Chi–Squares
In conducting a chi-square test for goodness of fit using a two-way table, why is considering the variability around the expected counts crucial?
To ensure each variable has at least one category with zero frequency.
To identify which variable has greater predictive power over the other.
To evaluate whether the differences between observed and expected counts are statistically significant.
To calculate the total sum of squares for all categories combined.
How would you interpret an interaction term that has been added into a logistic regression model analyzing categorical data from a two-way table with sufficient sample sizes?
Interaction terms indicate redundancy among predictors, which should be removed.
The interaction term signifies whether there's an effect modification between predictors on the response.
Adding an interaction term always increases model accuracy without affecting model interpretation.
The inclusion of interaction terms implies full independence among all predicting variables.
A survey was conducted to examine the preference for different smartphone brands among three age groups: teenagers (13-19 years), young adults (20-30 years), and adults (31-50 years). 50 teenagers preferred Apple, 30 teenagers preferred Samsung, 60 young adults preferred Apple, 40 young adults preferred Samsung, 40 adu...
50
44
47
45
If a researcher uses expected counts to assess homogeneity across groups in a two-way table but observes some expected counts below 5, how might this affect their conclusions?
It ensures more accurate results due to smaller count sizes.
It does not affect conclusions as chi-square is robust to such deviations.
It may inflate Type I error rates, falsely suggesting non-homogeneity.
It reduces Type II error rates by increasing sensitivity.
Which measurement would NOT be used to examine variability among expected counts within cells?
Correlation coefficient measures variance among expected counts in categorical data.
Standard deviation describes the amount of spread around the mean of observed counts.
Variance effectively summarizes the overall amount of spread in counted data.
Interquartile range (Q) compares the middle portion of frequencies between categories.
When researchers divide the population into groups based on characteristics and then randomly select from each group, they are using which method?
Cluster sampling
Simple random sampling
Stratified random sampling
Convenience sampling
Researchers investigated the relationship between gender (male and female) and hair color (blonde and brunette). There are 30 male blondes, 45 male brunettes, 20 female blondes, and 35 female brunettes. What is the table total?
4
130
55
75

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What statistic measures center in a single categorical variable's distribution presented in a two-way table?
Mean, or arithmetic average of values.
Median, or middle value when data are ordered.
Mode, or most frequently occurring category.
Range, or difference between maximum and minimum values.
Which phrase best describes "expected frequency" in the context of a contingency table?
Actual count observed from collected data.
Maximum value found across all categories.
Minimum value necessary for statistical significance.
Predicted number based on probability theory.
What challenge is presented by having all expected frequencies exceed five but one or two expected frequencies below five in a chi-square test for homogeneity?
One boosted power of the test due to larger sample size in certain categories.
Negated effects of outlier cells through liberty adjustments in other cells.
Increased potential for violating the test's assumptions leading to questioning validity of results.
Minimal impact, noteworthy as long as most frequencies are above five.