summary(assn$binary_edu)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 0.000 0.471 1.000 1.000
summary(assn$binary_trust)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0000 0.0000 0.4768 1.0000 1.0000
table(assn$binary_edu, assn$binary_trust)
##
## 0 1
## 0 1358 1095
## 1 1068 1116
# Kind of evenly distributed between the two binaries, though it looks like those without college educations have slightly less trust in government than those with college degrees
contingencyTable <- table(assn$binary_edu, assn$binary_trust)
View(contingencyTable)
#same interpretation as above
crosstab_output <- capture.output(
CrossTable(
contingencyTable,
fisher = FALSE, # I had to turn this off to run the code for some reason
chisq = TRUE,
expected = TRUE,
sresid = TRUE,
format = "SPSS",
simulate.p.value = TRUE
)
)
crosstab_output
## [1] ""
## [2] " Cell Contents"
## [3] "|-------------------------|"
## [4] "| Count |"
## [5] "| Expected Values |"
## [6] "| Chi-square contribution |"
## [7] "| Row Percent |"
## [8] "| Column Percent |"
## [9] "| Total Percent |"
## [10] "| Std Residual |"
## [11] "|-------------------------|"
## [12] ""
## [13] "Total Observations in Table: 4637 "
## [14] ""
## [15] " | "
## [16] " | 0 | 1 | Row Total | "
## [17] "-------------|-----------|-----------|-----------|"
## [18] " 0 | 1358 | 1095 | 2453 | "
## [19] " | 1283.368 | 1169.632 | | "
## [20] " | 4.340 | 4.762 | | "
## [21] " | 55.361% | 44.639% | 52.901% | "
## [22] " | 55.977% | 49.525% | | "
## [23] " | 29.286% | 23.614% | | "
## [24] " | 2.083 | -2.182 | | "
## [25] "-------------|-----------|-----------|-----------|"
## [26] " 1 | 1068 | 1116 | 2184 | "
## [27] " | 1142.632 | 1041.368 | | "
## [28] " | 4.875 | 5.349 | | "
## [29] " | 48.901% | 51.099% | 47.099% | "
## [30] " | 44.023% | 50.475% | | "
## [31] " | 23.032% | 24.067% | | "
## [32] " | -2.208 | 2.313 | | "
## [33] "-------------|-----------|-----------|-----------|"
## [34] "Column Total | 2426 | 2211 | 4637 | "
## [35] " | 52.318% | 47.682% | | "
## [36] "-------------|-----------|-----------|-----------|"
## [37] ""
## [38] " "
## [39] "Statistics for All Table Factors"
## [40] ""
## [41] ""
## [42] "Pearson's Chi-squared test with simulated p-value"
## [43] "\t (based on 2000 replicates) "
## [44] "------------------------------------------------------------"
## [45] "Chi^2 = 19.32548 d.f. = NA p = 0.0004997501 "
## [46] ""
## [47] "Pearson's Chi-squared test with simulated p-value"
## [48] "\t (based on 2000 replicates) "
## [49] "------------------------------------------------------------"
## [50] "Chi^2 = 19.32548 d.f. = NA p = 0.0004997501 "
## [51] ""
## [52] " "
## [53] " Minimum expected frequency: 1041.368 "
## [54] ""
#I was concerned that the larger number of 0's for education were throwing it off but this still looks like those without a college degree are slightly lower on average in their trust in government
createMosaicPlot <- function() {
mosaicplot(
contingencyTable,
main = "Mosaic Plot of Education vs Trust in Government",
xlab = "Education Level",
ylab = "Trust in Government",
color = TRUE,
shade = TRUE,
las = 1
)
}
if (dev.cur() == 1) dev.new()
createMosaicPlot()
# Interesting that this one shows what we found above but also demonstrates that those with a college degree tend to have higher faith in government than those without college degrees
model<-lm(binary_trust~binary_edu, data=assn)
summary(model)
##
## Call:
## lm(formula = binary_trust ~ binary_edu, data = assn)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5110 -0.4464 -0.4464 0.4890 0.5536
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.44639 0.01007 44.348 < 2e-16 ***
## binary_edu 0.06460 0.01467 4.404 1.09e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4985 on 4635 degrees of freedom
## Multiple R-squared: 0.004168, Adjusted R-squared: 0.003953
## F-statistic: 19.4 on 1 and 4635 DF, p-value: 1.085e-05
# overall, of those without a college degree, typically 44% of them have faith in the government.
# for those with college degrees, that goes up 6.5% so it's closer to 51% that have faith in the government
# The t-value and p-value indicate that this is statistically significant
assn$inverse_edu <- ifelse(assn$binary_edu == 1, 0, 1)
#to make the opposite of the binary variable
model2 <- lm(binary_trust~inverse_edu, data=assn)
summary(model2)
##
## Call:
## lm(formula = binary_trust ~ inverse_edu, data = assn)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5110 -0.4464 -0.4464 0.4890 0.5536
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.51099 0.01067 47.901 < 2e-16 ***
## inverse_edu -0.06460 0.01467 -4.404 1.09e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4985 on 4635 degrees of freedom
## Multiple R-squared: 0.004168, Adjusted R-squared: 0.003953
## F-statistic: 19.4 on 1 and 4635 DF, p-value: 1.085e-05
# as expected, the inverse of the education binary resulted in a negative coefficient compared to the first model;
# this one shows that about 51% of those with a college degree have faith in government, and that that falls by about 6.5% for those without college degrees
model3<-glm(binary_trust~binary_edu, data=assn, family=binomial)
summary(model3)
##
## Call:
## glm(formula = binary_trust ~ binary_edu, family = binomial, data = assn)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.21526 0.04062 -5.300 1.16e-07 ***
## binary_edu 0.25922 0.05901 4.393 1.12e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 6418.3 on 4636 degrees of freedom
## Residual deviance: 6398.9 on 4635 degrees of freedom
## AIC: 6402.9
##
## Number of Fisher Scoring iterations: 3
exp(coef(model3))
## (Intercept) binary_edu
## 0.8063328 1.2959212
# basically, individuals with a college education have higher log-odds of trust (by 0.259) compared to those without a college education.
# this model shows that those with a college degree have 29.6% higher trust than those without (based on the odds ratio)
# P-value indicates a high degree of significance
model4<-glm(binary_trust~inverse_edu, data=assn, family=binomial)
summary(model4)
##
## Call:
## glm(formula = binary_trust ~ inverse_edu, family = binomial,
## data = assn)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.04396 0.04281 1.027 0.304
## inverse_edu -0.25922 0.05901 -4.393 1.12e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 6418.3 on 4636 degrees of freedom
## Residual deviance: 6398.9 on 4635 degrees of freedom
## AIC: 6402.9
##
## Number of Fisher Scoring iterations: 3
exp(coef(model4))
## (Intercept) inverse_edu
## 1.0449438 0.7716519
#whereas the previous one model showed about 30% higher trust for government for those with college degrees, the inverse model confirms that those without college degrees have about 30% lower trust in government based on the odds ratio