SolarAesthetics
October 23, 2016
Statistics treatment for a survey study designed to test the hypothesis: If the means of solar energy generation are more aesthetically pleasing consumers will be more willing to convert to solar energy.
Overall Spearman Rank Correlation is 0.3728067 (p = 3.108624510^{-15} )
Summary of survey data
summary(solarDat)## RespondentID CollectorID StartDate EndDate
## Min. :4.851e+09 Min. :88545356 07/13/2016:323 07/13/2016:323
## 1st Qu.:4.852e+09 1st Qu.:88545356 07/14/2016: 37 07/14/2016: 37
## Median :4.852e+09 Median :88545356 07/15/2016: 18 07/15/2016: 18
## Mean :4.854e+09 Mean :88545356 07/18/2016: 18 07/18/2016: 18
## 3rd Qu.:4.853e+09 3rd Qu.:88545356 07/19/2016: 6 07/19/2016: 6
## Max. :4.952e+09 Max. :88545356 07/17/2016: 4 07/17/2016: 4
## (Other) : 18 (Other) : 18
## Consent1 USResident StateCde Homeowner1 ResidenceType
## Min. :1 Min. :1.000 FL : 52 Min. :1.000 Min. :0.000
## 1st Qu.:1 1st Qu.:1.000 GA : 52 1st Qu.:1.000 1st Qu.:1.000
## Median :1 Median :1.000 CA : 50 Median :1.000 Median :1.000
## Mean :1 Mean :1.014 : 48 Mean :1.189 Mean :1.007
## 3rd Qu.:1 3rd Qu.:1.000 NY : 47 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1 Max. :2.000 NJ : 38 Max. :2.000 Max. :2.000
## (Other):137 NA's :1 NA's :1
## ResidenceText AesImportant SolarPowerBetter
## :382 Min. :1.000 Min. :1.00
## Apartment : 9 1st Qu.:4.000 1st Qu.:3.00
## Condo : 9 Median :4.000 Median :4.00
## Condominium : 3 Mean :4.071 Mean :3.83
## Townhouse : 3 3rd Qu.:5.000 3rd Qu.:4.00
## Apartment Building: 2 Max. :5.000 Max. :5.00
## (Other) : 16 NA's :3 NA's :1
## WouldConsiderSolar AesInfluencedDecision ConvPanelsPleasing
## Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:2.000
## Median :4.000 Median :4.000 Median :2.000
## Mean :3.592 Mean :3.617 Mean :2.158
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :5.000 Max. :5.000 Max. :5.000
## NA's :2 NA's :1 NA's :5
## WindowPanelsPleasing RoofTilesPleasing RoadsPleasing WindowRate
## Min. :1.00 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.25 1st Qu.:3.000 1st Qu.:4.000 1st Qu.:1.000
## Median :4.00 Median :3.000 Median :4.000 Median :2.000
## Mean :3.86 Mean :3.295 Mean :3.939 Mean :1.868
## 3rd Qu.:4.00 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:2.000
## Max. :5.00 Max. :5.000 Max. :5.000 Max. :4.000
## NA's :2
## RoadsRate RoofTileRate ConvPanelsRate
## Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.:1.00 1st Qu.:2.000 1st Qu.:3.000
## Median :2.00 Median :3.000 Median :4.000
## Mean :2.12 Mean :2.515 Mean :3.461
## 3rd Qu.:3.00 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :4.00 Max. :4.000 Max. :4.000
## NA's :1 NA's :1
## Comments
## :335
## Good luck! : 2
## The appearance and the price are my concerns. : 1
## . : 1
## all are tough except windows in heavily treed areas : 1
## Already have 34 solar panels on my roof saves $500 a month: 1
## (Other) : 83
## ConvPanelsRateFlip RoofTileRateFlip RoadsRateFlip WindowRateFlip
## Min. :1.000 Min. :1.000 Min. :1.00 Min. :1.000
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:2.00 1st Qu.:3.000
## Median :1.000 Median :2.000 Median :3.00 Median :3.000
## Mean :1.539 Mean :2.485 Mean :2.88 Mean :3.132
## 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:4.00 3rd Qu.:4.000
## Max. :4.000 Max. :4.000 Max. :4.00 Max. :4.000
## NA's :1 NA's :1Setup variables
# Convert preference ratings from 1-4 to 4-1 to see positive correlation
solarDat$ConvPanelsRateFlip = abs(solarDat$ConvPanelsRate -5)
solarDat$RoofTileRateFlip = abs(solarDat$RoofTileRate -5)
solarDat$RoadsRateFlip = abs(solarDat$RoadsRate -5)
solarDat$WindowRateFlip = abs(solarDat$WindowRate -5)
# Common label sets
Likert5Labs = c("Strongly Disagree","Disagree","Neutral","Agree","Strongly Agree")
RevRankLabs = c("Rank 4th", "Rank 3rd", "Rank 2nd", "Rank 1st")
# Setup factor labels
Would_Consider_Solar = factor(solarDat$WouldConsiderSolar, labels=Likert5Labs)Build function to plot results and return spearman correlation and p value
# Func to print scatterplot with jitter and LM and print Spearman Corr and p value
plot_lm_spearman_corr <- function(data, xLikert5, yPrefRank4, ttl, zFactor5=NULL, zLabel=NULL) {
# get Spearman Rank Correlation and p value
catXY = c(xLikert5, y=yPrefRank4)
matXY = matrix(catXY, nrow=length(catXY)/2, ncol=2)
spCorr = rcorr(matXY, type="spearman")
# get lm intercept to use on plot
lmMod = lm(yPrefRank4 ~ xLikert5)
# decide if 5 level color Factor included
if (is.null(zFactor5)) {
ggp <- ggplot(data, aes(x=xLikert5, y=yPrefRank4))
} else {
ggp <- ggplot(data, aes(x=xLikert5, y=yPrefRank4, color=zFactor5)) +
geom_smooth(method=lm, se=FALSE, fullrange=FALSE, alpha=.2)
}
# build the rest of the plot
ggp <- ggp+
geom_point(pch = 16, alpha=.7, position = position_jitter(width = .5, height = .5)) +
# geom_smooth(method=lm, se=FALSE, fullrange=FALSE, alpha=.2) +
# Instead of linear model, show Spearman correlation line on plot -
# Since correlation has slope but does not have an intercept, use the intercept from lm
geom_abline(intercept = lmMod$coefficients[1], slope = spCorr$r[2,1], alpha = .1, size = 5) +
scale_x_continuous(breaks=c(1:5), labels=Likert5Labs) +
scale_y_continuous(breaks=c(1:4), labels=RevRankLabs) +
scale_color_discrete(name=zLabel, guide = guide_legend(reverse=TRUE)) +
ggtitle(ttl) +
labs(x="Aesthetically Pleasing", y="Preference Rank") +
theme(plot.title = element_text(color="#666666", face="bold", size=20, hjust=.5)) +
theme(axis.title = element_text(color="#666666", face="bold", size=14))
print(ggp);
return(spCorr)Show basic plots and correlations
spCor = plot_lm_spearman_corr(solarDat, solarDat$ConvPanelsPleasing, solarDat$ConvPanelsRateFlip,
"Conventional Solar Panels")
Spearman Rank Correlation is 0.3728067 (p = 3.108624510^{-15} )
spCor = plot_lm_spearman_corr(solarDat, solarDat$RoofTilesPleasing, solarDat$RoofTileRateFlip,
"Solar Roof Tiles")
Spearman Rank Correlation is 0.3614585 (p = 1.68753910^{-14} )
spCor = plot_lm_spearman_corr(solarDat, solarDat$RoadsPleasing, solarDat$RoadsRateFlip,
"Solar Roadways")
Spearman Rank Correlation is 0.1373006 (p = 0.0046219 )
spCor = plot_lm_spearman_corr(solarDat, solarDat$WindowPanelsPleasing, solarDat$WindowRateFlip,
"Solar Window Panels")
Spearman Rank Correlation is 0.2939677 (p = 7.388689710^{-10} )
Add “Would Consider Solar” factor in color
NOTE: The “Would Consider Solar” factor plots show a simple linear regression only to illustrate the relative relationships. The Overall Spearman Rank Correlation noted below each diagram is the statistic that measures the relationship. Further analysis could be done to measure the Spearman Rank Correlation by factor, including “Would Consider Solar” as well as other independent variables in the study.
spCor = plot_lm_spearman_corr(solarDat, solarDat$ConvPanelsPleasing, solarDat$ConvPanelsRateFlip,
"Conventional Solar Panels", Would_Consider_Solar, "Would\nConsider Solar")
Overall Spearman Rank Correlation is 0.3728067 (p = 3.108624510^{-15} )
spCor = plot_lm_spearman_corr(solarDat, solarDat$RoofTilesPleasing, solarDat$RoofTileRateFlip,
"Solar Roof Tiles", Would_Consider_Solar, "Would\nConsider Solar")
Overall Spearman Rank Correlation is 0.3614585 (p = 1.68753910^{-14} )
spCor = plot_lm_spearman_corr(solarDat, solarDat$RoadsPleasing, solarDat$RoadsRateFlip,
"Solar Roadways", Would_Consider_Solar, "Would\nConsider Solar")
Overall Spearman Rank Correlation is 0.1373006 (p = 0.0046219 )
spCor = plot_lm_spearman_corr(solarDat, solarDat$WindowPanelsPleasing, solarDat$WindowRateFlip,
"Solar Window Panels", Would_Consider_Solar, "Would\nConsider Solar")
Overall Spearman Rank Correlation is 0.2939677 (p = 7.388689710^{-10} )