Class Objectives A Review of Just How Far We have All Come Salkind Chapter 12 - Analysis of Variance
Review z The field of Counseling deals with various concepts that are called constructs (e.g., Depression, Anxiety, Intelligence, etc.). z Constructs can be quantified and then measured using valid and reliable assessment tools (tests). z Once a group of individuals have been tested a numbers of test scores are created. z Because we are often interested in nature of a whole group of individuals, once with have their scores we perform procedures that help describe the group.
Review z Descriptive Statistics – provide a picture of the group we have tested. yCentral tendency – Mean, Median, Mode yVariability – Range and Standard Deviation z If the group was administered two measures (Depression and Anxiety) we can calculate a correlation coefficient that captures the strength and direction of the relationship that exists between Depression and Anxiety within the group.
Review z Once we have tested and describe a group it is always fun to divide the whole group into two smaller groups to see and do different things to them to see if we can change them in some way. This process involves using a research design. R O x O R O O z When dividing the groups we want to do so randomly so as to not enter a bias we can control into the mix. zWe also always want to use valid and reliable measures to that when we eventually arrive at findings we know that they are in fact as accurate as possible – knowing full well that there will always be limitations to any findings that we may generate.
Review z When conducting research using the design below – or a variation of it - we are always looking for differences between group means. R O x O R O O z We start by: 1. Writing a Null Hypothesis (which assumes no differences between groups) and an alternative hypothesis and then z2. Next we setting our p level (.05 or.01 – the level of probability of being wrong or rejecting the null hypothesis when it is true – Type I error). zThus far we have used the t-test to establish if any difference between the means exist they are statistically significant differences. We have done this by calculating the t statistic (our obtained value) comparing it with our critical value (found in the Table of Critical Values for t) – and if our obtained value is more extreme than the Critical Value – we reject the null and accept our alternative hypothesis.
Analysis of Variance - ANOVA Again, empirical research often operates from a framework of establishing comparisons between groups (differences or lack of differences) and drawing a conclusion about those findings. We have also discussed that when we find a difference between the means of two or more groups we need to be concerned about whether those differences are statistically significant or not.
ANOVA We have seen in how we can test for significant differences between two group means using the t-test. Now we will move forward one more step to look at a situation were we need to test for significant differences between the means of more than two groups. Use the test chart in your text to determine the form (simple or repeated measures) analysis of variance we should perform given certain circumstances.
The Simple ANOVA The simple analysis of variance (a.k.a. - the one-way analysis of variance) is used when an examination of differences on one or more variables is being conducted and the same participants are not tested more that once. Does that last part sound familiar? It should. It is the same criteria we used for determining independent and dependent means. In fact it is very similar to the t-test only in this case we have more than two groups being tested.
A More Complex Simple ANOVA What? Well it is true. We can make the simple ANOVA more complex by not only testing for differences between groups but also by different factors across groups. Below is a 3X2 factorial design. Group 1 Group 2 Group 3 Female Dep. Score Dep. Score Dep. Score Male Dep. Score Dep. Score Dep. Score
Steps in Computing the F Statistic Step 1: A statement of the null hypothesis and research hypotheses - no difference between the means Group 1, Group 2, Group 3 and Alternative. The Null Hypothesis Ho: 1 = 2 = 3 The Research Hypothesis H 1 : X 1 = X 2 = X 3 Step 2: Set the level of risk (or level of significance) upon which your decision will be made to accept or reject the null hypothesis and risking Type I Error. Step 3: Select the appropriate F test statistic base on need for Simple or Repeated Measures ANOVA.
Steps in Computing the F Statistic Step 4: Compute the test statistic value (a.k.a. the Obtained Value). Step 5: Consult the appropriate table to determine the Critical Value needed for rejecting the null hypothesis for the statistic you are using. To use the table you must determine the Degrees of Freedom (df). For the F statistic there are two sets of degrees of freedom. For the numerator it is k-1 where k = the number of groups and the df for the denominator is n-k (n = participants).
Steps in Computing the F Statistic Step 6: Compare the Obtained Value (F Statistic) and the Critical Value. Step 7: Commit to a decision. If the Obtained Value is more extreme than the critical value (further in the tail of the normal curve) the test has been met. We can reject the null hypothesis and conclude that the difference between the means of our groups are Significantly Different and willing to risk saying the differences observed are not do to factors other than true difference in our variables of interest.
F (2,27) = 8.80 p <.05 So what does that mean? The statement above says that the differences that exist between the three groups are 8.80 times as extreme as the differences within in the three groups. “Houston we have a problem!”
Omnibus Tests The F test is an omnibus test - it tells us whether or not there are significant differences but not where those differences actually occurred. To find where the significant differences lie, we have to perform other specialized tests to tease out those significant differences. You will learn more about these tests in your next course in research and statistics.