Statistics Final Exam

ONE Way anova

One IV is tested

One-Way Between-Subjects ANOVA, 2 Sources of Variation

1. Between-groups variation: the variation attributed to mean difference between groups 2. Within-groups variation: the variation attributed to mean differences within each group. This source of variation cannot be attributed to differences between groups, and is therefore called "error variation" (attributed to error or chance).

assumptions for one way anova

1. Normality: assume that data in the population or populations being sampled from are normally distributed 2. Random Sampling: assume data measured were obtained from a sample that was selected using a random sampling procedure 3. Independence: assume that the probabilities of each measured outcome in a study are independent or equal 4. Homogeneity of Variance: assume that the variance in each population is equal to each other

F distribution

ANOVA's are also called "F Tests" Test Statistic for an ANOVA = F (i.e., Fcv; Fobt) Formula in Words: mean square (or variance) between groups divided by the mean square (or variance) within groups The distribution of all possible outcomes for the F test statistic is positively skewed (because variance cannot be negative!) The distribution, called the F distribution, is derived from a sampling distribution of F ratio

why use a factorial design??

Purpose of a Factorial Design: Usually to test whether the effect of one IV (Factor A) depends on the level of the other IV (Factor B)•Disadvantages of including more than one IV/factor: ◦complicates the design ◦requires more participantsAdvantage: we can see if there is something unique about the combination of certain levels of the two IVs/factors (i.e., whether the effect of one factor depends on the level of another factor!)

degrees of freedom

The df for a one-way between-subjects ANOVA is N - 1 You must split the total df (N - 1) into 2 parts: one for each source of variation: 1. Degrees of freedom between groups (dfBG ) or degrees of freedom numerator: dfBG is the df associated with the variance for the group means in the numerator of the test statistic. It is equal to the number of groups (k) minus 1è k-1 ◦ Degrees of freedom error (dfE), degrees of freedom within groups, or degrees of freedom denominator: dfE is the df associated with the error variance in the denominator. It is equal to the total sample size (N) minus the number of groups (k) è N-k k-1/N-k

TWO way anova

Two IV's are tested

one-way anova

a statistical procedure used to test hypotheses about ONE categorical IV (called a "factor") with two or more levels, concerning the variance among group means of one continuous DV

two-way anova

a statistical procedure used to test hypotheses about TWO categorical IV (called a "factor") with two or more levels, concerning the variance among group means of one continuous DV

ANOVA Terminology

n = number of participants per group(not total number in a sample) N = total number of participants in in the whole study (not total number in a population) k = the number of levels in one categorical IV (i.e. the number of levels in one factor variable)

Between subjects design

participants are measured only once at one level of the IV

within subjects design

participants experience/ are measured at every level of the IV

Between-subjects one-way anova

used when DIFFERENT participants are observed at each level of the one categorical IV

One-way within subjects ANOVA

used when the same participants are observed at each level of the one categorical IV.