df

Degrees of freedom refer to the number of observations in a sample that are "free to vary". Every observation increases degrees of freedom by one, but every coefficient the model estimates (including the constant) decreases the degrees of freedom by one.

Add a regression line

Graphs
     Chart Builder
          Gallery: Scatter/Dot
               Drag the Simple Scatter chart to the Chart preview
                Drag xxx from the variable list to the "X-axis" box
                Drag yyy from the variable list to the "Y-axis" box
     OK

double-click
Chart Editor

Elements
     Fit Line at Total

(multiple regression)
Options
     Reference Line from Equation
          Reference Line: Custom Equation: k + (bx)
          Apply
Close the Chart Editor

R square

The R-square statistic measures the regression model's usefulness in predicting outcomes --- indicating how much of the dependent variable's variation is due to its relationship with the independent variable(s).

Interpretation (p-value difference)

The coefficients will test the unique effect of each independent variables to the model, and the F-test will test the join effects of all the variables together.

B or slope

The unstandardized coefficient of an independent variable (also called B or slope) measures the strength of its relationship with the dependent variable. It is interpreted as the size of the average difference in the dependent variable that corresponds with a one-unit difference in the independent variable.

Linear regression

1. In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variable) denoted X. The case of one explanatory variable is called simple linear regression.
2. (source: google)
3. Analyze
4.      Regression
5.           Linear
6.                Dependent: xxx
7.                Independent: yyy
8.               OK

collective effects

One of the great benefits of regression analysis is its ability to document collective effects --- the interplay among factors on predicted outcomes...They also can measure the amount of variation in the dependent variable that can be attributed to the variables in the model, and conversely, how much of the variation is left unexplained.

paired-samples t test

Analyze
     Compare means
          Paired-Samples T test
               Paired Variables: xxx
                                            yyy
               OK

t value and sig.(2 tailed)

A t value close to 0 indicates that the two means are very similar and will result in a large significance value.

T tests

A t test is a special case of analysis of variance that compares the means of only two categories. There are two types --- an independent samples t test and a paired samples t test.

Equal variance assumption

A rule of thumb is that the ratio of the largest variance to the smallest group variance should be no larger than 9.

Histogram (normality assumption)

Graphs
     Chart Builder
          Gallery: Histogram
                Drag Simple Histogram to the Chart Preview
           Groups/Point ID: Columns Panel Variable
           Element Properties: Display normal curve
                Apply
            Drag xxx from "Variables" list to "X-axis?" box
            Drag yyy from "Variables" list to "Panel" box
            OK

Assumptions of ANOVA

ANOVA assumes the samples are independent, and each group's distribution is normal with the same standard deviation.

Post-hoc Tests

1. Because post hoc tests are run to confirm where the differences occurred between groups, they should only be run when you have a shown an overall significant difference in group means (i.e., a significant one-way ANOVA result).
2. (source: google)
3. Analyze
        Compare Means
             One-way ANOVA
                  Dependent List: xxx
                  Factor: yyy
                  Options
                       Statistics: Descriptive
                       Continue
4.                Post-hoc: Equal Variances Assumed: Tukey
5.                     Continue
6.                OK

One-way analysis of variance

Analyze
     Compare Means
          One-way ANOVA
               Dependent List: xxx
               Factor: yyy
               Options
                    Statistics: Descriptive
                    Continue
               OK

Point ID added

Graphs
     Chart Builder
          Gallery: Scatter/Dot
               Drag the Simple Scatter chart to the Chart preview
                Drag xxx from the variable list to the "X-axis" box
                Drag yyy from the variable list to the "Y-axis" box
          Groups/Point ID: check Point ID label
               Drag zzz from the Variables list to the new Point ID box in the Chart Preview
           OK

Scatterplots by SPSS

In these graphs, the independent variable is usually placed on X axis and the dependent variable is placed on the Y axis.

Graphs
     Chart Builder
          Gallery: Scatter/Dot
               Drag the Simple Scatter chart to the Chart preview
                Drag xxx from the variable list to the "X-axis" box
                Drag yyy from the variable list to the "Y-axis" box
     OK

concept of correlation

A correlation does not mean that one variable causes the change in the other variable to occur, only that their values are associated.

Pearson's correlation coefficient

Analyze
     Correlate
          Bivariate:
               Variables: xxx
                                 yyy
               Correlation Coefficients: Pearson
                Tests of Significance: Two Tailed
                OK

example of inverted U-shaped relationship (correlations)

Relationship between test anxiety and test performance is an inverted U.

People whose anxiety is very low (mentally sleepy) or very high (overwrought with anxiety) perform worse than those whose anxiety is moderate (alert and sharp).