Statistics Flashcards: Summarizing Categorical Data Two Way Tables

What this deck covers

This deck focuses on Summarizing Categorical Data Two Way Tables, giving you a quick way to review the definitions, rules, and examples that matter most for Statistics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: State the formula for a marginal relative frequency for row $i$.

Answer: $\frac{\text{row total } i}{\text{grand total}}$. Shows what proportion of all data is in that row.

Flashcard 2: What is the joint relative frequency for a cell with count $n_{ij}$ and grand total $N$?

Answer: $\frac{n_{ij}}{N}$. Divide the cell count by grand total for proportion in both categories.

Flashcard 3: State the formula for a conditional relative frequency of column $j$ given row $i$.

Answer: $\frac{\text{cell}(i,j)}{\text{row total } i}$. Shows distribution of columns within a specific row.

Flashcard 4: What is the correct comparison to check association using conditional relative frequencies?

Answer: Compare $P(A\mid B_1)$ to $P(A\mid B_2)$ (and other $B$ categories). Different conditional probabilities indicate association between variables.

Flashcard 5: What is the marginal relative frequency for a row total $n_{i\cdot}$ with grand total $N$?

Answer: $\frac{n_{i\cdot}}{N}$. Divide row total by grand total for proportion in that row category.

Flashcard 6: Identify the meaning of $P(A)$ in a two-way table context.

Answer: The marginal proportion for category $A$ (row or column total over grand total). Represents the overall probability of event $A$ occurring.

Flashcard 7: What is the sum of all joint relative frequencies in a complete two-way table?

Answer: $1$. All proportions must sum to the whole.

Flashcard 8: Find the joint relative frequency: cell count $12$, grand total $80$.

Answer: $\frac{12}{80}=0.15$. Apply the joint relative frequency formula.

Flashcard 9: What is the conditional relative frequency of column category $C_j$ given row category $R_i$?

Answer: $\frac{n_{ij}}{n_{i\cdot}}$. Divide cell count by row total for proportion within that row.

Flashcard 10: What is a marginal frequency in a two-way table?

Answer: A row total or column total (a total along the margin). Found at the edges where row/column totals are displayed.

Flashcard 11: What is a correct interpretation of a conditional relative frequency such as $\frac{n_{ij}}{n_{i\cdot}}$?

Answer: Among those in $R_i$, the proportion who are also in $C_j$. Conditional restricts to a subset before calculating proportion.

Flashcard 12: Identify the denominator for $P(A\mid B)$ when computed from a two-way table.

Answer: The total count (or total proportion) for category $B$. Condition on $B$ means we only consider those in category $B$.

Flashcard 13: What is a correct interpretation of a marginal relative frequency such as $\frac{n_{i\cdot}}{N}$?

Answer: The proportion of all individuals in row category $R_i$. Marginal ignores the other variable and gives overall proportion.

Flashcard 14: What pattern in conditional relative frequencies suggests an association?

Answer: Conditional relative frequencies differ noticeably between groups. Different distributions indicate dependence between variables.

Flashcard 15: Find the marginal relative frequency for a row total $18$ when the grand total is $72$.

Answer: $\frac{18}{72}=0.25$. Marginal relative frequency equals margin total divided by grand total.

Flashcard 16: What is a two-way frequency table used to display for two categorical variables?

Answer: Counts for each category combination (rows and columns) and totals. Two-way tables organize data by two categorical variables simultaneously.

Flashcard 17: What is a correct interpretation of a joint relative frequency such as $\frac{n_{ij}}{N}$?

Answer: The proportion of all individuals in both categories $R_i$ and $C_j$. Joint means the proportion satisfying both conditions simultaneously.

Flashcard 18: What is a two-way frequency table used to summarize?

Answer: Counts for two categorical variables, organized by rows and columns. Two-way tables display relationships between two categorical variables.

Flashcard 19: Find the joint relative frequency for the cell count $12$ when the grand total is $60$.

Answer: $\frac{12}{60}=0.20$. Joint relative frequency equals cell count divided by grand total.

Flashcard 20: Identify the meaning of $P(A\cap B)$ in a two-way table context.

Answer: The joint proportion in the cell where $A$ and $B$ occur together. Represents the probability of both events occurring together.

Flashcard 21: What condition suggests no association between two categorical variables in a two-way table?

Answer: Conditional relative frequencies are (approximately) equal across groups. Independence means conditioning doesn't change the proportions.

Flashcard 22: Find the marginal relative frequency: row total $30$, grand total $120$.

Answer: $\frac{30}{120}=0.25$. Divide the row total by the grand total.

Flashcard 23: What is the conditional relative frequency of row category $R_i$ given column category $C_j$?

Answer: $\frac{n_{ij}}{n_{\cdot j}}$. Divide cell count by column total for proportion within that column.

Flashcard 24: In a two-way table, what is the sum of the relative frequencies within a fixed row when row-conditional frequencies are used?

Answer: $1$. Row-conditional frequencies distribute the row total completely.

Flashcard 25: Identify whether variables are associated if $P(A\mid B_1)=0.40$ and $P(A\mid B_2)=0.10$.

Answer: Associated (conditional relative frequencies differ substantially). Large difference (0.40 vs 0.10) indicates strong association.

Flashcard 26: What is the marginal frequency for a row or column in a two-way table?

Answer: The row total or column total (a total along the margin). Marginal frequencies appear at the edges (margins) of the table.

Flashcard 27: What is a relative frequency?

Answer: A proportion: $frac{\text{count}}{\text{total}}$. Converts counts to proportions for comparison.

Flashcard 28: State the formula for a joint relative frequency for cell $(i,j)$.

Answer: $\frac{\text{cell}(i,j)}{\text{grand total}}$. Divides the cell count by the grand total.

Flashcard 29: Which phrase best matches $P(A\mid B)$ in a two-way table context?

Answer: The proportion in category $A$ among those in category $B$. Conditional probability restricts to those already in category $B$.

Flashcard 30: State the formula for a conditional relative frequency of row $i$ given column $j$.

Answer: $\frac{\text{cell}(i,j)}{\text{column total } j}$. Shows distribution of rows within a specific column.

Flashcard 31: What condition indicates no association between two categorical variables using conditional relative frequencies?

Answer: Conditional relative frequencies are (approximately) the same across groups. Independence means the condition doesn't affect the distribution.

Flashcard 32: What is the grand total in a two-way table?

Answer: The sum of all cell frequencies in the table. Add all interior cells to get the overall total.

Flashcard 33: Identify the association: $P(\text{Yes}\mid A)=0.70$ and $P(\text{Yes}\mid B)=0.20$.

Answer: Association is suggested because the conditional proportions differ. Large difference (0.70 vs 0.20) indicates variables are related.

Flashcard 34: Find and correct the formula error: joint relative frequency written as $\frac{n_{ij}}{n_{i\cdot}}$.

Answer: Correct joint relative frequency: $\frac{n_{ij}}{N}$. Joint uses grand total $N$, not row total $n_{i\cdot}$, as denominator.

Flashcard 35: Which denominator is used for $P(A\mid B)$ in a two-way table?

Answer: The total for category $B$ (the given condition). Conditional probability uses the condition's total as denominator.

Flashcard 36: Identify whether variables show little association if $P(A\mid B_1)=0.33$ and $P(A\mid B_2)=0.34$.

Answer: Little to no association (conditional relative frequencies are similar). Nearly equal values (0.33 vs 0.34) suggest independence.

Flashcard 37: Find $P(\text{Yes}\mid\text{Group A})$: Yes in Group A $18$, Group A total $60$.

Answer: $\frac{18}{60}=0.30$. Divide Yes count by Group A total for conditional probability.

Flashcard 38: Find the conditional relative frequency $P(C_1\mid R_2)$ if $n_{21}=9$ and $n_{2\cdot}=30$.

Answer: $\frac{9}{30}=0.30$. Conditional divides cell count by the conditioning category's total.