Lab 02 - Equivalence Tests

CPP 524

Jacqui Anderson

---

Packages

library( dplyr )
library( pander )
library( ggplot2 )

Data

# load lab data
URL <- "https://github.com/DS4PS/cpp-524-sum-2020/blob/master/labs/data/female-np-entrepreneurs.rds?raw=true"
dat <- readRDS(gzcon(url( URL )))
head( dat )

QUESTIONS

Question 1

Compare education levels of male and female entrepreneurs.

• Variable Name: edu.level
• Variable Type: factor
• Survey question: What is the highest level of education you have achieved?

levels(dat$edu.level)

## [1] "None"         "High School"  "Some College" "Bachelor"     "Graduate"

t<-table(dat$edu.level, dat$gender)
t%>%prop.table(margin=1)%>%round(2)%>%pander()

	Female	Male
None	0.47	0.53
High School	0.4	0.6
Some College	0.57	0.43
Bachelor	0.6	0.4
Graduate	0.52	0.48

summary(t)

## Number of cases in table: 554 
## Number of factors: 2 
## Test for independence of all factors:
##  Chisq = 4.383, df = 4, p-value = 0.3566
##  Chi-squared approximation may be incorrect

chisq.test(t)

## 
##  Pearson's Chi-squared test
## 
## data:  t
## X-squared = 4.3831, df = 4, p-value = 0.3566

chisq.test(t, simulate.p.value = TRUE, B=10000)

## 
##  Pearson's Chi-squared test with simulated p-value (based on 10000
##  replicates)
## 
## data:  t
## X-squared = 4.3831, df = NA, p-value = 0.3656

ANSWER: In the test for group equivalence, FAIL TO REJECT the null and conclude there is not enough statistical evidence to support a difference in education level betweeen male and female entrepreneurs.

Question 2

Compare work experience for male and female entrepreneurs.

• Variable Name: years.prof.exp
• Variable Type: factor
• Survey question: How many years of professional experience did you have prior to starting the nonprofit?

levels(dat$years.prof.exp)

## [1] "0"     "1-2"   "3-5"   "6-10"  "11-15" "15+"

t2<-table(dat$years.prof.exp, dat$gender)
t2%>%prop.table(margin=1)%>%round(2)%>%pander()

	Female	Male
0	0.73	0.27
1-2	0.67	0.33
3-5	0.62	0.38
6-10	0.57	0.43
11-15	0.58	0.42
15+	0.53	0.47

chisq.test(t2)

## 
##  Pearson's Chi-squared test
## 
## data:  t2
## X-squared = 4.0086, df = 5, p-value = 0.5482

chisq.test(t2, simulate.p.value = TRUE, B=10000)

## 
##  Pearson's Chi-squared test with simulated p-value (based on 10000
##  replicates)
## 
## data:  t2
## X-squared = 4.0086, df = NA, p-value = 0.5664

bon_alpha2<- 0.05/6
bon_alpha2

## [1] 0.008333333

ANSWER: In the test for group equivalence, FAIL TO REJECT the null and conclude there is not enough statistical evidence to support a difference in work experience betweeen male and female entrepreneurs.

Question 3

Compare success in accessing seed funding for male and female entrepreneurs.

• Variable Name: seed.funding
• Variable Type: factor
• Survey question: Did you receive any SEED FUNDING to start the organization? Seed funding supports development of the organization without requiring deliverables or program activities. Seed funding could also include funding for pilot programs.

levels(dat$seed.funding)

## [1] "No"  "Yes"

t3<-table(dat$seed.funding, dat$gender)
t3%>%prop.table(margin=1)%>%round(2)%>%pander()

	Female	Male
No	0.55	0.45
Yes	0.54	0.46

chisq.test(t3)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  t3
## X-squared = 0.0086147, df = 1, p-value = 0.9261

chisq.test(t3, simulate.p.value = TRUE, B=10000)

## 
##  Pearson's Chi-squared test with simulated p-value (based on 10000
##  replicates)
## 
## data:  t3
## X-squared = 0.033448, df = NA, p-value = 0.8621

bon_alpha3<-0.05/2
bon_alpha3

## [1] 0.025

ANSWER: In the test for group equivalence, FAIL TO REJECT the null and conclude there is not enough statistical evidence to support a difference in success in accessing seed funding betweeen male and female entrepreneurs.

Question 4

Compare the willingness to take on personal debt for male and female entrepreneurs.

• Variable Name: take.on.debt
• Variable Type: factor
• Survey question: Have any members of the organization taken on debt to finance the organization? Collectively:

levels(dat$take.on.debt)

## [1] "$0"        "$0k-$10k"  "$10k-$25k" "$25k-$50k" "$50k+"

t4<-table(dat$take.on.debt, dat$gender)
t4%>%prop.table(margin=1)%>%round(2)%>%pander()

	Female	Male
$0	0.57	0.43
$0k-$10k	0.6	0.4
$10k-$25k	0.39	0.61
$25k-$50k	0.47	0.53
$50k+	0.36	0.64

chisq.test(t4)

## 
##  Pearson's Chi-squared test
## 
## data:  t4
## X-squared = 8.6158, df = 4, p-value = 0.07145

chisq.test(t4, simulate.p.value = TRUE, B=10000)

## 
##  Pearson's Chi-squared test with simulated p-value (based on 10000
##  replicates)
## 
## data:  t4
## X-squared = 8.6158, df = NA, p-value = 0.07079

bon_alpha4<-0.05/5
bon_alpha4

## [1] 0.01

ANSWER: In the test for group equivalence, FAIL TO REJECT the null and conclude there is not enough statistical evidence to support a difference in willingness to take on personal debt betweeen male and female entrepreneurs.

Question 5

Compare sources of first year funding for male and female entrepreneurs.

• Variable Name: most.imp.fund.source
• Variable Type: factor
• Survey question: From the list of funding sources, which has been the MOST important in your first year of operations? Choose one.

levels(dat$most.imp.fund.source)

## [1] "Donations"        "Founder"          "Earned Revenues"  "Foundation Grant"
## [5] "Gov Grant"        "Member Fees"      "Parent Org"       "Angel"           
## [9] "Corp Grant"

t5<-table(dat$most.imp.fund.source, dat$gender)
t5%>%prop.table(margin=1)%>%round(2)%>%pander()

	Female	Male
Donations	0.51	0.49
Founder	0.56	0.44
Earned Revenues	0.66	0.34
Foundation Grant	0.59	0.41
Gov Grant	0.59	0.41
Member Fees	0.46	0.54
Parent Org	0.5	0.5
Angel	0.52	0.48
Corp Grant	0.67	0.33

chisq.test(t5)

## 
##  Pearson's Chi-squared test
## 
## data:  t5
## X-squared = 8.8304, df = 8, p-value = 0.3568

chisq.test(t5, simulate.p.value = TRUE, B=10000)

## 
##  Pearson's Chi-squared test with simulated p-value (based on 10000
##  replicates)
## 
## data:  t5
## X-squared = 8.8304, df = NA, p-value = 0.3565

#Bonferroni Corrected Alpha
bon_alpha5<-0.05/9
bon_alpha5

## [1] 0.005555556

ANSWER: In the test for group equivalence, FAIL TO REJECT the null and conclude there is not enough statistical evidence to support a difference in sources of first year funding betweeen male and female entrepreneurs.

Question 6

Compare age at the time of nonprofit formation for male and female entrepreneurs.

• Variable Name: age
• Variable Type: numeric
• Survey question: What was your age when you created the nonprofit?

is.numeric(dat$age)

## [1] TRUE

tapply(dat$age, dat$gender, summary)

## $Female
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   22.00   44.00   52.00   51.94   59.50   85.00      15 
## 
## $Male
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   29.00   45.25   57.00   55.05   64.75   82.00       5

boxplot(age~gender, data=dat, col=c("pink", "light blue"))

t.test(age~gender, data=dat)

## 
##  Welch Two Sample t-test
## 
## data:  age by gender
## t = -3.1749, df = 589.02, p-value = 0.001577
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -5.031881 -1.185709
## sample estimates:
## mean in group Female   mean in group Male 
##             51.93948             55.04828

ANSWER: In the test for group equivalence, REJECT the null and conclude there IS enough statistical evidence to support a difference age betweeen male and female entrepreneurs.

Question 7

Compare income levels prior to starting the nonprofit for male and female entrepreneurs.

• Variable Name: income
• Variable Type: numeric
• Survey question: Please specify your income range prior to working to create this nonprofit:

is.numeric(dat$income)

## [1] TRUE

tapply(dat$income, dat$gender, summary)

## $Female
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##      81   33139   61113   67742   86094  199147 
## 
## $Male
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1026   49437   69351   80883  107363  199684

boxplot(income~gender, data=dat, col=c("pink", "light blue"))

t.test(income~gender, data=dat)

## 
##  Welch Two Sample t-test
## 
## data:  income by gender
## t = -3.6353, df = 630.22, p-value = 0.0003003
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -20239.710  -6042.518
## sample estimates:
## mean in group Female   mean in group Male 
##             67741.83             80882.95

ANSWER: In the test for group equivalence, REJECT the null and conclude there IS enough statistical evidence to support a difference in prior income levels betweeen male and female entrepreneurs.

Question 8

Based upon these seven contrasts, would you conclude that the resources male and female nonprofit entrepreneurs have at the time of founding were equivalent?

Q8-A:

What is the adjusted decision criteria used for contrasts to maintain an alpha of 0.05 for the omnibus test of group equivalence?

Answer: In Omnibus hypotheses scenarios, the results are rejected contingent on the failure of any one test. The Bonferroni Correction divides alpha by the number of contrasts and compares the p-value to the new alpha.

Q8-B:

What is the lowest p-value you observed across the seven contrasts?

Answer: p-value = 0.0003003

Q8-C:

Can we claim study group equivalency? Why or why not?

bon_alpha<-0.05/7
bon_alpha

## [1] 0.007142857

Answer: The smallest p-value of 0.0003003 is much smaller than the Bonferroni Corrected Alpha of 0.007143. This concludes that we CANNOT claim group equivalency.