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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How to input data into the SPSS data editor

This page shows the basics of entering data into the SPSS data editor. The SPSS data editor can be a good choice for entering your data. It has a friendly interface that resembles an Excel spreadsheet and by entering the data directly into SPSS, you don't need to worry about converting the data from some other format into SPSS. For example, you might enter your data in Excel, and then try to convert it to SPSS and find out that you used the latest version of Excel, but your version of SPSS has trouble reading the latest Excel files.

Below is a screen snapshot of what the SPSS data editor looks like when you start SPSS. As you see, it does look like an Excel spreadsheet. In this editor, the columns will represent your variables, and the rows will represent your observations (sometimes called records, subjects or cases).When we are creating a new data set, it is typical to start by definining the names and other properties of the variables first and then entering the specific values into each variable for each independent source of data. Recall that there is one row for each independent source of data and one column for each characteristic (i.e., variable) that we have measured from each data source. There are times, however, when we decide to add additional variables after we have entered some of the data. Adding variables after the fact does not present any special challenges; we simply go to the variable view, click in an empty row, and start defining our new variables as we do below. The first step to defining variable names and properties is to select the variable view tab in the data window. Then we can create (or edit) each of the properties below.
Name

The name of each SPSS variable in a given file must be unique; it must start with a letter; it may have up to 8 characters (including letters, numbers, and the underscore _ (note that certain key words are reversed and may not be used as variable names, e.g., "compute", "sum", and so forth). To change an existing name, click in the cell containing the name, highlight the part you want to change, and type in the replacement. To create a new variable name, click in the first empty row under the name column and type a new (unique) variable name.

 

Notice that we can use "cat_dog" but not "cat-dog" and not "cat dog". The hyphen gets interpreted as subtraction (cat minus dog) by SPSS, and the space confuses SPSS as to how many variables are being named.

Type

The two basic types of variables that you will use are numeric and string. Numeric variables may only have numbers assigned. String variables may contain letters or numbers, but even if a string variable happens to contain only numbers, numeric operations on that variable will not be allowed (e.g., finding the mean, variance, standard deviation, etc...). To change a variable type, click in that cell on the grey box with ...

 

Clicking on this box will bring up the variable type menu:

 

If you select a numeric variable, you can then click in the width box or the decimal box to change the default values of 8 characters reserved to displaying numbers with 2 decimal places. For whole numbers, you can drop the decimals down to 0.

If you select a string variable, you can tell SPSS how much "room" to leave in memory for each value, indicating the number of characters to be allowed for data entry in this string variable.

Width

The width of a variable is the number of characters SPSS will allow to be entered for the variable. If it is a numerical value with decimals, this total width has to include a spot for each decimal, as well as one for the decimal point. You can change a width by clicking in the width cell for the desired variable and typing a new number or you can use the arrow keys at the edge of the cell

 

Decimals

The decimals of a variable is the number of decimal places that SPSS will display. If more decimals have been entered (or computed by SPSS), the additional information will be retained internally but not displayed on screen. For whole numbers, you would reduce the number of decimals to zero. You can change the number of decimal places by clicking int he decimals cell for the desired variable and typing a new number or you can use the arrow keys at the edge of the cell

 

Label

The label of a variable is a string of text to indentify in more detail what a variable represents. Unlike the name, the label is limited to 255 characters and may contain spaces and punctuation. For instance, if there is a variable for each question on a questionnaire, you would type the question as the variable label. To change or edit a variable label, simply click anywhere within the cell.

 

Values

Although the variable label goes a long way to explaining what the variable represents, for categorical data (discrete data of both nominal and ordinal levels of measurement), we often need to know which numbers represent which categories. To indicate how these numbers are assigned, one can add labels to specific values by clicking on the ... box in the values cell

 

Clicking here opens up the Value Labels dialogue box.

 

Click in the Value field to type a specific numeric value
Click in the Label field to type the corresponding label
Click on the Add button to add this pair of value and label to the list
You can remove a pairing created above by clicking on that pair and then clicking on the delete button. Similarly, you can change pairing by clicking on the pair, then typing in a new value, a new label, or both; then, you click on the Change button. When you are satisfied with the definitions of each value, click on the OK button

The real beauty of value labels can be seen in the Data View by clicking on the "toe tag" icon in the tool bar , which switches between the numeric values and their labels

 

Missing

We sometimes want to signal to SPSS that data should be treated as missing, even though there is some other numerical code recorded instead of the data actually being missing (in which case SPSS displays a single period -- this is also called SYSTEM MISSING data). In this example, after clicking on the ... button in the Missing cell, I declared "9", "99", and "999" all to be treated by SPSS as missing (i.e., these values will be ignored)

 

Columns

The columns property tells SPSS how wide the column should be for each variable. Don't confuse this one with width, which indicates how many digits of the number will be displayed. The column size indicates how much space is allocated rather than the degree to which it is filled.

Align

The alignment property indicates whether the information in the Data View should be left-justified, right-justified, or centered

 

Measure

The Measure property indicates the level of measurement. Since SPSS does not differentiate between interval and ratio levels of measurement, both of these quantitative variable types are lumped together as "scale". Nominal and ordinal levels of measurement, however, are differentiated

 

Entering the Data

The first step for entering the actual data is to click on the Data View tab.

To enter new data, click in an empty cell in the first empty row. The "Tab" key will enter the value and jump to the next cell to the right. You may also use the Up, Down, Left, and Right arrow keys to enter values and move to another cell for data input.

To edit existing data points (i.e., the change a specific data value), click in the cell, type in the new value, and press the Tab, Enter, Up, Down, Right, or Left arrow keys.

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MANOVA with SPSS

MANOVA with SPSS

If you instruct SPSS to perform a MANOVA, it automatically arranges your dependent 
variables into a canonical variate. The program, then, compares the mean canonical variate 
values for each independent variable group. You can include as many independent 
variables as you wish in the analysis by entering their names as fixed factors. For a oneway 
MANOVA, though, you should identify only one fixed factor, as explained in the following 
steps.
1. Choose the "General Linear Model" option in SPSS Analyze pull-down menu. 
2. Choose "Multivariate" from the prompts given. A window entitled Multivariate should 
appear.
The user performs a MANOVA in SPSS by moving the names of relevant variables from the box on the left side 
of the window to the Dependent Variables and Fixed Factor(s) boxes in the center of the window. Because the 
MANOVA involves multiple dependent variables, the Dependent Variables box should contain at least two 
variable names. The number of variable names moved to the Fixed Factor(s) box depends upon the number of 
independent variables involved in the analysis.
3. Identify the variables involved in the analysis. 
a. Move the names of dependent variables from the box on the left side of the window 
to the box labeled "Dependent Variables."
b. Move the name of the independent variable from the box on the left side of the 
window to the box labeled "Fixed Factor(s)."
4. To include descriptive statistics for the groups in the output, click on the window's 
"Options" button. 
a. Move the name of the independent variable to the box labeled "Display Means for" 
box.
b. Mark "Descriptive Statistics" in the "Display" box.
c. Click Continue to return to the Multivariate window.
As with almost all SPSS output, the first table shown simply identifies the categories and 
the number of subjects in each one. Of more interest that this information, however, is 
likely the "Descriptive Statistics" output table, which appears only if you included Step #4 
in the process of requesting the MANOVA. This table contains group means and standard 
deviations for each individual dependent variable. 
To assess the significance of differences between the mean values, you must evaluate 
values in the Multivariate Tests table and, in some cases, the Tests of Between-Subjects 
Effects table. The first of these tables contains F and p values for the MANOVA analysis 
comparing groups' canonical variate means. The "Tests of Between Subject Effects" table 
provides data for ANOVAs performed using each individual dependent variable.

 

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When to Use ANCOVA in spss

One will see it used in two primary ways, one good, the other invalid by most accounts.

Good: Experimental design

Manipulation of IV

Random Selection of Subjects

Random Assignment to Groups

IV does not affect the Covariate!!1

There are variables that might relate to the DV but one wants to control for them, i.e. partition out their variance from the residual variance

Leads to more statistical power, though the raw effect size should not change

Adjusted mean difference is the same as the adjustment is equal for the groups involved, and if one follows Kline and others' suggestion, the standardized effect dwould not change.

You may also see ANCOVA used as a followup procedure in MANOVA (again assuming experimental design

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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Steps for ANCOVA spss

Steps for ANCOVA spss

Consider the following:

All variables reliable?

Are groups sufficiently homogeneous, i.e., low within group variance?

Low to No correlation between IV & covariates?

Notable correlation between DV & covariates?

Can the design support causal inference (e.g., random assignment to manipulated IV, control confounds)?

Are means significantly different, i.e., high between group variance?

Do groups differ after controlling for covariate?

Just as with ANOVA, in ANCOVA we are very interested in the ratio of between-groups variance over within-groups variance.

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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