Two-way Tables (Joint Distributions)

Refer to Khan academy: Two-way tables
Refer to Khan academy: Distributions in two-way tables
Refer to Khan academy: Marginal distribution and conditional distribution

Refer to Mathbitsnotebook: Two-Way Frequency Tables

Definitions

Two-way Table

Two-way Table is a Joint distribution, which rows represent a kind of distribution, columns represent another kind of distribution.

Marginal Distribution

Marginal Distribution is simply an addon to the joint distribution, that as a TOTAL row or column at the margins.

Conditional Distribution

Conditional Distribution is one column(variable) in condition of another variable.

Trends in categorical data

Refer to Khan academy: Analyzing trends in categorical data
Refer to Khan academy: Filling out frequency table for independent events

▶ Practice on Khan academy: Trends in categorical data

Interpret the table:

• Row %: shows how much proportion of the cell is on the Row Total. etc., the cell Pond-Maple is 59.46% of all samples by _pond_.
• Column %: shows how much proportion of the cell is on the Column Total. etc., the cell Pond-Maple is 48.89% of all maples samples.
• Total %: shows how much proportion of the cell is on the Sample Total. etc., the cell Pond-Maple is 27.5% of all samples.

Example

Solve:

• Get the total number of people:

• Get the number of people from California: 500 * 0.5 = 250
• Analyze association. The logic is: The event A & B has association if A takes a big part in B, EVEN IF B only takes a SMALL part in total samples.

Example

Solve:

• The answer is not precise but we’re to guess it precisely.
• Been told those are entirely independent events, so we know that:

The probabilities are P(makes 1st shot) = P(makes 2nd shot), and P(misses 1st shot) = P(misses 2nd shot), regardless whether he makes or misses the 1st shot.

• We could get the “fixed” probability from the _marginal information_:

• And we apply the probability 80% to all “makes shot” cell to get:

Example

Solve:

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