(a) Construct a frequency marginal distribution. (b)...

(a) Construct a frequency marginal distribution. (b) Construct a relative frequency marginal distribution. (c) Construct a conditional distribution by x. (d) Draw a bar graph of the conditional distribution found in part (c). $$\begin{equation}\begin{array}{llll} & x_{1} & x_{2} & x_{3} \\\hline y_{1} & 20 & 25 & 30 \\\hline y_{2} & 30 & 25 & 50\end{array}\end{equation}$$

(a) Construct a frequency marginal distribution.
(b) Construct a relative frequency marginal distribution.
(c) Construct a conditional distribution by x.
(d) Draw a bar graph of the conditional distribution found in part (c).
$$\begin{equation}\begin{array}{llll} & x_{1} & x_{2} & x_{3} \\\hline y_{1} & 20 & 25 & 30 \\\hline y_{2} & 30 & 25 & 50\end{array}\end{equation}$$

Key Concepts

Conditional Distribution

A conditional distribution displays the frequency or relative frequency of one variable conditioned on a specific value or category of another variable. It is computed by focusing on a subset of the data where the conditioning event has occurred, and it reveals how the other variable is distributed within that subset, thereby providing insights into potential relationships between the variables.

Bar Graph Representation

A bar graph is a visual tool used to represent categorical data through bars where the height (or length) of each bar corresponds to the frequency or relative frequency of the category it represents. When depicting a conditional distribution, bar graphs effectively illustrate differences and patterns within groups by comparing the set of bars for distinct conditions side by side.

Frequency Marginal Distribution

A frequency marginal distribution is a summary of a two-way table where the totals are calculated for each row or column by summing the frequencies across the other variable. This distribution provides an aggregate view of how one variable is distributed, ignoring the influence of the other variable, and is useful for understanding the overall frequency counts in the dataset.

Relative Frequency Marginal Distribution

A relative frequency marginal distribution converts the frequency counts from the marginal totals into proportions or percentages by dividing each category's count by the total number of observations. This normalized view allows for the comparison of distributions across different groups or categories, even when the total counts vary, by showing the share of each category relative to the whole.

Transcript

00:01 Hello viewers, in this problem we have a table that gives us three values of x, two values of y, and we have to explain the idea behind the simpsom's paradox and construct in part a the frequency marginal distribution of this table.

00:15 Now, simpsons paradox in statistics is an effect that occurs when the marginal association between two categorical variables is qualitatively different from the partial association between the same two variables after controlling.

00:30 For one or more variables.

00:32 And a marginal distribution of a variable is defined as the frequency distribution of either row or column variable for the desired contingency table.

00:42 This table is useful to eradicate the influence of either row or column variable for the desired contingency table.

00:49 Now for this we will add individual values of each variable and make a table for the marginal distribution.

00:58 Hence this is the table for the frequency marginal distribution.

01:01 Where all the rows and columns are individually added.

01:07 That is, 20 plus 30 will give us 50 and 20 plus 25 plus 30 will give us 75.

01:14 And this process is repeated for all the three rows and columns.

01:19 Now, in part b we have to construct a relative frequency marginal distribution.

01:24 A relative frequency is defined as the number of times the value occurs divided by the total number of observations in the data system.

01:32 Set.

01:34 So, if we denote it as rf, that is relative frequency, it will be frequency divided by the total frequency.

01:52 The relative frequency marginal distribution for the row variable is obtained by calculating or dividing the total or the row total for each value by the contingency table...

Please give Ace some feedback