Blueprint for an Innovation Economy in Florida Research as Economic Foundation | Page 29
EXHIBIT D: Results
Prior to analysis, the data was examined for characteristics integral to normality and found to be non-
normal. It was therefore transformed using the natural log function (See Table 1 below). After the log
transformation, the predictor and outcome variable data were both normal as illustrated by the results of
a Shapiro-Wilk test of normality (Citations, W = .982, p = .16; Percent STEM jobs, W = .99, p = .59). The
descriptive data can be found in Table 1.
TABLE 1: Descriptive Statistics for Variables of Interest
Variable Mean
SD Min Max
NLogCitations
10.30 1.07 8.27 13.44
NLog%STEMJobs -2.88 .42 -3.87 -1.60
Next, the variables were entered into a simple linear regression. The predictor was scientific citations
and the outcome was percent of STEM jobs. The model was statistically significant, p < .01, and meaning
that citations was shown to predict percent of STEM jobs. The regression equation was: NLog%STEM =
-5.91 + 0.23 NLogCitations. One standard deviation increase in the natural log of percent STEM jobs was
associated with a .23-unit increase of the natural log of citations. However, when using the standardized
beta weight, one standard deviation increase in the natural log of percent STEM jobs was associated with
a .58 unit increase of the natural log of citations. The total variance explained by this model (R 2 ) was .33,
meaning that 33 percent of the variance seen in percent jobs can be explained by citations. A Shapiro-Wilk
test conducted on the residuals of Model 1 revealed no violations of normality, W = .99, p = .37.
TABLE 2: Regression Model 1
Variable
Unstandardized Beta
Con stant
SE
Standardized Beta
t
-5.198 .315 -16.476**
NLogCitations .225
.030 .581 7.39**
Note: ** p < .01, Adjusted R 2 = .33
Notes:
1. The data was transformed using the natural log function because the distribution was positively
(or right) skewed; the natural log is a standard transformation used to correct this specific type of
normality violation. The data was also converted into z-scores for ease of interpretation, particularly in
visualizations. Z-scores are used to standardize data, so that it is comparable across studies (comparing
“apples to apples”). The natural log transformation normalized the data distribution whereas the z-score
standardized the scores within the data. Confirmatory analysis in SPSS might be slightly different than
output on other applications, such as Excel.
2. In the original analysis, population was shown to correlate to citations and STEM jobs. Therefore,
population could be a mediating variable between the citations and percent STEM jobs, and this
relationship could be artificially driving the R 2 value.
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