Part I
Comparison of Regression Coefficients (Slopes)
The data set you will be working with are from Inupiat and Ugandan populations. Both groups represent different forms of ecogeographic adaptation. Inupiat populations thrived for many millenia in high latitude, cold environments with freezing winters and cold-moderate summers. Ugandan population lived for many millenia at low latitudes with warm, tropical environments with warm winters and hot, humid summers. Distal relative to proximal limb segments should be longer at low latitudes (increasing surface area) and shorter at high latitudes (reducing surface area). The goal of this analysis is to understand if there are differences in the regression coefficient representing tibial relative to femoral and radial relative to humeral lengths in these populations.
Please state the null hypotheses for these two comparisons.
Analyze General Linear Model Univariate.
Select tibial length (TL) as the dependent variable and femoral length (FL) as the covariate.
Group is going to be the fixed factor.
Select Model. Choose Build Custom Terms.
Send FL and Group into the Model box.
Highlight Group, and send into the lower box using the downward arrow key.
Select By* and then send FL into the lower box using the downward arrow key.
The box should contain this text: Group*Femoral Length.
Once this text is displayed, click on the Add button. This will send the Group*FL command into the Model box.
Click Continue. Click OK.
In the Output, under the Source column, Group*Femoral Length provides results of an F-test stating whether or not the regression coefficients between Jomon and Yayoi samples significantly differ.
Report results explaining if there is a difference in slope between the samples.
Run the same test for Group2 (fixed factor), humeral (HL) (covariate), and radial (RL) (dependent variable) lengths.
Report results explaining if there is a difference in slope between the samples.
Part II
Many relationships are not linear. Human growth and development is one of the most frequently encountered data in biological anthropology where linear estimations do not appropriately model relationships between variables. This data set consists of growth in stature among prehistoric hunter-gatherers from Japan, Siberia, and Alaska. Please use forward selection to model growth in these populations by fitting consecutive terms into the equation describing growth in stature relative to age and testing the null hypothesis that each greater term does not provide a better fit than the previous term(s).
Open file named Hunter Gatherer Stature.
Select Analyze, Regression, Curve Estimation.
Under Curve Estimation, select Linear, Cubic, Quadratic. Also select Show ANOVA tables. These tables will then provide estimate of best fit.
SPSS estimates the curve past the data, which is inappropriate for presentation.
Cut and paste the Age and Stature columns into Excel
Highlight the two columns
Select Insert X-Y graph
Right click on the data in the graph
Choose insert trend line
Under polynomial (or linear depending on your results), choose the most appropriate model.
Cut/paste the Excel graph into your answers.
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