DA
Holly House
07/23/2015
App on Sex and Love at First Sight
Do the Shiny app for the two-way table on sex and love_first.
How many times did you re-sample? 600
What percentage of the time did the re sampled chi-square statistic exceed the chi-square statistic in the actual study? 8%
Do you think there is overwhelming evidence that in the GC population the two sexes differ in whether they believe in love at first sight? No
chisqtestGC() on the sex and love at first sight Question
Here’s the code for a chi-square test to see if sex and belief in love at first sight are related in the GC population. Run the code:
chisqtestGC(~sex+love_first,data=m111survey,
graph=TRUE)## Pearson's Chi-squared test with Yates' continuity correction
##
## Observed Counts:
## love_first
## sex no yes
## female 22 18
## male 23 8
##
## Counts Expected by Null:
## love_first
## sex no yes
## female 25.35 14.65
## male 19.65 11.35
##
## Contributions to the chi-square statistic:
## love_first
## sex no yes
## female 0.44 0.77
## male 0.57 0.99
##
##
## Chi-Square Statistic = 2.0068
## Degrees of Freedom of the table = 1
## P-Value = 0.1566
Now look at the output and answer these question:
What’s the test statistic?
2.0068
About how big should it be if the Null is correct?
1
What’s the P-value? 0.1566
Race and Gun Owndership
Are race and gun owndership related in the U.S. population? In the code chunk below, insert the code needed to use chisqtestGC() to investigate this question. Tip: copy-paste and then modify the code from the previous problem.
chisqtestGC(~race+owngun,data=gss02,
graph=TRUE)## Pearson's Chi-squared test
##
## Observed Counts:
## owngun
## race No Yes
## AfrAm 106 16
## Hispanic 20 3
## Other 25 7
## White 454 284
##
## Counts Expected by Null:
## owngun
## race No Yes
## AfrAm 80.67 41.33
## Hispanic 15.21 7.79
## Other 21.16 10.84
## White 487.97 250.03
##
## Contributions to the chi-square statistic:
## owngun
## race No Yes
## AfrAm 7.96 15.53
## Hispanic 1.51 2.95
## Other 0.70 1.36
## White 2.36 4.61
##
##
## Chi-Square Statistic = 36.9779
## Degrees of Freedom of the table = 3
## P-Value = 0
Looking at the output, answer the following questions.
What’s the test statistic?
36.9779
About how big should it be if the Null is correct?
3
What’s the P-value?
0
Do you think we have strong evidence for a relationship in the population, or could the pattern in the data be due just to chance?
Yes
Simulated Sex and Seat
Try simulation on the sex and seating-preference study:
chisqtestGC(~sex+seat,data=m111survey,
simulate.p.value="random",
B=3000)Now try it again, without simulation:
chisqtestGC(~sex+seat,data=m111survey)Compare the P-values: are they about the same, or very different?
The p-values are about the same and differ .0023.
Sex and Wages
Let’s learn about a new data frame (its from the mosaicData package):
View(CPS85)
help(CPS85)Say that we wnat to know: Who makes more money, on average: a male or a female?
In the code chunk below, write some code that with favstats that will help you answer this question.
favstats(wage~sex, data = CPS85)Complete the chunk below to get a density plot to answer the same question, graphically:
densityplot( ~ wage | sex, data = CPS85,
main = "Wage by Sex",
xlab = "wage")
Who seems to make more? Males
Before we conclude that there is wage discrimination on the basis of sex we should think about possible confounding factors.
Maybe work-setor is a confounding factor. If men and women differ in what type of work they choose, and men tend to choose higher-paying types of work, then maybe that’s why their wages are higher?
In the code chunk below, produce some numerical output to help see whether men and women choose different types of work.
favstats(sex~sector, data=CPS85)## Warning in (function (x, ..., na.rm = TRUE) : Auto-converting factor to
## numeric.## Warning in (function (x, ..., na.rm = TRUE) : Auto-converting factor to
## numeric.## Warning in (function (x, ..., na.rm = TRUE) : Auto-converting factor to
## numeric.## Warning in (function (x, ..., na.rm = TRUE) : Auto-converting factor to
## numeric.## Warning in (function (x, ..., na.rm = TRUE) : Auto-converting factor to
## numeric.## Warning in (function (x, ..., na.rm = TRUE) : Auto-converting factor to
## numeric.## Warning in (function (x, ..., na.rm = TRUE) : Auto-converting factor to
## numeric.## Warning in (function (x, ..., na.rm = TRUE) : Auto-converting factor to
## numeric.## sector min Q1 median Q3 max mean sd n missing
## 1 clerical 1 1 1 1 2 1.216495 0.4139949 97 0
## 2 const 2 2 2 2 2 2.000000 0.0000000 20 0
## 3 manag 1 1 2 2 2 1.618182 0.4903101 55 0
## 4 manuf 1 1 2 2 2 1.647059 0.4814377 68 0
## 5 other 1 2 2 2 2 1.911765 0.2857456 68 0
## 6 prof 1 1 2 2 2 1.504762 0.5023753 105 0
## 7 sales 1 1 2 2 2 1.552632 0.5038966 38 0
## 8 service 1 1 1 2 2 1.409639 0.4947565 83 0In the code chunk below, produce some graphical output to help see whether men and women choose different types of work.
barchartGC(~sex+sector, data=CPS85)
In the code-chunk below, run a chi-square test to see if the relationship you see in the data provides storng evidence that sex and sector are related in the U.S. population.
chisqtestGC(~sector+sex, data=CPS85,graph=TRUE)## Pearson's Chi-squared test
##
## Observed Counts:
## sex
## sector F M
## clerical 76 21
## const 0 20
## manag 21 34
## manuf 24 44
## other 6 62
## prof 52 53
## sales 17 21
## service 49 34
##
## Counts Expected by Null:
## sex
## sector F M
## clerical 44.50 52.50
## const 9.18 10.82
## manag 25.23 29.77
## manuf 31.20 36.80
## other 31.20 36.80
## prof 48.17 56.83
## sales 17.43 20.57
## service 38.08 44.92
##
## Contributions to the chi-square statistic:
## sex
## sector F M
## clerical 22.29 18.90
## const 9.18 7.78
## manag 0.71 0.60
## manuf 1.66 1.41
## other 20.35 17.25
## prof 0.30 0.26
## sales 0.01 0.01
## service 3.13 2.65
##
##
## Chi-Square Statistic = 106.4973
## Degrees of Freedom of the table = 7
## P-Value = 0
In the code chunk below, produce some numerical output to help see whether wages vary by work sector.
In the code chunk below, produce some graphical output to help see whether wages vary by work sector.
Run the code below: what does it tell you?
densityplot(~wage|sector*sex, data =CPS85)
The following code gives the mean salary for each sex in each work sector. What does it tell you?
with(CPS85, tapply(wage, INDEX = list(sex,sector), FUN = mean))## clerical const manag manuf other prof sales service
## F 7.404211 NA 11.05619 5.713750 5.801667 11.10500 5.241765 6.059388
## M 7.489048 9.502 13.72176 9.302727 8.761774 12.77396 9.495714 7.226471Does it appear that the overall difference between men and women can be explained by the fact that they choose different sectors of work? Why or why not?