Two-Way Tables Normal Distributions
description
Transcript of Two-Way Tables Normal Distributions
Two-Way TablesNormal Distributions
Review: Categorical Variables place individuals into one of several groups or categories.
The values of a categorical variable are labels for the different categories.
The distribution of a categorical variable lists the count or percent of individuals who fall into each category.
Categorical Variables2
When a dataset involves two categorical variables, we begin by examining the counts or percents in various categories for one of the variables.
Two-way Table – describes two categorical variables, organizing counts according to a row variable and a column variable.
Two-Way Table
3
Young adults by gender and chance of getting rich
Female
Male Total
Almost no chance 96 98 194
Some chance, but probably not
426 286 712
A 50-50 chance 696 720 1416
A good chance 663 758 1421
Almost certain 486 597 1083
Total 2367 2459
4826
What are the variables described by this two-way table?
How many young adults were surveyed?
Practice 1: Complete the following tables
1) Students are asked if they prefer to go swimming or to the gym.
2) Some people are asked about their favorite outdoor
sport.
Swimming Gym Total
Boys 25 45
Girls
Total 64 100
Hiking Canoeing Climbing TotalUnder 15’s 42 150
15 – 30 30 47 100Over 30 30 15
Total 75 300
Fill in the gaps
SexTOTA
LSMale Female
Eat breakfast on a regular
basis
Yes 190 300
No 165
TOTALS 320 275
110
130 295
595
Marginal Distribution
6
The Marginal Distribution of one of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table.
Note: Percent's are often more informative than counts, especially when comparing groups of different sizes.
To examine a marginal distribution:
1. Use the data in the table to calculate the marginal distribution (in percent's) of the row or column totals.
2. Make a graph to display the marginal distribution.
BPS Chapter 6 7
Example: Age and Education
Variables
Marginal distributions
“Age groups” is the categorical explanatory variable “Education level” is the categorical response variable
BPS Chapter 6 8
Example: Marginal Totals
Variables
Marginal totals
37,786 81,435 56,008
27,85858,07744,46544,828
BPS Chapter 6 9
Marginal Distributions
%100 totaltable
totalmarginal percent marginal
Marginal distributions are used as background information only.
They do not address association
BPS Chapter 6 10
Marginal Distribution, Row Variable
% not completed HS = 27,859 / 175,230 × 100% = 15.9%
% graduated HS = 58,077 / 175,230 × 100% = 33.1%
% finished 1-3 yrs col. = 44,465 / 175,230 × 100% = 25.4%
% finished ≥4 yrs col. = 44,828 / 175,230 × 100% = 25.6%
BPS Chapter 6 11
Marginal Distribution, Column Variable
% age 25–34 = 37,786 / 175,230 × 100% = 21.6%
% age 35–54 = 81,435 / 175,230 × 100% = 46.5%
% 55 and over = 56,008 / 175,230 × 100% = 32.0%
Marginal Distribution
12
Young adults by gender and chance of getting rich
Female
Male Total
Almost no chance 96 98 194
Some chance, but probably not
426 286 712
A 50-50 chance 696 720 1416
A good chance 663 758 1421
Almost certain 486 597 1083
Total 2367 2459 4826
Response Percent
Almost no chance
194/4826 = 4.0%
Some chance 712/4826 = 14.8%
A 50-50 chance 1416/4826 = 29.3%
A good chance 1421/4826 = 29.4%
Almost certain 1083/4826 = 22.4%
Examine the marginal distribution of chance of getting rich.
Almost none
Some chance
50-50 chance
Good chance
Almost certain
05
101520253035
Chance of being wealthy by age 30
Survey Response
Perc
ent
Practice 2: Copy and complete the following two-way table about ways of eating potato and then answer the questions.
1) How many boys liked mashed?2) How many teachers preferred new potatoes?3) How many girls were asked?4) Out of the people who liked chips, how many were
boys?
New Chips Mashed Total
Boys 34 100
Girls 25 37
Teachers 12 22 50
Total 104 250
1) What is the probability the person picked is a boy?
2) What is the probability the person liked mash?
3) What is the probability the person was a teacher who preferred new potatoes?
4) What is the probability that, out of the girls, the person liked chips?
5) Out of the people who liked chips, what is the probability the person was a boy?
Practice 3: For the following two-way table answer the questions on probability. A person is picked at random from the sample.
New Chips Mash Total
Boys 15 51 34 100
Girls 25 37 38 100
Teachers 12 16 22 50
Total 52 104 94 250
TAILFor the following table, copy and complete it, then answer
the questions about types of coffee bought.
Next
Coffee is sold in three types and in three weights.
a) How many people bought 100g of powdered coffee?
b) How many people bought ground coffee?
c) Out of the packets weighing 200g, what is the probability the packet bought contained granules?
100g 200g 300g Total
Ground 50 120
Powder 80 35 26
Granules 40 45
Total 135 135 400
Are you ready for the answers ?
Answers
(a) 80(b) 120(c) 45/130
100g 200g 300g Total
Ground 15 50 55 120
Powder 80 35 26 141
Granules 40 45 54 139
Total 135 130 135 400
Task One – Data Collection
Has an IpodTOTA
LSYes No
Has been to Myrtle Beach
Yes
No
TOTALS
What is the probability that…
• A student has an Ipod?• A student has been to Myrtle Beach?• A student does not have an Ipod?• A student has not been to Myrtle Beach?• A student has an Ipod and has been to the
Myrtle Beach?• A student has an Ipod or has been to Myrtle
Beach) • A student does not have an Ipod or has not
been to the Myrtle Beach?
Example Two
Brown HairTOTA
LSYes No
Hours watching TV
last night
Less than 2 hours
2 or more hours
TOTALS
What is the probability that…
• A student has brown hair?• A student spent less than 2 hours
watching TV last night?• A brunette student spent less than 2
hours watching TV last night?• A student who was watching TV for
more than 2 hours last night is brunette?
Example 3
Did HomeworkTOTA
LSMale Female
Has correct supplies for
class
Yes
No
TOTALS
Questions?
• Write your own set of at least 5 questions you could answer using the previous two-way table.
Homework