This document provides an overview of key concepts in inferential statistics used in communication research. It defines statistical significance, normal distribution, random sampling, confidence level, confidence interval, parametric vs non-parametric statistics. It also explains t-tests, analysis of variance (ANOVA), correlation, and types of error. Specific statistical techniques are defined including t-test, correlation, regression and ANOVA.

1. Introducing Communication Research 2e © 2014 SAGE Publications
Chapter Seven
Generalizing From Research
Results: Inferential Statistics

2. Key Concepts
• Statistical significance.
• Normal distribution.
• Random sampling.
• Confidence level & confidence interval.
• Parametric vs. non-parametric.
• t-test, ANOVA & correlation.
• Type I and Type II error.
Introducing Communication Research 2e © 2014 SAGE Publications

3. Inferential Statistics
Inferential statistics help us –
• Estimate the probability that a sample
represents the population it came from.
• Decide whether groups differ significantly on a
variable.
• Decide whether there are significant
relationships among or between variables.
Introducing Communication Research 2e © 2014 SAGE Publications

4. Inferential Statistics and
the Normal Curve
• Inferential statistics assume that the values of a
variable in a population are normally
distributed.
• Assuming a normal distribution of values in a
population, we can calculate the probability that
a sample of that population has captured its
characteristics.
Introducing Communication Research 2e © 2014 SAGE Publications

5. The Normal Curve and
Standard Deviation
In a normal distribution –
• 68% of values occur plus or minus one
standard deviation (SD) from the mean.
• 95% of its values occur plus or minus two SDs
from the mean.
• 99.7% of its values occur plus or minus three
SDs from the mean.
Introducing Communication Research 2e © 2014 SAGE Publications

6. Statistical Significance
• Significance means that there is a better than
random chance that a relationship exists.
Introducing Communication Research 2e © 2014 SAGE Publications

7. Confidence Interval and
Confidence Level
• Confidence Interval
The possible range of values for a variable in a
population, calculated from a sample of the
population.
• Confidence Level
The probability of a calculated value occurring.
• Example –
There is a 95% probability that the mean lies between 0.98
and 10.42.
Introducing Communication Research 2e © 2014 SAGE Publications

8. For a Sample
• The distribution of the sample results is
called the sampling distribution.
• The standard deviation is called the
standard error.
• Standard error decreases as sample size
increases.
Introducing Communication Research 2e © 2014 SAGE Publications

9. Parametric vs Non-parametric
Statistics
• Parametric Statistics
Used where we can assume a normal distribution
of values in the population.
• Non-Parametric Statistics
Used where we cannot assume a normal
distribution of values in the population.
Introducing Communication Research 2e © 2014 SAGE Publications

10. Standard Deviation
• A measure of the extent to which a set of scores
vary on either side of their mean value.
• The square root of variance.
• For a sample, standard deviation is referred to as
the standard error.
Introducing Communication Research 2e © 2014 SAGE Publications

11. t-Test
Compares mean scores from two groups to
determine the probability the groups are
different.
• t-test for independent samples -
Used where the groups are different.
• t-test for dependent samples -
Used where the groups are the same.
• The higher the t-value, the lower the probability
it will occur.
Introducing Communication Research 2e © 2014 SAGE Publications

12. Degrees of Freedom
• A measure of “room to move.”
▫ How many ways could our data be combined and
still produce the same values for a statistic?
Introducing Communication Research 2e © 2014 SAGE Publications

13. One and Two-tailed Tests
• One-tailed Test
Presupposes that a difference between groups
will be directional
for example, that a value for group A will be
higher than for group B.
• Two-tailed Test
Presupposes that the difference will be non-
directional
for example, group A and group B simply differ;
either group could score higher or lower.
Introducing Communication Research 2e © 2014 SAGE Publications

14. Analysis of Variance (ANOVA)
• Assesses the probability of difference among two
or more groups.
• Compares the variance within groups with the
variance between groups.
• One-way ANOVA compares one variable across
more two or more groups.
• Multiple Analysis of Variance (MANOVA)
assesses relationships among multiple variables
across two or more groups.
Introducing Communication Research 2e © 2014 SAGE Publications

15. Correlation and Regression
Correlation – a measure of the strength of
association among and between variables.
Correlation coefficient - expresses the
strength of association between variables.
Regression - predicts a value for one variable
given a value for another variable.
• Relationships between variables may plot out as
linear or curvilinear
Introducing Communication Research 2e © 2014 SAGE Publications

16. Type I and Type II Error
Accept null hypothesis Reject null hypothesis
Null hypothesis is true in
the wider population.
No problem. Type I Error.
Decided wrongly that
there was a significant
result.
Null hypothesis is false
in the wider population.
Type II Error.
Decided wrongly that
there was no significant
result.
No problem.
Introducing Communication Research 2e © 2014 SAGE Publications

17. Chapter Summary
• Inferential statistics assess –
▫ the probability that a sample represents a population
▫ the strength of relationships among variables
▫ the strength of differences among groups.
• t-test – compares values of a continuous variable for two
groups.
• Correlation - assesses the strength of association
between variables.
• Regression - computes the values of one variable, given
the values of another.
• ANOVA compares values of a variable across multiple
groups.
Introducing Communication Research 2e © 2014 SAGE Publications

18. Vocabulary Review
Introducing Communication Research 2e © 2014 SAGE Publications

19. Web Resources
t- test Calculators
• http://www.physics.csbsju.edu/stats/t-test_NROW_form.htm
• http://graphpad.com/quickcalcs/ttest1.cfm
Introducing Communication Research 2e © 2014 SAGE Publications