descriptive v inferential
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These slides will assist you in determining if your problem or question is inferential or descriptive in nature.
Descriptive
Inferential
These slides will assist you in determining if your problem or question is inferential or descriptive in nature.
Statistics tell a story about what is going on in the world.
In general there are two types of stories that are told using statistics:
In general there are two types of stories that are told using statistics:
Descriptive Stories
Inferential Stories
A descriptive story describes what is going on in a population.
What is a population?
A population is every member of a defined group.
A population can be defined as ALL individuals
A population can be defined as ALL individuals in a classroom.
A population can be defined as ALL individuals in a classroom.
A population can be defined as ALL individuals in a classroom.
30 individuals
A population can be defined as ALL individuals in a school.
A population can be defined as ALL individuals in a school.
A population can be defined as ALL individuals in a school.
2,000 individuals
A population can be defined as ALL individuals in a religion.
A population can be defined as ALL individuals in a religion.
A population can be defined as ALL individuals in a religion.
15,000,000 individuals
A population can be defined as ALL individuals in a country.
A population can be defined as ALL individuals in a country,
A population can be defined as ALL individuals in a country,
350,000,000 individuals
A population can be defined as ALL individuals in the world.
A population can be defined as ALL individuals in the world.
A population can be defined as ALL individuals in the world.
7,000,000,000 individuals
A population can be made up of people as in the last examples.
Populations can also be made of observations.
An observation can be the observing of EVERY TIME a car makes a complete stop at an intersection.
An observation can be the observing of EVERY TIME a car makes a complete stop at an intersection.
Or observing ALL THE TIMES gorillas use a specific type of sign language.
If the numbers you are using tell the story about EVERYONE in a group or ALL the possible observations in a study,
If the numbers you are using tell the story about EVERYONE in a group or ALL the possible observations in a study, then you use descriptive statistics to tell the story about that population.
Examples of Word Problems that Use Descriptive Statistics
Example #1
Example #1
Mrs. Jones has asked you to determine the average test score for all of the students in her five geography classes.
Example #1
Mrs. Jones has asked you to determine the average test score for all of the students in her five geography classes.
Example #1
Mrs. Jones has asked you to determine the average test score for all of the students in her five geography classes.
This is a descriptive question because we are describing what is happening with the entire
population (all students in Mrs. Jones geography classes)
Example #2
Example #2
A state census shows that only 30% of all Californians support Proposition X. You have been asked to find out of all those who support Prop X, what percentage would actually vote for it.
Example #2
A state census shows that only 30% of all Californians support Proposition X. You have been asked to find out of all those who support Prop X, what percentage would actually vote for it.
What is the population we want to describe?
Example #2
A state census shows that only 30% of all Californians support Proposition X. You have been asked to find out of all those who support Prop X, what percentage would actually vote for it.
What is the population we want to describe?
Example #2
A state census shows that only 30% of all Californians support Proposition X. You have been asked to find out of all those who support Prop X, what percentage would actually vote for it.
Notice that the question is not asking something about all Californians?
Example #2
A state census shows that only 30% of all Californians support Proposition 2. You have been asked to find out of all those who support Prop X, what percentage would actually vote for it.
Its asking something about the percentage of all those who support Prop X.
Here are some words to look for in your word problem to determine if it is descriptive:
• All
• Everyone
• The entire group
• Population
• Leaving no one out
• Etc.
Here are some words to look for in your word problem to determine if it is descriptive:
• All
• Everyone
• The entire group
• Population
• Leaving no one out
• Etc.
Remember to always define the population in your word problem
Here are some words to look for in your word problem to determine if it is descriptive:
• All
• Everyone
• The entire group
• Population
• Leaving no one out
• Etc.Is it defined as broadly as
all the people living in Japan?
Here are some words to look for in your word problem to determine if it is descriptive:
• All
• Everyone
• The entire group
• Population
• Leaving no one out
• Etc. Or is it defined as narrowly as all the real estate
lawyers in Sidney, Australia?
Here are some words to look for in your word problem to determine if it is descriptive:
Are you ready to make your decision?
Is your word problem descriptive?
Is your word problem descriptive?
Descriptive
Inferential
Now let’s determine how to tell if your word problem tells an inferential story.
Because it is not feasible to collect information about everyone in a country, state, or school,
nor would it be possible to look at all observations, we can take a smaller sample and then generalize it to a larger population.
The methods used to do this are called inferential statistics
Because it is not feasible to collect information about everyone in a country, state, or school,
nor would it be feasible to look at all observations, we can take a smaller sample and then generalize it to a larger population.
The methods used to do this are called inferential statistics
Because it is not feasible to collect information about everyone in a country, state, or school,
nor would it be feasible to look at all observations, we can take a smaller sample and then generalize it to a larger population.
The methods used to do this are called inferential statistics
Because it is not feasible to collect information about everyone in a country, state, or school,
nor would it be feasible to look at all observations, we can take a smaller sample and then generalize it to a larger population.
The methods used to do this are called inferential statistics.
Inferential statistics use information about a sample (a group within a population) to tell a story about a population.
Inferential statistics use information about a sample (a group within a population) to tell a story about a population.
The word inferential means we are inferringsomething about a population based on information
from a smaller but representative sample
Consider the following inferential problem:
Using a sample of 5th grade student verbal acuity scores, determine the average scores of 5th
graders in the state of Montana.
Consider the following inferential problem:
The population is defined as all of the fifth grader verbal acuity scores in the state of Montana.
The population is defined as all of the fifth grader verbal acuity scores in the state of Montana.
Let’s take a random sample of a 100 fifth grade students scores from across the entire
state.
100 Fifth Grade Verbal Acuity
Scores
Let’s take a random sample of a 100 fifth grade students scores from across the entire
state.
100 Fifth Grade Verbal Acuity
Scores
Average Score of
Sample = 34
100 Fifth Grade Verbal Acuity
Scores
Average Score of
Sample = 34
We generalize by saying there is a
strong probability that Montana 5th
graders averaged a 34 on their verbal
acuity test
100 Fifth Grade Verbal Acuity
Scores
Average Score of
Sample = 34
We generalize by saying there is a
strong probability that Montana 5th
graders averaged a 34 on their verbal
acuity test
The generalizing from a sample (100 Fifth Graders) to
the population (all Fifth Graders in Montana) is an example of what we call -
Inferential Statistics
Once again, with inferential statistics, we are telling the story about a sample
Once again, with inferential statistics, we are telling the story about a sample
Story about a Sample
Once again, with inferential statistics, we are telling the story about a sample and then generalizing that story to a larger population.
Once again, with inferential statistics, we are telling the story about a sample and then generalizing that story to a larger population.
Story about a Sample
Once again, with inferential statistics, we are telling the story about a sample and then generalizing that story to a larger population.
Story about a Sample
Generalizing to a
Once again, with inferential statistics, we are telling the story about a sample and then generalizing that story to a larger population.
Story about a Sample
Larger Population
Generalizing to a
Let’s look at an example of an inferential statistic word problem
Skating rink officials want to know if teenagers in PoDunk Town prefer rink skating better than park skate boarding. They ask a sample of teenagers and record their responses.
versus
Skating rink officials want to know if teenagers in PoDunk Town prefer rink skating better than park skate boarding. They ask a sample of teenagers and record their responses.
It will most likely be an inferential
question if you see the word sample
Skating rink officials want to know if teenagers in PoDunk Town prefer rink skating better than park skate boarding. They ask a sample of teenagers and record their responses.
that generalizes to a population
Here are some words to look for in your word problem to determine if it is inferential:
• sample
• some
• several
• random
• generalize
• Etc.
Here are some words to look for in your word problem to determine if it is inferential:
Would you classify the problem you are working on as inferential?
Would you classify the problem you are working on as inferential?
Descriptive
Inferential
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