Analyzing Data: Comparing Means

Chapter 8

Are there differences?

One of the fundament questions of survey research is if there is a difference among respondents

When seeking to evaluate differences in means, we can use t-test or ANOVA = analysis of variance

t-test 2-Sample t (independent) performs a

hypothesis test of the difference between two population means when standard deviation's are unknown and samples are drawn independently from each other. It is based upon the t-distribution

If the sample is small, it works best if data were drawn from distributions that are normal or close to normal.

Select: Stat > Basic Statistics > 2-Sample t

Equal Variances?

Many statistical procedures assume that although different samples may come from populations with different means, they have the same variance.

We can test for this – use Bartlett's and Levene's tests.

Select: Stat > ANOVA > Test for Equal Variances

t-test

Paired t performs a hypothesis test of the difference between two population means when observations are paired (matched).

When data are paired, as with before-and-after measurements, the paired t-procedure results in a smaller variance and greater power of detecting differences than the 2-sample t.

Select: Stat > Basic Statistics > Paired t

One-Sample t

1-Sample t performs a hypothesis test of the mean.

We use this in survey research, when testing known values of the population or another group values

Really for comparison purposes

Select: Stat > Basic Statistics > 1-Sample t

ANOVA – Analysis of Variance ANOVA is similar to regression in that it is used to

investigate and model the relationship between a dependent (response) variable and one or more independent (explanatory) variables.

It is different the independent variables are qualitative (categorical)

no assumption is made about the nature of the relationship

ANOVA really extends the two-sample t-test for testing the equality of two population means to a more general null hypothesis of comparing the equality of more than two means, versus them not all being equal.

One-way ANOVA Select: Stat > ANOVA > One-way

Performs an one-way ANOVA, with the dependent variable in one column, subscripts in another.

Select: Stat > ANOVA > One-Way (Unstacked)

Performs a one-way ANOVA, with each group entered in its own column

Response: Select the column containing the response

Factor: Select the column containing the factor levels

Two-Way ANOVA Select: Stat > ANOVA > Two-way

A two-way ANOVA tests the equality of populations means when classification of treatments is by two variables or factors. All cells must have the same number of observations

Factors must be fixed

If your data are unbalanced or if you wish to compare means using multiple comparisons, utilize General Linear Model

Response: Enter the column containing the response variable Row Factor: Enter one of the factor level columns Column factor: Enter the other factor level column

Differences

Both the t and F-test tell us if a difference exists, but it does not tell us any thing about the strength

Sometimes there is a need to utilize several statistical techniques

Your job is to choose the best stats for your purpose and objectives