Presenting Results Analysis and pretty pictures

Results Section Link data to hypothesis General trends in data No inference Yes: “Our face proportions do not seem to be explained by the Golden Ratio.” No: “The Golden Ratio does not seem to explain cranio-facial proportions of college students.” (Better in conclusions.) Neat representation of how you came to your conclusions (make easy for reader).

Results Section, cont. Layout: Text AND tables, charts, figures. Do not leave your reader to figure out tables; give tables to facilitate summarizing data, then summarize for reader. Provide a couple of illustrative examples.

Sample Results Text E.g. “My head is quite disproportionate by the Golden Ratio’s standards; for example, my breadth to width ratio was a paltry 1.2 (Table 1). The only measurement that came even close was my neck to chin ratio (1.55). This, I came upon by measuring every ratio I could think of until I found one near 1.6. Overall, the Golden Ratio does not seem to explain my proportions very well (Table 1).”

Organizing Data What is the best layout for tables? What is the most effective way to summarize data? It all depends…

Kinds of Data Quantitative v. qualitative Refresh my senile memory… Categorical v. continuous Continuous data are measured on a continuum (duh!); most numeric values; divisible into meaningful subunits. As precise as measurement units allow. Relationship to quantitative? Anyone? E.g.?

Continuous Data Examples from previous labs Leg length Step length Standing height Sitting height Age (though often measured categorically…)

Categorical Data Data that are not measured quantitatively, but can be grouped into meaningful categories. Relationship to qualitative? Anyone? Bueller? Can be divided into sub-categories: Nominal: data in groups, with no specified order (e.g. marital status). Other ex? Ordinal: data in groups, with inherent order (e.g. education level). Other ex?

Summarizing Data Always include N Look for outliers and mistakes Continuous E.g. leg length. Mean, median, mode, percentiles, range SD: a measure of the spread in your distribution (average deviation from the mean value) Let’s try a few of these in Excel…

Summarizing Data Categorical Data List N and proportions in each category Let’s try a few of these in Excel… For obtaining counts in certain “bins” =frequency(data_array,bin_array) First, add column to define bins (how many age 18 or less? 19? 20? Etc.) Next, enter formula. Finally, select number of rows necessary under formula (# bins) then cntrl + U followed by command + enter. To get proportions, need to divide by N.

Summary Stats, cont. If easily formatted into a table, do that. If not, just make sure to include in report.

Testing hypotheses Now that we have all those, let’s take a look at your hypotheses: Girls have shorter leg-length than boys. Longer step-length is associated with longer leg-length, all else equal. First, look at your data. What do you expect to see based on hypotheses? Let’s look at Excel…

Charts and Summarizing So, to graph or get values for a continuous outcome based on a categorical predictor, you need pivot tables. This is much easier in other programs (or by hand!). Other pretty plots, e.g., boxplots, can be done in other programs. Continuous by continuous = simple scatter plot. Categorical by categorical = table of values in each category.

How about Tests? You’ve already done the hard part. You can look at your charts/ tables and have a good sense of whether the differences you have found (or not) are meaningful. But here are a couple of tests that do it more formally.

Tests! Continuous outcome, binomial predictor = t- test. Continuous outcome, categorical predictor = ANOVA. Continuous outcome, continuous predictor = correlation! Categorical predictor, categorical outcome = chi-square. You can do all of these in Excel with a little finagling and a good stats textbook. It is MUCH easier to do these in other programs.

Just for Kicks T-test on step length v. sex. First, sort data by sex. Then, use this command: =ttest(array 1, array 2, tails, type) Array 1 is values of step length for males Array 2 is values of step length for females Tails = 1 b/c you have hypothesized a directional change Type = 2 (don’t worry about this) Woah! It’s significant! (Amazing when you make up the data yourself.) :)

Writing Up If you have tests of significance, include the name of the test, p-value, and any special software used to find these. If you are an analysis-heavy group, see me for help. Otherwise, concentrate on how your data look. Does it look like there’s a difference? Is it in the predicted direction? Then, in conclusions, make general statements about findings and limitations.