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# Inferential tests analysis tools update 2011

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• In the prior lesson, you learned how to generate descriptive data for a set of numbers. Once we have looked at the descriptive data (usually a set of means and standard deviations) what do we do next? The next step is inferential testing to see if the variables are related to each other. This video will go over analysis tools that are used in inferential testing.We have a long list of tools from which we can choose to run these tests. It can be daunting to look at all the choices and try to figure out which one fits our particular situation. But, there is a strategy to help you get to the correct tool.
• Although the list of analysis tools is long, there is a way to simplify our task by grouping the tools into categories. As you can see on this slide, there are basically three kinds of tools in the Analysis Toolbox as follows: a) Chi square-based b) ANOVA–based and c) and Regression-based Note that regression tools can be thought of as a special, more detailed application of ANOVA tools.Next, I will show you how to make the correct tool selection for each model.(For detailed explanations of each tool, go to the PowerPoint lesson specific to that tool. See the Course Menu for the corresponding URL.)
• This slide is a branching diagram of the steps we take to pinpoint the correct analysis tool. Step 1 is to identify the type of model. Is it a Linking Model? Is it a Data Reduction Model? Or, is it a Hybrid Model, combining aspects of both Data Reduction and Linking Models? After Step 1 you can go down one of three branches. These branches, in turn, will take you in a different direction at Step 2.As you can see along the bottom row of the slide, all of the Analysis Tools we will need can be grouped into one of the categories from the prior slide. The groups, again, are a) Chi-Square-Based, b) ANOVA-Based, &amp; c) Regression-Based. We will look at each section of the slide in turn, starting with the steps for Linking Models (in red).In the next slide, I will reproduce just the red part of the diagram.
• As you can see in this slide, once you have identified the model as a Linking Model, you will move downward and to the left on the diagram.(If you aren’t sure whether your design is a Linking Model, go back to the lesson on Internal Validity.)In Step 2, you will answer the question: “What is the level of measurement of the variables in the model?” Remember from our lesson on levels of measurement, there are four levels: nominal, ordinal, interval, or ratio. (You can use the acronym NOIR to help you remember these levels. Maybe add this to Construct Validity lesson).
• This slide shows that there is a way to simplify Step 2 as follows:In most studies, ordinal, interval, and ratio level data are analyzed the same way. Thus, we can simplify, by putting all ordinal, interval, and ratio level data into a single category called continuous data.Nominal level variables are treated a little differently than other variables in the analysis step. Thus, we will put nominal level data into a class all by itself called: categorical data Review the PowerPoint on Construct Validity if you are not sure what level of measurement you are using.The next several slides will help you use the information about measurement level to choose the correct analysis tool.
• Here is a 3 cell Decision Table that leads you to the general category of analysis for each data combination. First identify the level of measurement for your Predictor Variable and Criterion Variable. That is, are they categorical (nominal level) or continuous (ordinal, interval, or ratio level)? Find the correct row for the Predictor Variable and the correct column for the Criterion variable. At the intersection of this row and column you will find a cell with the correct category of analysis needed for your problem. If both the Predictor and Criterion Variables are categorical, use a chi-square-based tool. If the Predictor Variable is categorical and the Criterion Variable is continuous, use an ANOVA-based tool. If the Predictor Variable is continuous, you will use a Regression-based tool no matter what the level of the Criterion variable. The next slide is a more detailed decision table. Note 1: Both Decision Tables are to be applied when the sample size is relatively large (i.e. at least 30 subjects per group).Note 2: Although we use the terms Independent and Dependent Variables with a causal model, the terms Predictor and Criterion are more general and cover both causal and non-causal models. Therefore, for the sake of brevity, we will use the more general terms to cover both types of models.
• This is a more detailed table that breaks the Predictor and Criterion variables into single or multiple variable sets. This leads to a 4 x 4 table of possibilities for the various combinations. The following tools appear at one place or another in the table. You can see for yourself which combinations call for which analysis tools. 1) Chi square 2) log linear analysis 3) ANOVA – t test, F test 4) MANOVA 5) Logistic regression 6) Simple regression 7) Multivariate regression 8) Discriminant Analysis 9) multiple regression 10) canonical correlationThis table provides more information than the prior table. The added information tells you what type of analysis to use if you have multiple versus single variable sets in your model.You will find a complete Video Tutorial in the Menu of Contents covering each one of these analysis tools. You may have a study that doesn’t seem to fit any of the spaces on the table. For example, what would you do if you had a study with a continuous level criterion variable and BOTH continuous and categorical predictor? This combination does not appear on the table….Not to worry, there is an analysis tool to cover this. It’s called ANCOVA. You will find a Video Tutorial on ANCOVA in the Menu of Contents. This course can teach you an analysis tool for virtually any combination of variables you can come up with.
• OK, we have completed all the steps needed to pinpoint the analysis tools for a Linking Model. Now, we will move on to the steps needed for a Data Reduction Model. These steps are highlighted here in blue. The blue part of the diagram is reproduced on the following slide.
• If you have a Data Reduction Model, Step 2 requires you to ask, “Am I searching through the data with a specific theory in mind or am I going into it with an open mind?” In other words, is the analysis going to be theory driven or not?If you have a clear idea how the variables in the dataset will cluster, the analysis is confirmatory and it is called a Factor Analysis (FA). You are trying to confirm your theory about how the variables will cluster.On the other hand, if this is your first pass through the data and you don’t have a lot of background or insight about the variables, it is called an exploratory or Principal Components Analysis (PCA).Both FA and PCA are Regression-Based tools.
• This slide shows the middle branch of the diagram. The is the branch you will choose if you have a Hybrid Model, that is, a model that is a combination of a Linking Model and a Data Reduction Model. The Hybrids require Structural Equation Modeling, which is a sophisticated application of Chi-Square and Regression-Based tools.You can find more information on Structural Equation Modeling on a separate Video Tutorial listed in the Course Menu.
• In sum, you now know how to use a branching diagram to pinpoint the correct analysis for a particular research model. For a Linking Model, you must first identify the level of measurement for your variables. Then use the Decision Table to pinpoint the correct tool.For Data Reduction Models, you must first discern whether the analysis will be theory-driven, or not. Then pick the appropriate tool, Factor Analysis or Principal Components Analysis, both of which are Regression-Based.For Hybrid Models, you will use Structural Equation Modeling, which is a sophisticated application of both Chi Square and Regression Tools.Finding a correct analysis tool can seem a daunting task, but if you take it step-by-step, it is a very straightforward process.
• ### Inferential tests analysis tools update 2011

1. 1. Inferential Tests: Analysis Tools
2. 2. Analysis Tools Chi-Square-Based ANOVA- Based Regression- Based
3. 3. Step 1: Identify Model Step 2: Level of Measurement Structural Equation Modeling Step 2: Theory Driven? Step 3: Go to Decision Table PCA FA YesNo Chi- Square- Based ANOVA & Regression Based Regression-Based Chi-Square & Regression- Based
4. 4. Step 1: Identify Model Step 2: Level of Measurement Step 3: Go to Decision Table Chi-Square Based ANOVA & Regression- Based
5. 5. Step 2: What is the Level of Measurement for Each Variable? 4 Levels 2 Categories Nominal categorical Ordinal Interval continuous Ratio
6. 6. Decision Table: Analysis Tools for Linking Models Criterion Variable(s) categorical continuous Predictor Variable(s) categorical Chi-Square Based ANOVA- Based continuous Regression-Based
7. 7. Decision Table : Analysis Tools for Linking Models with Single and Multiple Variables Criterion Variable(s) Non continuous continuous SV MV SV MV Predictor Variable(s) Non continuous Single Variable Chi Square Log Linear A V O V A M A N O V A Multiple Variable Log Linear continuous Single Variable Logistic Regression/ Discriminant Analysis Simple Regression Multivariate Regression Multiple Variable Logistic Regression/ Discriminant Analysis Multiple Regression Canonical Correlation
8. 8. Step 1: Identify Design Step 2: Level of Measurement Structural Equation Modeling Step 2: Theory Driven? Step 3: Go to Decision Table PCA FA YesNo Regression-Based
9. 9. Step 2: Theory Driven? Principal Components Analysis (PCA) Factor Analysis (FA) YesNo Step 1: Identify Design Regression-Based
10. 10. Step 1: Identify Model Structural Equation Modeling Chi-Square & Regression- Based
11. 11. How to Find the Analysis Tool for Your Model A. Linking Model 1) Identify levels of measurement 2) Use Decision Table to pinpoint analysis tools: chi-square, ANOVA and Regression-Based B. Data Reduction Model 1) Theory-Based: Factor Analysis– Regression-Based 2) Not theory-Based: Principal Components Analysis – Regression-Based C. Hybrid Model: Both a Linking Model and a Data Reduction Model - Chi-Square-Based and Regression- Based tools