# CRIM 320 Lecture Notes - Lecture 8: Null Hypothesis, Statistical Hypothesis Testing, Dependent And Independent Variables

86 views8 pages

24 Nov 2016

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Lecture 7: Analysis of Variance ANOVA

-ANOVA best thought of as an extension of t tests

-like t tests, ANOVA starts by comparing differences in means between groups

-also comparing sample means

-what happens when your grouping variable has more than two categories?

-comparing group means of an outcome variable of interest to determine these means are

significantly different from each other

-today, focus on one-way ANOVA

-comparing group means when we have more than 2 independent groups

-categories on a variable, 3 or more groups

the logic of ANOVA

-variance is spread of our data

-within-group variability

-spread of the data around the mean of each group

-how observations within each group vary

-between-group variability

-each group will have their own mean score on the outcome

-group means may be equal or difference

-how much our group means vary from each other

-based on these two estimates of variability, draw conclusions about the population means

-are they significantly different from each other?

what is the purpose of different categories?

-to group like things together

-similar scores on an outcome

within-group variability - spread around the mean

-group 1 is the most spread out around the mean (most difference)

-group 2 is small distribution, more clustered around the mean

find more resources at oneclass.com

find more resources at oneclass.com

between-group variability - each group will have a mean score

-each group will have own mean score

-how each mean values vary between groups

the procedure

-first question: are there differences in means across the groups?

-usually there is some difference in means

-are they statistically significant or not

-chance: are observed differences attributable to random variability in the sample?

-not statistically different

OR

-true difference: is there reason to believe that someone of the groups have different values in

the population?

-statistically different

-large enough we would expect them to be real relationships in the actual population

hypothesis testing

-null hypothesis: the population means for all groups is the same

-there are no differences between group mean scores on the dependent variable

-alternative hypothesis: there are differences between groups

-mean score on dependent variable

-note: the alternative hypothesis does not state which group differences are significant

-ANOVA on its own only tells if one of groups are significantly different from another group but

will not tell which group is different from each other

-use post hoc comparison tests

one-way ANOVA

-called one-way because it utilizes one grouping variable

-categorical variable with three of more categories (i.e., groups)

-interested in comparing in terms of mean score on their outcome

-grouping variable is often referred to a factor

find more resources at oneclass.com

find more resources at oneclass.com

-factors will normally be nominal level of measurement

-dependent variable will be interval or ratio level of measurement

assumptions

-1. Dependent variable is normally distributed for each of the populations as defined by the

different levels of the factor

-requires testing for normality

-dependent variable is not skewed or chaotic

-2. The variances of the dependent variable are the same for all populations

-requires usig Leee’s test

-3. The cases are obtained via random sampling

-4. The cases are independent of one another

how does ANOVA test for group differences?

-calculate the F ratio

-F = between-groups mean square / within-groups mean square

-requires calculating the between- and within-group variability

-sum of squares and degree of freedom for within-group and separately for between-group

estimating within-group variability I

-1. Compute within-groups sum of squares

-sum of our squared standard deviations from group means

-a) obtain variance for each group (SD2)

-b) multiple each variance by (group N-1)

-c) sum up

-2. Compute the degrees of freedom

-sum of (group N-1) for all groups

-have two different degrees of freedom

-3. Divide the sum of squares by its degrees of freedom

-4. WMS – within mean square

-average of the variances in each of the groups, adjusted for the number of observations

in each group (how spread out our scores are)

*know bolded points for exam

estimating between-group variability I

-1. Compute between-groups sum of squares

-a) subtract overall mean from each group mean

-b) square each of these differences

-c) multiply the square by number in each group

-d) sum up

-2. Compute the degrees of freedom

-number of groups – 1

-3. Divide the sum of squares by its degrees of freedom

find more resources at oneclass.com

find more resources at oneclass.com