Inferential
Statistics
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.
Estimating a Mean or Proportion with a
Confidence Interval
Contingency Table and Chi Square Statistic
T-test or Anova
Pearson Correlation
Bi-variate Regression
Multi-variate Regression
Inferential Statistics
 First consider uni-variate statistics.
 Estimating a Mean or Proportion with a Confidence
Interval
When is it used?
To estimate a population mean or proportion
based on the sample mean or proportion of the
participants in your sample. (i.e. Population SAT
scores based on the mean SAT score of college
students in your sample).
How do you interpret it?
A 95% confidence interval indicates you are
95% confident that you can predict/infer the
mean or proportion of a population within a
specified range based on the mean or
proportion of your sample.
Inferential Statistics
 Next consider bi-variate statistics.
 Contingency tables and Chi-Square statistic
 When is it 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 it?
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 of 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 ___ 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.
 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 These Pearson Correlations and Bi-variate regressions 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 chi-square of outcome measurement by race, and then do the same for
males.)
Inferential Statistics
Finally let us consider multi-variate 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.