Multivariate Analysis ANOVA PDF

MULTIVARIA TE ANALYSIS 1ST TOPICS: ANOVA, FACTORIAL ANOVA SOURCES: HTTPS://WWW.STATISTICSHOWTO.COM/PROBABILITY-AND-STATISTICS/MULTIVARIATE-A NALYSIS/ HTTPS://WWW.STATISTICSHOWTO.COM/PROBABILITY-AND-STATISTICS/HYPOTHESIS- TESTING/ANOVA/ What is Multivariate Analysis?  Multivariate analys...

MULTIVARIA TE ANALYSIS 1ST TOPICS: ANOVA, FACTORIAL ANOVA SOURCES: HTTPS://WWW.STATISTICSHOWTO.COM/PROBABILITY-AND-STATISTICS/MULTIVARIATE-A NALYSIS/ HTTPS://WWW.STATISTICSHOWTO.COM/PROBABILITY-AND-STATISTICS/HYPOTHESIS- TESTING/ANOVA/ What is Multivariate Analysis?  Multivariate analysis is used to study more complex sets of data than what univariate analysis methods can handle. This type of analysis is almost always performed with software (i.e. SPSS or SAS), as working with even the smallest of data sets can be overwhelming by hand.  Multivariate analysis can reduce the likelihood of Type I errors. Sometimes, univariate analysis is preferred as multivariate techniques can result in difficulty interpreting the results of the test. For example, group differences on a linear combination of dependent variables in MANOVA can be unclear. In addition, multivariate analysis is usually unsuitable for small sets of data.  There are more than 20 different ways to perform multivariate analysis. Which one you choose depends upon the type of data you have and what your goals are. For example, if you have a single data set you have several choices:  Additive trees, multidimensional scaling, cluster analysis are appropriate for when the rows and columns in your data table represent the same units and the measure is either a similarity or a distance.  Principal component analysis (PCA) decomposes a data table with correlated measures into a new set of uncorrelated measures.  Correspondence analysis is similar to PCA. However, it applies to contingency tables.  Although there are fairly clear boundaries with one data set (for example, if you have a single data set in a contingency table your options are limited to correspondence analysis), in most cases you’ll be able to choose from several methods.  Cluster analysis showing three groups. The ANOVA Test  An ANOVA test is a way to find out if survey or experiment results are significant. In other words, they help you to figure out if you need to reject the null hypothesis or accept the alternate hypothesis.  Basically, you’re testing groups to see if there’s a difference between them. Examples of when you might want to test different groups:  A group of psychiatric patients are trying three different therapies: counseling, medication and biofeedback. You want to see if one therapy is better than the others.  A manufacturer has two different processes to make light bulbs. They want to know if one process is better than the other.  Students from different colleges take the same exam. You want to see if one college outperforms the other. What Does “One-Way” or “Two-Way Mean?  One-way or two-way refers to the number of independent variables (IVs) in your Analysis of Variance test.  One-way has one independent variable (with 2 levels). For example: brand of cereal,  Two-way has two independent variables (it can have multiple levels). For example: brand of cereal, calories. What are “Groups” or “Levels”?  Groups or levels are different groups within the same independent variable. In the above example, your levels for “brand of cereal” might be Lucky Charms, Raisin Bran, Cornflakes — a total of three levels. Your levels for “Calories” might be: sweetened, unsweetened — a total of two levels.  Let’s say you are studying if an alcoholic support group and individual counseling combined is the most effective treatment for lowering alcohol consumption. You might split the study participants into three groups or levels:  Medication only,  Medication and counseling,  Counseling only.  Your dependent variable would be the number of alcoholic beverages consumed per day.  If your groups or levels have a hierarchical structure (each level has unique subgroups), then use a nested ANOVA for the analysis. What Does “Replication” Mean?  It’s whether you are replicating (i.e. duplicating) your test(s) with multiple groups. With a two way ANOVA with replication , you have two groups and individuals within that group are doing more than one thing (i.e. two groups of students from two colleges taking two tests). If you only have one group taking two tests, you would use without replication. Two Way ANOVA  A Two Way ANOVA is an extension of the One Way ANOVA. With a One Way, you have one independent variable affecting a dependent variable. With a Two Way ANOVA, there are two independents. Use a two way ANOVA when you have one measurement variable (i.e. a quantitative variable) and two nominal variables. In other words, if your experiment has a quantitative outcome and you have two categorical explanatory variables, a two way ANOVA is appropriate.  For example, you might want to find out if there is an interaction between income and gender for anxiety level at job interviews. The anxiety level is the outcome, or the variable that can be measured. Gender and Income are the two categorical variables. These categorical variables are also the independent variables, which are called factors in a Two Way ANOVA.  The factors can be split into levels. In the above example, income level could be split into three levels: low, middle and high income. Gender could be split into three levels: male, female, and transgender. Treatment groups are all possible combinations of the factors. In this example there would be 3 x 3 = 9 treatment groups. Main Effect and Interaction Effect  The results from a Two Way ANOVA will calculate a main effect and an interaction effect. The main effect is similar to a One Way ANOVA: each factor’s effect is considered separately. With the interaction effect, all factors are considered at the same time. Interaction effects between factors are easier to test if there is more than one observation in each cell. For the above example, multiple stress scores could be entered into cells. If you do enter multiple observations into cells, the number in each cell must be equal. ANOVA: Hypotheses  Two null hypotheses are tested if you are placing one observation in each cell. For this example, those hypotheses would be:  H01: All the income groups have equal mean stress.  H02: All the gender groups have equal mean stress.  For multiple observations in cells, you would also be testing a third hypothesis:  H03: The factors are independent or the interaction effect does not exist. Assumptions for Two Way ANOVA  The population must be close to a normal distribution.  Samples must be independent.  Population variances must be equal (i.e. homoscedastic).  Groups must have equal sample sizes. Procedure and Interpretation in SPSS  Other reference link;  https://www.statisticssolutions.com/free-resources/directory-of- statistical-analyses/factorial-anova/