Chi-Square Tests and Contingency Tables MCQs 2026

Phi coefficient is special case of association measure for

1. A10×10 tables only✓
2. Bcontinuous variables✓
3. Cpaired t tests✓
4. D2×2 tables✓

Cramér's V measures

1. Aonly Type I error✓
2. Bonly expected counts✓
3. Cstrength of association in contingency tables✓
4. Donly regression R²✓

Simpson's paradox can appear in

1. Aonly continuous regression✓
2. Bcontingency tables when marginal and conditional associations differ✓
3. Conly one cell tables✓
4. Donly goodness of fit✓

Likelihood-ratio chi-square G² is

1. Aan alternative statistic that also approaches χ² distribution asymptotically✓
2. Balways negative✓
3. Cequal to t² always✓
4. Dunrelated to contingency tables✓

If all Oi equal Ei exactly, χ² equals

1. A1✓
2. Bdf✓
3. Cundefined✓
4. D0✓

For 4×3 contingency table, minimum df is

1. A5✓
2. B11✓
3. C6✓
4. D2✓

Chi-square test is classified as

1. Aa test on paired normal means only✓
2. Ba test on categorical/count data✓
3. Conly for regression slopes✓
4. Donly for time series trend✓

Expected counts under independence sum to

1. Azero✓
2. Beach Oi✓
3. Cdf✓
4. Dgrand total n in the full table✓

Rejecting independence implies

1. Acausation is proven✓
2. Bevidence of association between the two categorical variables✓
3. Cmeans are different✓
4. Dvariances differ✓

Goodness-of-fit to binomial with unknown p estimates p from data, reducing df by

1. A0✓
2. B1✓
3. C2✓
4. Dk✓

When r = 1 or c = 1, independence test is

1. Adf = 0 still valid✓
2. Bχ² = 0 always✓
3. Cuse paired t✓
4. Dnot applicable — need at least 2×2✓

Contribution of one cell to χ² is

1. A(Oi−Ei)²/Ei✓
2. BOi·Ei✓
3. C(Oi−Ei)✓
4. D√Ei only✓

Pearson chi-square requires

1. Arandom sampling and mutually exclusive categories✓
2. Bnormal distribution of each cell✓
3. Cequal variances of means✓
4. Dpaired differences normal✓

In 5×2 table, df for independence equals

1. A9✓
2. B5✓
3. C4✓
4. D1✓

Larger discrepancy between O and E produces

1. Asmaller χ²✓
2. Bdf = 0✓
3. Cautomatic acceptance✓
4. Dlarger χ² value✓

χ² statistic cannot be negative because

1. AOi are always negative✓
2. Bit sums squared standardized differences✓
3. CEi are zero always✓
4. Ddf is negative✓

Pooling adjacent categories may be done when

1. AEi are all large✓
2. Bexpected counts are too small to meet chi-square rules✓
3. Cdf is already maximum✓
4. DH0 is certainly true✓

Chi-square homogeneity test compares

1. Adistribution of a categorical variable across several populations✓
2. Bmeans of normal variables only✓
3. Cvariances only✓
4. Dcorrelation only✓

McNemar's test applies to

1. Apaired nominal data in 2×2 table (before–after)✓
2. Bindependent two samples proportion z-test✓
3. Cr×c independence with large n✓
4. Dgoodness of fit to normal✓

Fisher's exact test is used for

1. Alarge r×c tables always✓
2. Bcontinuous normal data✓
3. C2×2 tables with small expected counts✓
4. Dpaired t situations✓

Standardized residual for cell (i,j) is approximately

1. AOi−Eij without square root✓
2. B(Oi − Eij)/√Eij✓
3. CEij/Oi✓
4. Dχ²/df✓

Test of independence H0 states

1. Aequal means across groups✓
2. Bvariance ratio equals 1✓
3. Cπ = 0.5✓
4. Dno association between row and column variables✓

For goodness of fit to equally likely k categories, each Ei equals

1. An·pi with unknown pi✓
2. BOi✓
3. Cn/k✓
4. Dk/n✓

Chi-square distribution is

1. Asymmetric like normal always✓
2. Bnegative for large df✓
3. Cright-skewed and defined for positive values only✓
4. Didentical to t✓

Marginal totals in contingency table are

1. Aonly diagonal cells✓
2. Bonly χ² statistic✓
3. Conly expected counts✓
4. Drow sums and column sums✓

Observed frequencies in contingency table are

1. Aalways equal to expected under H0✓
2. Bthe p-value✓
3. Cthe actual sample counts in each cell✓
4. Dthe degrees of freedom✓

If χ² calculated exceeds χ²_{α, df}, decision at level α is

1. Afail to reject always✓
2. Baccept with certainty✓
3. Cuse t-test instead✓
4. Dreject H0 of independence (or goodness of fit)✓

Yates continuity correction for 2×2 tables

1. Aadds 1 to every cell✓
2. Bdoubles all df✓
3. Creplaces χ² with F✓
4. Dsubtracts 0.5 from |Oi−Ei| before squaring (in standard formula)✓

Chi-square approximation is unreliable when

1. Aall Ei exceed 100✓
2. Bmany expected cell counts are less than 5✓
3. Cn is large with adequate Ei✓
4. Donly r = 2✓

A 3×4 contingency table has df for independence test equal

1. A6✓
2. B11✓
3. C7✓
4. D3✓

A 2×2 contingency table for independence has

1. A1 degree of freedom✓
2. B0✓
3. C2✓
4. D3✓

Expected frequency under independence in cell (i,j) is

1. AOi only✓
2. B(row i total × column j total) / grand total✓
3. Crow total only✓
4. Dcolumn total − row total✓

Chi-square test of independence in an r×c contingency table has df

1. Ar + c − 1✓
2. Brc − 1✓
3. Cn − 1✓
4. D(r − 1)(c − 1)✓

In a goodness-of-fit test with k categories, df equal

1. Ak − 1 − (number of parameters estimated from data)✓
2. Bk✓
3. Ck + 1✓
4. Dn − 1 always✓

Goodness-of-fit test evaluates whether

1. Atwo categorical variables are independent only✓
2. Bsample data conform to a specified theoretical distribution✓
3. Cmeans of two groups are equal✓
4. Dσ² is zero✓

Pearson chi-square statistic for goodness of fit is

1. Aχ² = Σ[(Oi − Ei)²/Ei]✓
2. BΣ(Oi·Ei)✓
3. CΣ(Oi−Ei)✓
4. DOi/Ei only✓

χ²_{0.05, 1} is approximately

1. A1.96✓
2. B6.635✓
3. C3.841✓
4. D0✓

For testing Poisson goodness of fit, cells with small λ may need

1. Acombining categories to ensure adequate Ei✓
2. Bignoring df✓
3. Cusing z-test on means only✓
4. Ddropping χ²✓

χ² test p-value is area to the right of observed χ² under

1. Anormal with n−1 df✓
2. Bt distribution always✓
3. Cχ² distribution with appropriate df✓
4. Duniform✓

Before chi-square, categories should be

1. Aoverlapping to boost n✓
2. Bwithout totals✓
3. Cmutually exclusive and collectively exhaustive✓
4. Dalways continuous✓