Introducing Communication Research 2e © 2014 SAGE Publications

Chapter SevenGeneralizing From Research Results: Inferential Statistics

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

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

Inferential Statistics andthe 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

The Normal Curve andStandard 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

Statistical Significance

•Significance means that there is a better than random chance that a relationship exists.

Introducing Communication Research 2e © 2014 SAGE Publications

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 LevelThe 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

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

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

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

t-TestCompares 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

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

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

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

Correlation and RegressionCorrelation – 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

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

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

Vocabulary Review

Introducing Communication Research 2e © 2014 SAGE Publications

Web Resources

t- test Calculators

• http://www.physics.csbsju.edu/stats/t-test_NROW_form.html

• http://graphpad.com/quickcalcs/ttest1.cfm

Introducing Communication Research 2e © 2014 SAGE Publications