Inferential
Statistics
What are they?
When would you
use them?
Inferential Statistics
What are inferential statistics?
Why learn about inferential statistics?
Why use inferential statistics?
When are inferential statistics utilized?
Which types of inferential statistics
are most commonly used and when?
What is important for you to know
about inferential statistics?
Inferential Statistics
What are inferential statistics?
 Inferential statistics infer from the sample to the
population
 They determine probability of characteristics of
population based on the characteristics of your
sample
 They help assess strength of the relationship
between your independent (causal) variables, and
you dependent (effect) variables.
Inferential Statistics
Why learn about inferential statistics?
 BEFORE you use any intervention, you should do some
research and determine if there is evidence that it works.
(i.e., Does the head start program increase educational
performance for low income children)
 BEFORE you work with any group, you want to base your
judgments on research, not on stereotypes (i.e., You may
want to know what proportion of Latino boys join gangs?)
 BEFORE you make recommendations, you want to understand
the probabilities of success (i.e., What is the probability that a
child will have success in school if they participate in your
tutorial program?)
 Before you continue on with a program/intervention, you want
to reassure yourself that this program is worth your time and
effort.
 As you apply for grants, you want to ensure the grantees that
you can implement a evidence based program.
 When making policy recommendations or participating in
political advocacy, you want to provide empirical support that
your intervention actually works.
Inferential Statistics
Why use inferential statistics?
 Many top-tiered journals will not publish articles
that do NOT use inferential statistics.
 Allows you to generalize your findings to the larger
population.
Can determine not just what CAN happen, but
what tends to happen in programs like yours.
 Helps assess strength of the relationship between
your independent (causal) variables, and you
dependent (effect) variables.
Can assess the relative impact of various program
inputs on your program outcomes/objectives.
Inferential Statistics
When are inferential statistics utilized?
 Inferential statistics can only be used under the
following conditions.
 You have a complete list of the members of the population.
 You draw a random sample from this population
 Using a pre-established formula, you determine that your
sample size is large enough.
Can you use inferential statistics even if
you data do not meet these criteria?
 Inferential statistics can help determine strength of
relationship within your sample. In other words, you
can assess the strength of the impact of your
independent variables (program inputs) on your
outcomes (program outputs)
 IF it is very difficult to obtain a population list and/or
draw a random sample, then you do the best you can
with what you have. In this case, you can use
inferential statistics and journals may publish it.
Inferential Statistics
Which types of inferential statistics are most
commonly used and when?
 The following types of inferential statistics are
relatively common and relatively easy to interpret.
One sample test of difference/One sample
hypothesis test
Confidence Interval
Contingency Tables and Chi Square Statistic
T-test or Anova
Pearson Correlation
Bi-variate Regression
Multi-variate Regression
Inferential Statistics
First consider uni-variate statistics.
One sample test of difference OR one
sample hypothesis test
When is it used?
To compare responses of program participants
on a pre and post test.
To determine if implemented program had an
impact on one particular outcome.
How do you interpret it?
If the probability is .05 or less that you will
make a mistake in asserting there is a
difference between the pre and post-test
scores in the population, then you can assert
that the program did make a difference on this
outcome. In other words, your program is
working.
Inferential Statistics
First consider uni-variate statistics.
Confidence Interval
When is it used?
To estimate a value/score in a population based
on the score of the participants in your sample.
How do you interpret it?
A 95% confidence interval indicates you are
95% confident that you can predict/infer the
value/score of a population within a specified
range based on the value/score of your sample.
Inferential Statistics
Next consider bi-variate statistics.
Contingency tables and Chi-Square
statistic
When are they used?
When you have two categorical variables,.
AND you want to know if they are related. (i.e.,
gender and score on outcome measurement).
How do you interpret them?
The chi-square statistics can be used to
determine the strength of the relationship (i.e.,
Does knowing someone’s gender help you
predict their outcome score/value). If the
probability associated with the chi-square
statistics is .05 of less, then you can assert that
the independent variable can be used to predict
scores on the dependent or outcome variable.
You can also use the contingency table to
compare the actual scores across the
independent variable on the dependent variable
or outcome measurement (i.e., compare the
number/percent of males who agreed that the
program had a positive impact on their lives to
the percent of females who agreed.)
Inferential Statistics
Next consider bi-variate statistics.
T-test or Anova
When is it used?
When you have a categorical and continuous
variable.
And you want to compare mean scores of two
or more groups (i.e., you want to compare mean
GRP of students you have tutored across race).
How do you interpret it?
The T-test or F statistic can be used to
determine if the groups have significantly
different means. If the probability associated
with the F statistics is .05 or less then we can
assert that there is a difference in the means.
Inferential Statistics
Next consider bi-variate statistics.
Pearson Correlation
When is it used?
When you have a continuous
independent variable and a
continuous dependent variable.
How do you interpret it?
When the probability associated
with the T statistics is .05 of less
then you can assume there is a
relationship between the dependent
and independent variable. For
instance you may want to know if
the number of hours participants
spend in your program is positively
related to their scores on school
exams.
Inferential Statistics
Next consider bi-variate statistics.
Bi-variate Regression
When is it used?
When you have a continuous independent
variable and a continuous dependent (outcome)
variable. For instance, you may want to know if
the number of hours participants spend in your
program is positively related to their scores on
school exams.
How do you interpret it?
When the probability associated with the F
statistic is .05 or less then you can assume
there is a relationship between the dependent
and the independent variable.
* NOTE
The Pearson Correlation and Bi-variate regression are very similar.
Inferential Statistics
Finally let us consider multi-variate statistics
Elaborated Chi-Square statistic
When is it used?
When you have more than one independent
categorical variable, and one dependent
categorical variable.
How is it interpreted?
You divide one of the independent variables into
two groups and then do a chi square for each
group (i.e., divide gender into males and
females, then do a chi-square of males and one
for females. So for females you can do a chisquare of outcome measurement by race, and
then do the same for males.)
Inferential Statistics
Multivariate Regression
When is it used?
Multivariate regression is used you have more
than one independent (causal) variable and one
dependent (effect or outcome) variable.
You not only want to know if you intervention
has an impact on the outcome, but you want to
know WHICH aspects of your intervention has
an impact and/or the relative impact of different
aspects of your intervention.
How do you interpret it?
If the probability associated with the F statistic
is .05 of less, then you can
If the probability associated with the T statistic
for each of the independent variables is .05 or
less, then you can assert that independent
variable has an impact on the outcome,
independent of the other variables. The
value of the T statistics can be compared
across the independent variables to determine
the relative value of each.
Inferential Statistics
What is important for you to know
about inferential statistics?
 You should be able to
1. Read and understand computer printouts
2. Construct tables and graphs from the computer
printouts.
3. Interpret and explain these tables and graphs to an
audience.
4. Make wise decisions based on valid and accurate data.
What if you NEVER intend to
use Inferential Statistics?
All of us are consumers of information
 We can learn about inferential statistics and be wiser
consumers of information. We are empowered, and
have the tools to determine if the information we are
reading is accurate/valid.
If you implement programs, you are ethically
bound to your participants to be able to
accurately measure the outcomes of your
intervention.
If you use government/foundation funding to
implement your programs, then you are
responsible for using their monies wisely and
efficiently.
Dr. Carol Albrecht
USU Extension Specialist
carol.albrecht@usu.edu
979-777-2421