One-way Between Groups ANOVA

What are the six steps of the hypothesis test for ANOVAs

1. identify pop, distribution, and assumptions 2. state null/ research hypothesis 3. Determine characteristics 4. Determine critical values 5. Calculate the test statistic 6. Make a decision

What are the assumptions for ANOVAs?

1. randomly selected 2. normal distribution 3. Homoscedastic

TRUE OR FALSE. If there is very little spread among the means, this suggests that a reliable differences does exist among them.

False, a small spread signifies that the means are close together, hence they are similar to one another. This concludes that there is no REALIABLE difference.

In real life, what type of variance do we often find?

Herteroscedastic, particularly with smaller samples.

Why do we use ss between to find R squared?

It does access variability only among means, without regard to the variability within each sample.

What is the Bonferroni test

It is a more conservative test that uses a smaller critical cutoff. This test merely divides the p level by the number of comparisons.

How do we calculate MS within and MS between?

MSwithin= SS within/df within Msbetween= SS between/ df between

TRUE OR FALSE. F statistic is a ratio that measures the variance 1. between groups variance, which indicates differences among sample means and 2. within-groups variance, which is an average of the sample variances.

True

TRUE OR FALSE. If there is a great deal of spread among several means, this suggests that a difference does exist.

True

What are some types of post-hoc tests?

Turkey HSD and Bonferroni Test

The statistic is calculated by dividing a numerator of difference ______groups by a denominator of the variability _______groups.

between; within

What does the Turkey HSD involve?

calculation of differences between each pair of means and the division of each difference by the standard error. (M1-M2/Sm)

How do we calculate df total?

df between +df within

What are the formulas to find the df's?

df(between)= Ngroups-1 df (within)=df1+df2+df3+d4+df....etc. (for each df we must conduct df= n-1)

Why do we conduct planned comparisons and post-hoc tests?

help us determine which groups are significantly different from one another.

How do we check for homoscedasticity

if the largest variance is not more than twice the smallest. We usually calculate this at the end. We take the variance of each sample (SSwithin) and then add them together. We then divide it by the df of each sample.

What is N'?

it is the extended calculation of the standard error when the population sizes are not the same.

Why do we use SS total as the denominator to find R squared?

it takes both between and within groups variance into account.

What is the grand mean?

mean of every score in a study, regardless of the sample each score came from.

An ANOVA that analyzes a study with just one independent variable is called a_______.

one-way ANOVA.

A one-way ANOVA includes _____nominal independent variable with more than _____levels and a scale dependent variable.

one; two

What is heteroscedasticity?

populations are those that have different variances.

What is homoscedasticity?

populations are those that have the same variances. Also called, homogeneity of variance.

We use the F table to determine whether the ratio of the differences within each of our groups is extreme enough to _____the null hypothesis and conclude that there is a ______.

reject; difference

How do we find R squared?

ss between/ ss total

What is a post hoc test?

statistical procedure carried out after we reject the null, hence the research hypothesis true. It is often referred to as the "follow-up" test.

How do we calculate SS between

subtract each mean from the grand mean (M-GM) and then square it.

How do we calculate SS total?

subtract each score from the grand mean and then square it. (X-GM)

How do we calculate SS within?

subtract each score from the mean of its respective sample (X-M) and then square it.

What is the third factor that the F distribution table has that the z nor the t distribution tables have?

the number of samples.

How do we write the null hypothesis?

u1=u2=u3=u4=........etc

To calculate the numerator, we determine the _______ (spread) among the _____ (or more) means.

variability; 3

When do we use ANOVAs?

when there is a comparison between one or more nominal variables (with at least 3 groups) and a scale dependent variable.

A one-way ANOVA can have which two types of research designs?

within- groups ANOVA and between-groups ANOVA.

F distributions are complex variations of _______distributions and ________distributions.

z; t

When we calculate effect size for the z and t distribution we perform______. When we calculate for an ANOVA we find ______. What is r squared?

Cohen's d, R squared. proportion of variance in the dependent variable that is accounted for by the independent variable.

What type of distribution is the f statistic based off of?

F distribution

TRUE OR FALSE. A between groups variance estimates a difference within each of the (3 or more) sample distributions.

FALSE. This is what a within groups variance is. A between groups variance estimates the differences AMONG the means.

TRUE OR FALSE. If the between groups variance is larger than the within-groups variance, then we can infer that the sample means are different from one another.

True. There is more difference among the means.

When comparing two or more groups, it is tempting to conduct a t test, however, multiple t-tests increases the probability of what type of error?

Type 1 Error (chance of rejecting the null hypothesis when the null hypothesis is true).

What is the difference between a Within-Groups ANOVA and a Between-Groups ANOVA?

WITHIN: more than two samples, each sample has the same participants BETWEEN: more than two samples, different participants

What does the source table provide us with?

important calculations and final results of an ANOVA in a consistent and easy-to-ready format.

What is a planned comparison?

test conducted when there are multiple groups of scores but specific comparison have been specified prior to data collection; also called an a priori comparison. * Based off of previous research

What is turkey HSD?

test that determines differences between means in terms of standard error; the HSD is compared to a critical value.

Why is the f statistic always positive?

the F is based on estimates of variance instead of standard deviation or standard error.