Statistics with SPSS

Never, ever, run any statistical test without performing EDA first!

Correlation & Regression:

There are numerous methods for calculating correlations, e.g:

• The parametric Pearson, or "r value", correlation
• The nonparametric Spearman correlation
• Many others

In SPSS:

As with other tests in SPSS, variables must be entered in separate columns. Before examining correlation, always draw a scatterplot to identify outliers and ensure the data is suitable for analysis:

Graphs: Scatter and select Simple Scatter or Matrix Scatter (for more than one pair of variables)

A correlation between two variables is called a bivariate correlation. In SPSS, select:

Analyze: Correlate: Bivariate

Select the variables you are interested in comparing and the type of correlation analysis you want to perform:

• Pearson: Pearson's correlation coefficient requires:
  • Data consists of interval or ratio variables
  • Variables are normally distributed
• Spearman: Spearman's correlation coefficient is non-parametric and does not have the above requirements, so can be used for skewed or ordinal variables. However, the parametric Pearson test should always be used if it is appropriate to do so. The Spearman test does not look at the data directly, but at ranked (coded) variables. Kendals's tau is an alternative non-parametric correlation test which may be preferable to Spearman for small datasets containing many "tied ranks", i.e. equal scores. In practice, it is usual to run both of these tests and interpret the lower value.

The output reports the correlation coefficient and whether the outcome is statistically significant (i.e. p <.05).

Formal Reporting:  When you report the outcome of a correlation test, cite the value of the coefficient, degrees of freedom (N - 2) in brackets and the significance value, e.g:

Regression predicts an outcome from one or more variables. Simple regression examines the outcome from a single variable, multiple regression is where several variables are combined to predict an outcome. In reality, this involves constructing a simple statistical model consisting of a straight line which is the line of best fit between the variables. This is achieved by considering the differences between the datapoints and this line of best fit, which are known as residuals. To perform simple regression in SPSS:

Analyze: Regression: Linear

The output includes the Model Summary, e.g:

R = the correlation coefficient
R² = the coefficient of determination. This value determines how much of the variation in one variable is due to the other variable. In the example above, R² = 0.149, so 14.9% of the variation in the outcome is determined by the predictor variable (and 85.1% of the variation is caused by something else!).

The ANOVA output reports whether the model results in statistically significant prediction. In this case, Significance = .000, so the outcome is statistically significant (i.e. p <.05).

The coefficients output makes specific predictions about the magnitude of the effects predicted and confirms the significance of the model.

Formal Reporting:  When you report the outcome of simple regression, cite the value of R², the number of degrees of freedom and significance value, e.g:

To plot a regression line in SPSS:

Analyze: Regression: Curve Estimation: Linear (or other if required)

Student's t-test:

The t-test is used to compare two groups and comes in three versions:

• Paired (dependent) t-test: used when each data point in one group corresponds to a matching data point in the other group.

• Unpaired (independent) t-test: used whether or not the groups contain matching datapoints:
  • Two-sample assuming equal variances
  • Two-sample assuming unequal variances
    Levene's test for equality of variances, run as part of the SPSS independent t test procedure, will tell you if there is a significant difference between the variances of the datasets.

Where correlation and regression are used to examine relationships between datasets, the t test is the primary example of how to examine differences between datasets, so, as with any statistical investigation, the starting point is to think about what question you want to ask. In SPSS:

• Analyze: Compare Means: One-Sample T Test   Used to test whether the mean of one variable differs from a constant, e.g. does the mean mark of 52% for a sample of students differ significantly from the pass mark of 40%? When p<.05, the conclusion is that the group mean is significantly different from the constant.
• Analyze: Compare Means: Independent-Samples T Test   Used when the datasets being compared are independent, e.g. rainfall at two locations.
• Analyze: Compare Means: Paired-Samples T Test   Used when there is a direct one to one correspondence between the all points in each dataset, e.g. testing the same experimental subjects under two different conditions (before and after treatment for example).

If the data does not meet the criteria for a t test, it is sometimes possible to transform it so that the test can be used, but not always. In other cases, alternative tests must be used:

Performing a paired T test in SPSS is straightforward:

Analyze: Compare Means: Paired-Samples T Test

and select the pair of variables to be compared.

Performing an independent samples T test is slightly more complicated. SPSS requires that in addition to the values to be compared, a grouping variable must be entered. This is a dummy coding variable (remember, in SPSS, variables are always columns), which indicates the different groups, e.g:

Analyze: Compare Means: Independent-Samples T Test

Select the Test Variable (data), and the Grouping Variable (dummy). Click the Define Groups button and use the dummy coding variable you entered to select the groups to be compared (don't forget to label the groups in the Variable View window so you know what the output means!):

The output (in this case for a paired t test) includes:

The output reports the correlation coefficient for the datasets (similarity) as well as the t test result (difference). In the above example, Sig < .05, so there is evidence of a significant difference between the means of the two groups.

Formal Reporting:  When you report the outcome of the t test, cite the value of the t statistic, the number of degrees of freedom (in brackets) and significance value, e.g:

c²-test (chi-square test):

This is an example of a non-parametric test. c² (pronounced "kye-square") is used when data consists of nominal or ordinal variables rather than quantitative variables, i.e. when we are interested in how many members fall into given descriptive categories (not for quantitative measurements, such as weight, etc). The c² test is by default one-tailed and should only be carried out on raw data (not percentages, proportions or other derived data). Based on the decision tree table above, a "real" statistician would advise using tests such as the Mann-Whitney U Test or Wilcoxon Test for Paired Data in cases where the t test is not appropriate. The c² should be reserved for categorical data, e.g. male or female, pregnant or not pregnant.

There are two versions of the c² test in SPSS:

1. One-way chi-square goodness of fit test:
Used to analyze whether a frequency distribution for a categorical or nominal variable is consistent with expectations:

Example:

As with the t-test, the data is entered into SPSS with dummy coding variables which are used to define groups (e.g. sex in this example):

Note that the "coding data" (Sex in this case) must be entered as a numerical variable not as alphanumeric data or SPSS will not perform the test. The Variable View window can be used to add labels to the coded data. After the data has been entered, click  Data: Weight Cases  and weight the cases by the variable to be analyzed (Freq in this case).

Note that there is no need to enter the expected data in this case since SPSS can calculate equal expected values. Select Analyze: Nonparametric Tests: Chi-square, select Test Variable (Freq in this case) and click OK. Output:

So in this case, we conclude:

2. Chi square test of independence:
Used to analyze whether two categorical or nominal variables are related or associated with each other.

Example:

Enter the data as follows:

As in the previous examples, the dummy coding variable (Gender and Subject in this case) must be entered as numerical variables not as alphanumeric data or SPSS will not perform the test. Remember: The Data View window only contains data (numbers). The Variable View window should be used to add labels to the coded data so you can interpret the output. After the data has been entered, click  Data: Weight Cases  and weight the cases by the variable to be analyzed (Freq in this case).

• Analyze: Descriptive Statistics: Crosstabs  and  Statistics: Chi-Square

Output:

Since none of the cells have an expected count of less than 5, we can ignore Fisher's Exact test and use the (Pearson) Chi-Square result. In this case, we conclude:

© MicrobiologyBytes 2009.