Discriminant Analysis with SPSS

Discriminant Analysis with SPSS

Rather than working with pre-existing classifications of subjects, as the other tests in 
Chapter 9 do, a discriminant analysis attempts to create classifications. To conduct a 
discriminant analysis in SPSS, therefore, you cannot use the "General Linear Model" 
function. The following process allows you to use continuous values to predict subjects' 
group placements.
1. Choose the "Classify" option in SPSS Analyze pull-down menu. 
2. Identify your desired type of classification as "Discriminant." Choose "Discriminant" 
from the prompts given. A window entitled a window entitled Discriminant Analysis
should appear. 
FIGURE 9.9 –SPSS DISCRIMINANT ANALYSIS WINDOW
The user identifies the variables involved in a one-way discriminant analysis by selecting their names from 
those listed on the left side of the Discriminant Analysis window. SPSS performs the test using variables with 
names placed into the "Independents" and variables with names placed into the "Grouping Variables" box.The user identifies the variables involved in a one-way discriminant analysis by selecting their names from 
those listed on the left side of the Discriminant Analysis window. SPSS performs the test using variables with 
names placed into the "Independents" and variables with names placed into the "Grouping Variables" box.
3. In this window, you can define the variables involved in the analysis as follows
a. Move the name of the categorical dependent variable from the box on the left to the 
"Grouping Variable" box. You must also click on the "Define Range" button below 
this box and type the values for the lowest and highest dummy-variable values used 
to identify groups. 
b. Identify the continuous measure(s) used to predict subjects' categories by moving 
the names of the predictor(s) to the "Independents" box. 
4. Click OK.
The Discriminant Analysis' "Independents Variable" box allows you to identify more than 
one predictor of subjects' categories. Inputting more than one independent variable leads 
to a multiple discriminant analysis. The analysis presented in Chapter 9's examples, though, 
use a single independent variable.

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use spss One-Way Analysis of Covariance

use spss One-Way Analysis of Covariance

The one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. This guide will provide a brief introduction to the one-way ANOVA, including the assumptions of the test and when you should use it. We will then show you how to run a one-way ANOVA in SPSS using an appropriate example, which options to choose and how to interpret the output. Should you wish to learn more about the one-way ANOVA before running the procedure in SPSS, please click here.
What does this test do?
The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are statistically significantly different from each other. Specifically, it tests the null hypothesis:

where µ = group population mean and k = number of groups. The alternative hypothesis (HA) is that there are at least two group means that are significantly different from each other. Briefly stated, if the result of a one-way ANOVA is statistically significant, we accept the alternative hypothesis; otherwise, we reject the alternative hypothesis.
At this point, it is important to realise that the one-way ANOVA is an omnibus test statistic and it cannot tell you which specific groups were significantly different from each other (just that at least two groups were different). To determine which specific groups differed from each other you need to use a post-hoc test. Post-hoc tests are described later in this guide (here).
What is required
Your independent variable should be dichotomous.
Your dependent variable has either an interval or ratio (continuous) scale (see our guide on Types of Variable).
Assumptions
Your dependent variable is approximately normally distributed for each category of the independent variable (technically the residuals need to be normally distributed).
There is equality of variances between the independent groups (homogeneity of variances).
You have independence of cases.
You will need to run statistical tests in SPSS to check all of these assumptions before carrying out a one-way ANOVA. If you do not run these tests of assumptions, the results you get when running a one-way ANOVA might not be valid. If you are unsure how to do this correctly, we show you how, step-by-step in our enhanced one-way ANOVA in SPSS guide. To learn more about our enhanced guides, Take the Tour or go straight to Plans & Pricing (complete access to all our guides starts from just $3.99/£2.99/€3.99).
Example
A manager wants to raise the productivity at his company by increasing the speed at which his employees can use a particular spreadsheet program. As he does not have the skills in-house, he employs an external agency which provides training in this spreadsheet program. They offer 3 packages: a beginner, intermediate and advanced course. He is unsure which course is needed for the type of work they do at his company, so he sends 10 employees on the beginner course, 10 on the intermediate course and 10 on the advanced course. When they all return from the training he gives them a problem to solve using the spreadsheet program and times how long it takes them to complete the problem. He wishes to then compare the three courses (beginner, intermediate, advanced) to see if there are any differences in the average time it took to complete the problem.

 

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ANCOVA Examples Using SPSS

ANCOVA Examples Using SPSS

Statistical Package for the Social Sciences (SPSS) is a program for analyzing data collected by researchers in the social sciences. An ANCOVA (Analysis of Covariance) is used to analyze data in which there is one or more independent variables and a dependent variable when the researcher wants to remove the influence of one or more predictor variables on the dependent variable.

Data requirements. In all GLM models, the dependent(s) is/are continuous. The independents may be categorical factors (including both numeric and string types) or quantitative covariates. Data are assumed to come from a random sample for purposes of significance testing. The variance(s) of the dependent variable(s) is/are assumed to be the same for each cell formed by categories of the factor(s) (this is the homogeneity of variances assumption).

Regression in GLM is simply a matter of entering the independent variables as covariates and, if there are sets of dummy variables (ex., Region, which would be translated into dummy variables in OLS regression, for ex., South = 1 or 0), the set variable (ex., Region) is entered as a fixed factor with no need for the researcher to create dummy variables manually. The b coefficients will be identical whether the regression model is run under ordinary regression (in SPSS, under Analyze, Regression, Linear) or under GLM (in SPSS, under Analyze, General Linear Model, Univariate). Where b coefficients are default output for regression in SPSS, in GLM the researcher must ask for "Parameter estimates" under the Options button. The R-square from the Regression procedure will equal the partial Eta squared from the GLM regression model.

The advantages of doing regression via the GLM procedure are that dummy variables are coded automatically, it is easy to add interaction terms, and it computes eta-squared (identical to R-squared when relationships are linear, but greater if nonlinear relationships are present). However, the SPSS regression procedure would still be preferred if the reseacher wishes output of standardized regression (beta) coefficients, wishes to do multicollinearity diagnostics, or wishes to do stepwise regression or to enter independent variables hierarchically, in blocks. PROC GLM in SAS has a greater range of options and outputs (SAS also has PROC ANOVA, but it handles only balanced designs/equal group sizes).

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CONDUCTING THE ONE-WAY ANCOVA spss

The one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. This guide will provide a brief introduction to the one-way ANOVA, including the assumptions of the test and when you should use it. We will then show you how to run a one-way ANOVA in SPSS using an appropriate example, which options to choose and how to interpret the output. Should you wish to learn more about the one-way ANOVA before running the procedure in SPSS, please click here.
What does this test do?
The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are statistically significantly different from each other. Specifically, it tests the null hypothesis:

where µ = group population mean and k = number of groups. The alternative hypothesis (HA) is that there are at least two group means that are significantly different from each other. Briefly stated, if the result of a one-way ANOVA is statistically significant, we accept the alternative hypothesis; otherwise, we reject the alternative hypothesis.
At this point, it is important to realise that the one-way ANOVA is an omnibus test statistic and it cannot tell you which specific groups were significantly different from each other (just that at least two groups were different). To determine which specific groups differed from each other you need to use a post-hoc test. Post-hoc tests are described later in this guide (here).
What is required
Your independent variable should be dichotomous.
Your dependent variable has either an interval or ratio (continuous) scale (see our guide on Types of Variable).
Assumptions
Your dependent variable is approximately normally distributed for each category of the independent variable (technically the residuals need to be normally distributed).
There is equality of variances between the independent groups (homogeneity of variances).
You have independence of cases.
You will need to run statistical tests in SPSS to check all of these assumptions before carrying out a one-way ANOVA. If you do not run these tests of assumptions, the results you get when running a one-way ANOVA might not be valid. If you are unsure how to do this correctly, we show you how, step-by-step in our enhanced one-way ANOVA in SPSS guide. To learn more about our enhanced guides, Take the Tour or go straight to Plans & Pricing (complete access to all our guides starts from just $3.99/£2.99/€3.99).
Example
A manager wants to raise the productivity at his company by increasing the speed at which his employees can use a particular spreadsheet program. As he does not have the skills in-house, he employs an external agency which provides training in this spreadsheet program. They offer 3 packages: a beginner, intermediate and advanced course. He is unsure which course is needed for the type of work they do at his company, so he sends 10 employees on the beginner course, 10 on the intermediate course and 10 on the advanced course. When they all return from the training he gives them a problem to solve using the spreadsheet program and times how long it takes them to complete the problem. He wishes to then compare the three courses (beginner, intermediate, advanced) to see if there are any differences in the average time it took to complete the problem.

 

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interpret data in SPSS for a paired samples T-test

interpret data in SPSS for a paired samples T-test

It is vitally important to check these assumptions because if they are violated the result of the dependent t-test can be invalid. How to first calculate the difference scores, and then to check the above assumptions on these scores, is presented in the enhanced version of this guide, available as part of our Laerd Statistics Premium content. To get a sense of the advantages of purchasing access to Laerd Statistics Premium, you can view our enhanced Independent-samples t-test in SPSS guide for free (normally Premium). To go straight to the relevant section for testing assumptions, click here. This enhanced guide also explain what to do if you violate any of the assumptions. You can check out our low prices for access to all the enhanced content in our Premium section here.
Example
A group of Sports Science students (n = 20) are selected from the population to investigate whether a 12 week plyometric training programme improves their standing long jump performance. In order to test whether this training improves performance, the sample group are tested for their long jump performance before they undertake a plyometric training programme and then again at the end of the programme.
Test Procedure in SPSS
[If you are unsure of how to correctly enter your data into SPSS in order to run a dependent t-test then read our guide on how to do it here. Our enhanced guide includes a description of the file set-up and the ability to download the SPSS file for the guide.]
Click Analyze > Compare Means > Paired-Samples T Test... on the top menu.

Published with written permission from SPSS Inc, an IBM company.
You will be presented with the following:

Published with written permission from SPSS Inc, an IBM company.
You need to transfer the variables "JUMP1" and "JUMP2" into the "Paired Variables:" box. There are two ways to do this. You can either highlight both variables (use the cursor and hold down the shift key and press the button, or you can drag and drop each variable into the boxes). If you are using older versions of SPSS, you will need to transfer the variables using the former method.
You will end up with a screen similar to the one below:

Published with written permission from SPSS Inc, an IBM company.
button shifts the pair of variables you have highlighted down one level.
button shifts the pair of variables you have highlighted up one level.
button shifts the order of the variables with a variable pair itself.
If you need to change the confidence level limits or to exclude cases then press the button:

Published with written permission from SPSS Inc, an IBM company.
Click on the button.
Click the button to generate the output.
SPSS Output of the Dependent T-Test
You will be presented with three tables in the Output Viewer under the title "T-Test" but you only need to look at two tables - the Paired Sample Statistics table and the Paired Samples Test table, as discussed below:
Paired Sample Statistics Table
The first table titled Paired Sample Statistics is where SPSS has generated descriptive statistics for your variables. You can use the data here to describe the characteristics of the first and second jumps in your results.

Published with written permission from SPSS Inc, an IBM company.
Paired Samples Test Table
The Paired Samples Test table is where the results of the dependent t-test are presented. A lot of information is presented here and it is important to remember that this information refers to the differences between the two jumps (the subtitle reads "Paired Differences"). As such, the columns of the table labelled "Mean", "Std. Deviation", "Std. Error Mean", 95% CI refer to the mean difference between the two jumps and the standard deviation, standard error and 95% CI of this mean difference, respectively. The last 3 columns express the results of the dependent t-test, namely the t-value, the degrees of freedom and the significance level.

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Independent T-Test using SPSS

Independent T-Test using SPSS

Take a look at this box. You can see each variable name in left most column. If you have given your variables meaningful names, you should know exactly which conditions these variable names represent. You can find out the number of participants, mean and standard deviation for each condition by reading across each of the two condition rows.

Example

In the Paired Samples Statistics Box, the mean for the caffeine condition (CAFDTA) is 5.40. The mean for the no caffeine condition (NOCAFDTA) is 9.40. The standard deviation for the caffeine condition is 1.14 and for the no caffeine condition, also 1.14. The number of participants in each condition (N) is 5.

Paired Samples Test Box

This is the next box you will look at. It contains info about the paired samples t-test that you conducted. You will be most interested in the value that is in the final column of this table. Take a look at the Sig. (2-tailed) value.

Sig (2-Tailed) value

This value will tell you if the two condition Means are statistically different. Often times, this value will be referred to as the p value. In this example, the Sig (2-Tailed) value is 0.005.

If the Sig (2-Tailed) value is greater than 05…

You can conclude that there is no statistically significant difference between your two conditions. You can conclude that the differences between condition Means are likely due to chance and not likely due to the IV manipulation.

If the Sig (2-Tailed) value is less than or equal to .05…

You can conclude that there is a statistically significant difference between your two conditions. You can conclude that the differences between condition Means are not likely due to change and are probably due to the IV manipulation.
Our Example
The Sig. (2-Tailed) value in our example is 0.005. This value is less than .05. Because of this, we can conclude that there is a statistically significant difference between the mean hours of sleep for the caffeine and no caffeine conditions. Since our Paired Samples Statistics box revealed that the Mean number of hours slept for the no caffeine condition was greater than the Mean for the caffeine condition, we can conclude that participants in the no caffeine condition were able to sleep significantly more hours than participants in the caffeine condition.

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