Question 1

In chi-square analysis, degrees of freedom provide a way of adjusting for:&#10;A) the size of the research sample.&#10;B) the number of cells that contribute to the chi-square value.&#10;C) the difference between observed and expected frequencies.&#10;D) the difference between nominal and ordinal level measurement.

Accepted Answer

Degrees of freedom in chi-square analysis adjust for the number of cells that contribute to the chi-square value. It calculates the number of independent pieces of information in the data set, which helps in determining the appropriate critical value of chi-square. It does not adjust for the size of the research sample, difference between observed and expected frequencies, or nominal and ordinal level measurement.

Question 2

When conducting chi-square analysis, &#34;collapsing&#34; refers to:&#10;A) adding one or more additional variables to the analysis.&#10;B) combining cells to be able to meet the requirements for using the chi-square formula.&#10;C) combining the expected frequencies and the observed frequencies in each cell.&#10;D) calculating the mean for the observed and expected frequencies for each cell.

Accepted Answer

Collapsing refers to combining cells in a contingency table to meet the requirements for using the chi-square formula. This is typically done when there are too many cells with expected frequencies less than 5. By collapsing cells, we can increase the expected frequencies and ensure the validity of the chi-square test.

Question 3

In reporting the results of chi-square analysis, it is a good idea to also report one or more measures of association such as Yules Q or phi. What additional information do they give the reader of a research report?

A) The probability that sampling error may have produced a relationship between variables.
B) The probability that sampling bias may have produced a relationship between variables.
C) An estimate of the strength of the relationship between variables.
D) all of the above

Accepted Answer

Measures of association like Yules Q or phi provide information about the strength of the relationship between variables, which is important in helping readers understand the practical significance of the statistical significance found through chi-square analysis. They do not provide information about the likelihood of sampling error or bias.

Question 4

In chi-square analysis, the numbers that best reflects the null hypothesis are the:&#10;A) column totals.&#10;B) row totals.&#10;C) observed frequencies.&#10;D) expected frequencies.

Accepted Answer

In chi-square analysis, the null hypothesis assumes that there is no significant difference between the observed frequencies and the expected frequencies. Therefore, the numbers that best reflect the null hypothesis are the expected frequencies. The column and row totals are simply sums and do not provide information about the expected values. The observed frequencies are the actual values that were observed in the data, and these may or may not align with the expectations under the null hypothesis.

Question 5

If the requirements for use of chi-square cannot be met, what statistical test can be substituted for it?&#10;A) the median test&#10;B) McNemar's test&#10;C) Fisher's exact&#10;D) Cramer's V

Accepted Answer

If the assumptions of the chi-square test cannot be met, Fisher's exact test can be used as an alternative. This test can be used when the sample sizes are small or when one or more expected cell frequencies are less than 5. The test is based on the exact probabilities of observing the observed data or more extreme data if the null hypothesis is true. In contrast, chi-square relies on an approximation of the distribution of the test statistic.

Question 6

A dummy table uses asterisks to indicate where there will be disproportionately large frequencies if:&#10;A) requirements for using chi-square cannot be met.&#10;B) there is support for a one-tailed research hypothesis.&#10;C) there is support for a two-tailed research hypothesis.&#10;D) there is support for the null research hypothesis.

Accepted Answer

A dummy table is used to predict expected frequencies under a null hypothesis. If there is support for a one-tailed research hypothesis, we can expect that disproportionately large frequencies will occur in one direction. Thus, we can use a dummy table to test and support our one-tailed research hypothesis.

Question 7

Chi-square determines if there is support for a relationship between variables by comparing:&#10;A) a sample mean with a population mean.&#10;B) the mean of two research samples.&#10;C) observed frequencies and expected frequencies.&#10;D) observed frequencies and degrees of freedom.

Accepted Answer

Chi-square test compares observed frequencies with expected frequencies to determine if there is a significant relationship between two variables. It is commonly used in hypothesis testing and analysis of categorical data.

Question 8

Chi-square is a test for between variables.&#10;A) cause and effect.&#10;B) correlation.&#10;C) association.&#10;D) all of the above

Accepted Answer

Chi-square is a test for association, meaning it determines whether there is a relationship between two variables without implying causation or directionality. While it can be used to determine correlation, it cannot prove cause and effect.

Question 9

How many degrees of freedom are there in a 2 X 3 crosstabulation table?&#10;A) 6&#10;B) 3&#10;C) 2&#10;D) 1

Accepted Answer

A 2 X 3 crosstabulation table has two rows and three columns, and it has one degree of freedom, which is calculated as the number of cells minus one. Therefore, the number of degrees of freedom in a 2 X 3 crosstabulation table is (2-1) x (3-1) = 2.

Question 10

When conducting chi-square analysis, it is possible to examine the effect of a third, control variable by using:&#10;A) the median test.&#10;B) McNemar's test.&#10;C) multiple crosstabulation tables.&#10;D) Lambda.

Accepted Answer

Multiple crosstabulation tables can be used to analyze the effect of a control variable in chi-square analysis. This involves creating separate crosstabulation tables for each level of the control variable and comparing the results across the tables to identify any patterns or trends. The median test is not applicable to chi-square analysis, McNemar's test is used to analyze paired data, and Lambda is a measure of association that does not specifically address control variables.

Question 11

When the effect of a control variable is examined:&#10;A) the relationship between the independent and dependent variables may be stronger.&#10;B) the relationship between the independent and dependent variables may be weaker.&#10;C) the relationship between the independent and dependent variables may be unchanged.&#10;D) all of the above

Accepted Answer

The answer of When the effect of a control variable...

Question 12

When using chi-square, statistically significant but very weak relationships between variables are likely to occur if:&#10;A) samples sizes are large.&#10;B) sample sizes are small.&#10;C) the independent variable contains many different value categories.&#10;D) the dependent variable contains many different value categories.

Accepted Answer

The answer of When using chi-square, statistically significant but very...

Question 13

The Yates correction factor for continuity is a mathematical correction that is made to the chi-square formula when:&#10;A) the sample size is very large.&#10;B) the sample size is small.&#10;C) there are only four cells in the crosstabulation table.&#10;D) The observed frequencies in one or more cells is less than 5.

Accepted Answer

The answer of The Yates correction factor for continuity is...

Question 14

Should a researcher ever use chi-square to examine the relationship between two variables that are interval level and normally distributed?&#10;A) Yes, since chi-square can be computed with any level of data.&#10;B) Yes, since it can produce a significant saving in data analysis time.&#10;C) Yes, since it is more powerful than tests designed for use with higher levels of level.&#10;D) No, because it wastes the available precision of measurement, and can result in a Type II error.

Accepted Answer

The answer of Should a researcher ever use chi-square to...

Question 15

What is a requirement for the use of chi-square?&#10;A) a 2 X 2 cross tabulation table.&#10;B) an expected frequency of 5 or more in at least 80% of the cells.&#10;C) an observed frequency of 5 or more in at least 80% of the cells.&#10;D) a sample size of at least 100.

Accepted Answer

The answer of What is a requirement for the use...

Deck 8: The Chi-Square Test of Association Between Variables