sample t-test

The denominator of the correlation coefficient measures the extent to which two variables

vary independently

If r = .25, then the coefficient of determination is .= ___________06.

.06 (.0625 without rounding)

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?

0.01

If X (squared)= 5.32 and n = 40, then what is the value of the coefficient of determination?

0.133

A researcher measures the relationship between two variables, X and Y. If SS(xy) = 340 and SS(x)SS(y) = 320,000, then what is the value of the correlation coefficient?

0.60

A researcher measures the correlation in rankings for a sample of restaurants and consumers' rankings of their favorite restaurants. If SUM D(squared)= 96 and n = 12, then what is the value of the correlation coefficient?

0.66

A researcher measures the relationship between narcissism and willingness to help. If SS(xy) = 240, SS(x)= 320, and SS(y) = 410, then what is the value of the correlation

0.66

A researcher selects a sample of 110 participants and computes the following phi correlation coefficient: r(pie)= 0.31. What is the value of S(squared)?

10.57

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?

2

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?

5.99

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?

5.99A 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 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.

50 people

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

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

When the chi-square test for independence is significant, this indicates that there is significant variability between groups

False

A chi-square goodness-of-fit test leads to a decision to retain the null hypothesis. Which of the following correctly explains this decision?

Frequencies observed were statistically similar to the frequencies expected at each level of the categorical variable

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 D (squared)= 165 and n = 20, then what is the decision for this correlation test?

Reject the null hypothesis

A researcher computes the following phi correlation coefficient: r(pie) = 0.42. If the sample size was 20, then what is the decision for this correlation test?

Retain the null hypothesis

A researcher determines that X (squared) = 3.76 to test for significance for a phi correlation coefficient. What was the decision for this phi correlation test?

Retain the null hypothesis

A researcher conducts a chi-square goodness-of-fit test in which k = 3 and X (squared) = 4.32. What is the decision for this test at a .05 level of significance?

Retain the null hypothesis.

The formula for the chi-square test measures the size of the discrepancy between observed and _____________frequencies.

expected

Which of the following is the assumption that there is an equal variance of data points dispersed along the regression line?

homoscedasticity

A researcher can correct for having expected frequencies smaller than five by

increasing the number of cells increasing the sample size both A and B

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

is greater than four

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 variable

One way a researcher can correct for having expected frequencies smaller than five is to increase the sample size such that

it is five times larger than the number of cells

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

Which of the following is the assumption that the best way to describe the pattern of data is using a straight line?

linearity

A researcher conducts two chi-square tests. The 2 × 2 chi-square was X(squared) = 3.82. The 2 × 3 chi-square was X(squared) = 5.02. Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance?

none; both chi-square tests result in a decision to retain the null hypothesis

When finding the critical value in a chi-square distribution, how many tails do you look in for the cutoff?

one tail

The sign test is used as a nonparametric alternative to which parametric test?

one-sample t-test, related samples t-test, both A and C

The Kruskal-Wallis H test is used as a nonparametric alternative to which parametric test?

one-way between-subjects ANOVA

The Spearman correlation coefficient is used to measure the correlation between two variables that are measured on a(n) _______________________ scale.

ordinal

The Spearman rank-order correlation coefficient is a measure of the direction and strength of the linear relationship between two ________ variables.

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

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

We compute the frequency expected in each category using known ________ stated in the null hypothesis

proportions

The Wilcoxon signed-ranks T test is used as a nonparametric alternative to which parametric test?

related samples t-test

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?

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

retain the null hypothesis

(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 computes a 2 × 4 chi-square test for independence. What are the degrees of freedom for this test?

3

A researcher reports the following results for a chi-square test: X(squared) (1) = 5.386, p < .05 (V = 0.224). If this test were a test for independence, then how many groups were observed?

4

A researcher conducts two chi-square tests. The 2 × 2 chi-square was X(squared) = 3.92. The 2 × 3 chi-square was X(squared) = 5.92. Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance?

the 2 × 2 chi-square

The formula for the Spearman correlation coefficient was derived from the formula for________________________.

the Pearson correlation coefficient (or just "Pearson r")

The appropriate correlation coefficient for measuring the direction and strength of the linear relationship between two ranked or ordinal variables is

the Spearman correlation coefficient

The most common measure of effect size for the correlation coefficient is called

the coefficient of determination

If the expected frequencies equal to observed frequencies for a chi-square test for independence, what do we conclude?

the test statistic value is equal to 0

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

Outliers can change the _____ of a correlation.

A) direction B) strength C) sign (+, -) 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

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

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

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

The numerator of the correlation coefficient measures the extent to which two variables

vary together, Covary, both A and C