Construct and Interpret Two-Way Tables - 8th Grade Math
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What is a row total in a two-way table?
What is a row total in a two-way table?
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The sum of all frequencies across one row. Shows how many subjects are in that row's category.
The sum of all frequencies across one row. Shows how many subjects are in that row's category.
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Decide if there is association: $P(A\mid B)=0.52$ and $P(A\mid \text{not }B)=0.51$.
Decide if there is association: $P(A\mid B)=0.52$ and $P(A\mid \text{not }B)=0.51$.
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No clear association; the conditional relative frequencies are nearly equal. Similar conditional probabilities (0.52 vs 0.51) suggest independence.
No clear association; the conditional relative frequencies are nearly equal. Similar conditional probabilities (0.52 vs 0.51) suggest independence.
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What does the term frequency mean in a two-way table?
What does the term frequency mean in a two-way table?
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The number of subjects in a cell (a count). Each cell contains how many subjects fall in that category combination.
The number of subjects in a cell (a count). Each cell contains how many subjects fall in that category combination.
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What does the term relative frequency mean in a two-way table?
What does the term relative frequency mean in a two-way table?
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A proportion: $$cell count$ divided by a total (row, column, or grand). Shows what fraction of a total each cell represents.
A proportion: $$cell count$ divided by a total (row, column, or grand). Shows what fraction of a total each cell represents.
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What is the grand total in a two-way table?
What is the grand total in a two-way table?
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The total number of subjects in the entire table. Sum of all cells; represents all subjects surveyed.
The total number of subjects in the entire table. Sum of all cells; represents all subjects surveyed.
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What is a column total in a two-way table?
What is a column total in a two-way table?
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The sum of all frequencies down one column. Shows how many subjects are in that column's category.
The sum of all frequencies down one column. Shows how many subjects are in that column's category.
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What formula gives a row relative frequency for a cell?
What formula gives a row relative frequency for a cell?
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$\frac{\text{cell count}}{\text{row total}}$. Shows what fraction of that row the cell represents.
$\frac{\text{cell count}}{\text{row total}}$. Shows what fraction of that row the cell represents.
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Identify the correct step to construct a two-way table from paired survey responses.
Identify the correct step to construct a two-way table from paired survey responses.
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Tally each subject once in the cell matching both category choices. Each subject goes in exactly one cell based on their two responses.
Tally each subject once in the cell matching both category choices. Each subject goes in exactly one cell based on their two responses.
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Choose the correct conclusion if row relative frequencies are the same in every row.
Choose the correct conclusion if row relative frequencies are the same in every row.
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No association is suggested between the two categorical variables. Equal row proportions mean the variables are independent.
No association is suggested between the two categorical variables. Equal row proportions mean the variables are independent.
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Decide if there is association: $P(\text{Chores}\mid\text{Curfew})=0.70$ and $P(\text{Chores}\mid\text{No Curfew})=0.30$.
Decide if there is association: $P(\text{Chores}\mid\text{Curfew})=0.70$ and $P(\text{Chores}\mid\text{No Curfew})=0.30$.
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Yes; the conditional relative frequencies are different. Different conditional probabilities (0.70 vs 0.30) indicate association.
Yes; the conditional relative frequencies are different. Different conditional probabilities (0.70 vs 0.30) indicate association.
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In a $2\times 2$ table, identify the cell for “Curfew: Yes” and “Chores: No.”
In a $2\times 2$ table, identify the cell for “Curfew: Yes” and “Chores: No.”
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The intersection of the “Curfew: Yes” row and “Chores: No” column. Find where the row and column categories meet.
The intersection of the “Curfew: Yes” row and “Chores: No” column. Find where the row and column categories meet.
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Find the joint relative frequency: cell count $18$, grand total $60$.
Find the joint relative frequency: cell count $18$, grand total $60$.
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$\frac{18}{60}=0.3$. Divide cell count by grand total: $\frac{18}{60}=\frac{3}{10}=0.3$.
$\frac{18}{60}=0.3$. Divide cell count by grand total: $\frac{18}{60}=\frac{3}{10}=0.3$.
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Find the column relative frequency: cell count $9$, column total $36$.
Find the column relative frequency: cell count $9$, column total $36$.
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$\frac{9}{36}=0.25$. Divide cell count by column total: $\frac{9}{36}=\frac{1}{4}=0.25$.
$\frac{9}{36}=0.25$. Divide cell count by column total: $\frac{9}{36}=\frac{1}{4}=0.25$.
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Find the row relative frequency: cell count $12$, row total $30$.
Find the row relative frequency: cell count $12$, row total $30$.
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$\frac{12}{30}=0.4$. Divide cell count by row total: $\frac{12}{30}=\frac{2}{5}=0.4$.
$\frac{12}{30}=0.4$. Divide cell count by row total: $\frac{12}{30}=\frac{2}{5}=0.4$.
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Which comparison best checks association: row relative frequencies or only raw counts?
Which comparison best checks association: row relative frequencies or only raw counts?
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Row or column relative frequencies (not raw counts alone). Relative frequencies reveal patterns; counts alone can mislead.
Row or column relative frequencies (not raw counts alone). Relative frequencies reveal patterns; counts alone can mislead.
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Identify the meaning of the conditional relative frequency $P(A\mid B)$ in a two-way table.
Identify the meaning of the conditional relative frequency $P(A\mid B)$ in a two-way table.
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The relative frequency of $A$ within the group that has $B$. Conditional probability: proportion of $A$ given $B$ occurred.
The relative frequency of $A$ within the group that has $B$. Conditional probability: proportion of $A$ given $B$ occurred.
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What formula gives a marginal relative frequency for a row or column total?
What formula gives a marginal relative frequency for a row or column total?
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$\frac{\text{row or column total}}{\text{grand total}}$. Shows what fraction of all subjects are in that category.
$\frac{\text{row or column total}}{\text{grand total}}$. Shows what fraction of all subjects are in that category.
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What is a two-way table used for in bivariate categorical data?
What is a two-way table used for in bivariate categorical data?
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A table that shows counts for two categorical variables at once. Displays frequencies for two variables simultaneously.
A table that shows counts for two categorical variables at once. Displays frequencies for two variables simultaneously.
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What formula gives a joint relative frequency for a cell?
What formula gives a joint relative frequency for a cell?
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$\frac{\text{cell count}}{\text{grand total}}$. Shows what fraction of all subjects the cell represents.
$\frac{\text{cell count}}{\text{grand total}}$. Shows what fraction of all subjects the cell represents.
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What formula gives a column relative frequency for a cell?
What formula gives a column relative frequency for a cell?
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$\frac{\text{cell count}}{\text{column total}}$. Shows what fraction of that column the cell represents.
$\frac{\text{cell count}}{\text{column total}}$. Shows what fraction of that column the cell represents.
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Which relative frequencies help you compare groups: row relative or overall relative?
Which relative frequencies help you compare groups: row relative or overall relative?
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Row or column relative frequencies (conditional relative frequencies). Conditional frequencies reveal group differences.
Row or column relative frequencies (conditional relative frequencies). Conditional frequencies reveal group differences.
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Decide association: $P(\text{chores}|\text{curfew})=0.70$ and $P(\text{chores}|\text{no curfew})=0.30$.
Decide association: $P(\text{chores}|\text{curfew})=0.70$ and $P(\text{chores}|\text{no curfew})=0.30$.
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Yes, there is evidence of association. Large difference (0.70 vs 0.30) indicates association.
Yes, there is evidence of association. Large difference (0.70 vs 0.30) indicates association.
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Find the overall relative frequency: cell = $9$, grand total = $60$.
Find the overall relative frequency: cell = $9$, grand total = $60$.
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$\frac{9}{60}=0.15$. Divide cell count by grand total.
$\frac{9}{60}=0.15$. Divide cell count by grand total.
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What is the meaning of a column relative frequency in words?
What is the meaning of a column relative frequency in words?
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The percent of a column category that falls in a row category. Given the column, what percent is in this row.
The percent of a column category that falls in a row category. Given the column, what percent is in this row.
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Compute $P(\text{chores}|\text{curfew})$: chores and curfew $=24$, curfew total $=40$.
Compute $P(\text{chores}|\text{curfew})$: chores and curfew $=24$, curfew total $=40$.
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$\frac{24}{40}=0.6$. Divide joint count by curfew total.
$\frac{24}{40}=0.6$. Divide joint count by curfew total.
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What is the meaning of a row relative frequency in words?
What is the meaning of a row relative frequency in words?
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The percent of a row category that falls in a column category. Given the row, what percent is in this column.
The percent of a row category that falls in a column category. Given the row, what percent is in this column.
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Which comparison tests if curfew is associated with chores: $P(\text{chores}|\text{curfew})$ vs $P(\text{chores}|\text{no curfew})$?
Which comparison tests if curfew is associated with chores: $P(\text{chores}|\text{curfew})$ vs $P(\text{chores}|\text{no curfew})$?
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Compare $P(\text{chores}|\text{curfew})$ and $P(\text{chores}|\text{no curfew})$. Compares chore rates between curfew groups.
Compare $P(\text{chores}|\text{curfew})$ and $P(\text{chores}|\text{no curfew})$. Compares chore rates between curfew groups.
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Find the row relative frequency: cell $=18$, row total $=30$.
Find the row relative frequency: cell $=18$, row total $=30$.
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$\frac{18}{30}=0.6$. Divide cell count by row total.
$\frac{18}{30}=0.6$. Divide cell count by row total.
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What is a column total (marginal frequency) in a two-way table?
What is a column total (marginal frequency) in a two-way table?
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The total count down a column for one category. Sums all values in that column.
The total count down a column for one category. Sums all values in that column.
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What is a relative frequency in a two-way table?
What is a relative frequency in a two-way table?
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A proportion: $ rac{\text{part}}{\text{whole}}$. Converts counts to proportions for comparison.
A proportion: $ rac{\text{part}}{\text{whole}}$. Converts counts to proportions for comparison.
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