**Advanced
Analysis in Biology Fall 2002**

**Data Entry**

Generally, data should be entered by stacking dependent-variable data into one column, and having subsequent 'grouping' columns that define membership of each datapoint to a specific treatment cell. The dependent variable is labeled Y (option-click), with grouping (independent) variables labeled X (shift-click). The one exception to this is in repeated measures and 'test' (t, z, etc.) designs. Often in these cases it is important to preserve the integrity of a row of data. In these cases, enter each treatment level as a separate dependent variable, ensuring that a subject's data is specific per row. In these cases, each level is labeled Y.

Data entered by the first method may be switched to the second by selecting the dependent variable as Y, the grouping variable as X, and then go MANIP > SPLIT INTO VARIABLES BY GROUP. Data entered by the second method may be switched to the first by selecting each of the separate dependent variable columns as Y, and selecting MANIP > APPEND AND MAKE GROUP VARIABLE.

**Printing**

To print more than one result or data window, compile the individual results into a LAYOUT (DATA > NEW > LAYOUT). Click-dragging the document icon in the top right-hand side of the window bar drags Windows into a layout. You can add comments (name, etc.) by using a SCRATCHPAD (DATA > NEW > SCRATCHPAD). Before printing, make sure the correct printer is selected.

**Descriptive Statistics
("Reports")**

To pre-select the descriptive statistics you need, go CALC > CALCULATIONS OPTIONS > SELECT SUMMARY STATISTICS. To obtain those statistics on an entire variable, select the variable of interest (as Y or X), and go CALC > SUMMARIES > REPORTS.

To obtain statistics on a variable categorized into groups, select the dependent variable as Y, the relevant grouping variable as X, and go CALC > SUMMARIES > REPORTS BY GROUPS. This command divides the dependent variable into groups as specified by the grouping variable, and then performs statistics on each subset.

**Tests (t, z, etc.)**

Select one variable as X, the other as Y, and
go CALC > TEST. From the pull-down menu select the appropriate
test, then define the parameters of the test (Total alpha level =
0.05 is the equivalent of a two-tail test; the null hypothesis is
usually defined as µ_{1} - µ_{2} = 0;
switching Ha from ‚ to > or < also moves the test from two- to
one-tail). Finally, select RESULTS.

**Between subjects ANOVA**

Select the dependent variable as Y, and the grouping variable(s) as X. There are the two possible ways to complete the analysis; either go CALC > ANOVA (select ANOVA for a one-way, or ANOVA WITH INTERACTIONS for a two-way), or go CALC > LINEAR MODEL. The first method provides a rudimentary ANOVA result. The second provides a 'model' screen that needs to be set up. For a one-way ANOVA, ensure OLS ANOVA is selected, and click on SHOW RESULTS. For a factorial ANOVA, select OLS ANOVA, and under FACTORS, select ALL interactions before clicking SHOW RESULTS. In more complex designs under the INTERACTION panel one can control the types of interaction the model computes.

Once SHOW RESULT is clicked, the first table provided is the source table for the ANOVA. Ignore the Constant line&emdash;it has no relevance to the type of designs you would be working with. The RESULTS FOR FACTOR option provides COEFFICIENTS (not usually needed), EXPECTED CELL MEANS (provides means per group), and POST HOC TESTS (option of SCHEFFE, BONFERRONI, or LSD; to be most conservative, always select SCHEFFE). The latter of these provides pairwise comparisons for all pairs of levels per grouping variable, giving the difference between the means (Y), and the probability associated with the test ( as always, p < 0.05 for a significant difference).

**Repeated/Within subjects
ANOVA**

Select each level as Y, and go CALC > LINEAR MODEL. The resultant 'model' screen then needs to be modified. For a one-way ANOVA, ensure REPEATED MEASURES (not MANOVA) is selected, and click on SHOW RESULTS. For a factorial ANOVA, select REPEATED MEASURES, and under FACTORS, select ALL interactions before clicking SHOW RESULTS. In more complex designs under the INTERACTION panel one can control the types of interaction the model computes.

Once SHOW RESULT is clicked, the first table provided is the source table for the ANOVA. Ignore the Constant line&emdash;it has no relevance to the type of designs you would be working with. The RESULTS FOR FACTOR option is usually not available in repeated subjects ANOVA.

**Correlation**

Select variables as X and Y, and go CALC >
CORRELATION > PEARSONS PRODUCT MOMENT. A triangular table provides
'r' for every pairwise combination of variables. Selection of CALC
> CORRELATION > COVARIANCE provides accounts of SS_{Y}
(Y versus Y), SS_{X} (X versus X), and SP_{XY} (Y
versus X).

**Regression**

Select the dependent variable as Y, and the
independent variable as X. Then go CALC > REGRESSION. The
resultant table provides R^{2} (ignore adjusted
R^{2}), a source table that tests R using an F-ratio, and a
coefficients table. In this latter table, the coefficients column
provides the regression equation constants (m = coefficient
associated with independent variable, b = coefficient associated with
constant). Ignore the t-ratio and probability associated with the
constant row. The t-ratio and probability associated with the
independent variable row is also a test of R for that regression
(t^{2} = F).

**Scatterplots**

Select variables as X and Y, and then go PLOT > SCATTERPLOTS. A number of statistical operations can be achieved from this graph. In the top left-hand corner of the window bar for the plot, click on the triangle. This allows access to a REGRESSION of the two variables, a CORRELATION, and a best fit REGRESSION LINE.