Exam #4 Stat Methods of Psychology

D) 5.99

D) 5.99

Suppose a correlation is computed in each of two samples. If the value of is the same in each sample, and is larger in Sample 1, then in which sample will the value of the correlation coefficient be larger?

Sample 2

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

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

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

k - 1

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

Observed Results 28 52

promote the creamsicle flavored drink

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

proportions

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)

One nonparametric statistical test is the chi-square test. Name three others.

sign test, Mann-Whitney U test, Wilcoxen signed ranks T test, Kruskal-Wallis H test, Friedman test.

How does the difference between fe and fo influence the outcome of a chi-square test?​

the larger the difference, the larger the value of chi-square, and the greater the likelihood of rejecting the null hypothesis

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

two independent sample t tests

High 32 18

0.52

C) There is not enough information to answer this question.

B) Reject the null hypothesis.

D) 4

D) 4

As the sample size gets larger, what happens to the size of the correlation that is needed for significance?​

It gets smaller

High Income 8 12 28

education and income level are related

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

five

A scatter plot shows data points that are widely scattered around a line that slopes down to the right. Which value would be closest to the correlation for these data?​

-0.40

The correlation coefficient ranges between ____ and ____.

-1; + 1

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

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

.06 (.0625 without rounding)

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

0.20

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

0.60

A researcher reports the following results for a chi-square test: χ2(1) = 5.386, p < .05 (V = 0.224). If this test were a test for independence, then how many groups were observed?

4

Ten years ago, only 15% of the U.S. population consisted of people more than 65 years old. A researcher plans to use a sample of n = 300 people to determine whether the population distribution has changed during the past ten years. If a chi-square test is used to evaluate the data, what is the expected frequency for the older-than-65 category?

45

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 chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into three categories and the second of which is classified into four categories. The chi-square statistic for this test would have a df value equal to ____.​

6

A linear regression equation has b = 3 and a = - 6. What is the predicted value of Y for X = 4?​

6

A set of X and Y scores has MX = 4, SSX = 10, MY = 5, SSY = 40, and SP = 20. What is the regression equation for predicting Y from X?

=2x-3

D) There is not enough information to answer this question.

A) 0.133

D) There is not enough information to answer this question.

A) 0.61

D) Both B and C are appropriate.

A) Education and income level are related.

D) No linear pattern is evident.

A) The more a person works, the more coffee he or she tends to drink.

D) The proportion in each cell is equal to zero.

A) The observed frequencies are independently recorded in each cell.

D) (k - 1)(n - 1)

A) k - 1

D) both variables are on a nominal scale

A) one is continuous, and one is dichotomous

D) 0.35

B) 0.20

D) 0.56

B) 0.28

D) There is not enough information to answer this question.

B) 10.57

D) 8

B) 3

D) 12.59

B) 5.99

D) 200 people

B) 50 people

B) False

B) False

D) Graph B; Graph B

B) Graph B; Graph A

D) all of the above

B) Observed frequencies are independently recorded in each cell.

D) There is not enough information to answer this question.

B) Promote the creamsicle flavored drink.

D) There is not enough information to answer this question.

B) Sample 2

D) that the correlation is due to outliers

B) a stronger relationship between two factors

D) is minimal

B) is greater than four

D) restriction of range

B) linearity

D) ratio

B) ordinal

D) effect sizes

B) proportions

C) no decision was made

B) retain the null hypothesis

D) the larger the level of significance will be

B) the larger the critical value will be

D) (k - 1)(n - 1)

C) (k1 - 1)(k2 - 1)

D) -(infinity); +(infinity)

C) -1; +1

D) 0.11

C) 0.01

D) almost a zero correlation

C) 0.60

D) 0.69

C) 0.66

D) 0.94

C) 0.66

D) all of the above

C) Cramer's V

D) restriction of range

C) Homoscedasticity

D) Both A and B are appropriate.

C) Job security and job satisfaction are independent.

D) all of the above

C) Participants liked the high calorie meal more than was expected.

D) homoscedasticity

C) a confound variable

D) coincidence

C) a correlation

D) restriction of range

C) homoscedasticity

D) it is seven times smaller than the number of cells

C) it is five times larger than the number of cells

D) both A and C

C) related samples t-test

D) the strength and direction of the correlation

C) the critical values for each test

D) none of the above

C) the phi correlation coefficient

Which of the following is a limitation for interpreting a correlation?

Coreelations do not demonstrate cause and effect, outliers can change the direction and or strength of the correlation, conclusions should not be drawn beyond the range of scores measured, (ALL OF THE ABOVE)

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

Cramers V

D) (row total × column total)/grand total

D) (row total x column total)/grand total

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

D) all of the above

D) all of the above

D) both A and B

D) both A and B

D) distribution-free tests

D) distribution-free tests

D) five

D) five

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

D) one-way within-subjects ANOVA

D) one-way within-subjects ANOVA

D) strength; direction

D) strength; direction

For a chi-square test for independence, the expected frequencies for any row are exactly the same as the expected frequencies in every other row.​

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 statisticallya similar to the frequencies expected at each level of the categorical variable.

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 B; Graph A

Give the definition for a "third variable" or confound in correlational research.

It is an unanticipated variable no accounted for in the study that could be causing or correlating with observed changes in one or more other variables.

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.

A researcher obtains a negative value for a chi-square statistic. What can you conclude because the value is negative?​

The researcher made a mistake; the value of the chi-square cannot be negative.

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

A researcher classifies people by gender and by whether or not they routinely watch the evening news on television. For the resulting data, the correct correlation method for measuring the relationship between the two variables would be the phi-coefficient.

True

For a chi-square test, the observed frequencies are obtained from the sample.​

True

The Pearson correlation measures the degree and the direction of the linear relationship between two variables.

True

The Spearman correlation can be +1.00 or 1.00 even when there is no linear relationship between the two variables.

True

The chi-square test for independence uses the same formula for the chi-square statistic as the chi-square test for goodness-of-fit.​

True

The observed frequencies for a chi-square test are always whole numbers (no fractions or decimals).​

True

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

Vary independently

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)

​If there is a positive correlation between X and Y then in the regression equation, Y = bX + a, ____.

b>0

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

A linear regression equation is computed for a sample of n = 13 pairs of X and Y scores. For the analysis of regression testing the significance of the equation, what are the df values for the F-ratio?​

df = 1, 11​

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

direction

Outliers can change the _____ of a correlation.

direction, strength, sign (+, -) (ALL OF THE ABOVE)

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 scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle. For these data, what is the most likely value for the correlation?​

either positive or negative near zero

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

expected

A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable.

false

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

homoscedasticity

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

homoscedasticity

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

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

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

linearity

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

observed frequencies are independently recorded in each cell

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

one tail

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

one way between subjects ANOVA

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

one way within subjects ANOVA

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

related (or dependent or correlated)

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

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

strength, direction

To summarize the chi-square goodness-of-fit test, which of the following is reported?

test statistic, p value, degrees of freedom (ALL OF THE ABOVE)

A researcher conducts two chi-square tests. The 2 × 2 chi-square was χ2 = 3.92. The 2 × 3 chi-square was χ2 = 5.92. Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance?

the 2 x 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 formula for the Spearman correlation coefficient was derived from the formula for _____.

the Pearson correlations coefficient (or just "pearson r")

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

the coefficient of determination

Select the description below that identifies the following correlation: r = .28, p < .01.

the correlation is positive, the correlation is statistically signififgant, the coefficient of determination is 0.8 (ALL OF THE ABOVE)

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

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?

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

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 normality assumption states that the population of X and Y scores form a bivariate ("two variable") normal distribution, such that

the population of X and Y scores are normally distributed, for each X score, the distribution of Y is normally distributed, for each Y score the distribution of X scores is normally distributed (ALL OF THE ABOVE)

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

D) -0.42

A) 0.04

For a linear regression, if X = MX, then the predicted Y value is MY.

True

D) homoscedasticity

B) restriction of range

D) the test statistic

B) the coefficient of determination

D) both B and C

B) the test statistic value is equal to 0

D) Pearson correlation

C) chi-square test

D) both A and C

D) both A and C

For a fixed level of significance, the critical value for chi-square increases as the size of the sample increases.​

False

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 table

The observed frequencies can be summarized,

in a table, in a figure, in the main test (ALL OF THE ABOVE)

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

one is continuos, and one is dichotomous

In the general linear equation, Y = bX + a, what is the value of b called?​

the slope

A researcher obtains a Pearson correlation of r = 0.43 for a sample of n = 20 participants. For a two-tailed test, which of the following accurately describes the significance of the correlation?​

​The correlation is not significant with either α = .05 or α = .01.

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

(k1-1)(k2-1)

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 corect - need to be nominal scale variables)

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 x column total)/grand total

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

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

0.04

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 = 9.06 and = 11, then what is the value of the correlation coefficient?

0.61

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

0.64

A researcher measures the correlation in rankings for a sample of restaurants and consumers' rankings of their favorite restaurants. If = 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 = 240, = 320, and = 410, then what is the value of the correlation coefficient?

0.66

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

1

4. rankings of runners on place (1st-8th) and birth order (1st-8th).

1. Pearson r

4. rankings of runners on place (1st-8th) and birth order (1st-8th).

1. pearson r

A researcher selects a sample of 110 participants and computes the following phi correlation coefficient: = 0.31. What is the value of ?

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

For the linear equation Y = 2X + 4, if X increases by 1 point, how much will Y increase?​

2 points

A set of X and Y scores has SSX = 20, SSY = 10, and SP = 40. What is the slope for the regression equation?​

2.0

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

3

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?

5.99

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.

50 people

D) 80

A) 2

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.

C) There is not enough information to answer this question.

A) Retain the null hypothesis.

B) False

A) True

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

A) the 2 x 2 chi-square

D) none of the above

A) the Spearman correlation coefficient

D) both A and C

B) two-independent sample t-test

D) both A and C

B) vary independently

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

Both A and B ---- increasing the number of cells and increasing the sample size

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

Both A and C

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

Both A and C ----- one samke t test abd related samples t test

D) all of the above

C) chi-square test

C) large

C) large

D) one-way within-subjects ANOVA

C) one-way between-subjects ANOVA

D) phi

C) point-biserial

D) r = +0.88

C) r = -0.90

In a test for significance of a Pearson correlation for a sample of n = 30 individuals, one determines the critical value by using df = 29.​

False

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

False

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

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.

(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 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.

Which of the following is an appropriate measure of effect size for a 2 × 2 chi-square test for independence?

Proportion of variance, the phi coefficient, cramer's V (ALL OF TEH ABOVE)

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

Reject the null hypothesis

For the regression equation, = -2X + 6, what can be determined about the correlation between X and Y?​

The correlation definitely will be negative

A researcher measures IQ and weight for a group of college students. How can you tell whether there is a linear relationship between these two variables?​

Use a scatterplot to assess the linearity of the relationship.

(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 and the other factors could be affected by the first factor, then you could conclude that factor 1 caused the different outcomes in factor 2.

(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.

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

A researcher conducts two chi-square tests. The 2 × 2 chi-square was χ2 = 3.82. The 2 × 3 chi-square was χ2 = 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

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

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

parametric tests

10 10 10

participants liked the high calorie meal more than was expected.

A researcher records the odometer reading and age of used Hondas. What kind of correlation is likely to be obtained for these two variables?​

positive correlation

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

For which of the following correlations would the data points be most widely scattered around the regression line?​ a. ​r = 0.80 b.​r = 0.10 c.​r = 0.99 d.​r = 0.50

r = 0.10

For which of the following correlations would the data points be clustered most closely around a straight line? a.​r = -0.00 b.​r = +0.40 c.​r = -0.10 d.​r = -0.70

r=-0.70

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

reject the null hypothesis

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

retain the null hypothesis

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?

retain the null hypothesis

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

retain the null hypothesis

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

To summarize correlations, we report:

the strength of the correlation, the direction of the correlation, the p value (ALL OF THE ABOVE)

For a positive correlation, decreases in X tend to be accompanied by decreases in Y.

true

If the Pearson correlation between X and Y is r = 0.60, then the regression equation predicts 36% of the variance in the Y scores.

true

It is possible for a regression equation to have none of the actual (observed) data points located on the regression line.

true

Multiple regression involves obtaining the regression equation for predicting the criterion using more than one predictor variable.

true

One characteristic of nonparametric tests is that they make few, if any, assumptions about the populations being investigated.​

true

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

true

For a linear regression equation, the sum of the squared residuals can be computed directly by finding the difference between each Y and its predicted Y, then squaring the difference and adding the squared values. An alternative procedure is to calculate ____.​

​(1 - r2)SSY

A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference among 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.

For a group of graduating college seniors, a researcher records each student's rank in his/her high school graduating class and the student's rank in the college graduating class. Which correlation should be used to measure the relationship between these two variables?​

​Spearman correlation

A Pearson correlation is computed for a sample of n = 18 pairs of X and Y values. What correlations are statistically significant with α = .05, two tails?​

​correlations greater than or equal to 0.468 and correlation less than or equal to -0.468

A researcher used a sample of n = 60 individuals to determine whether there are any preferences among four brands of pizza. Each individual tastes all four brands and selects his/her favorite. If the data are evaluated with a chi-square test for goodness of fit using α = .05, then how large does the chi-square statistic need to be to reject the null hypothesis?​

​greater than 7.81