DA
Maddy Ramser
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? 57200
What percentage of the time did the re sampled chi-square statistic exceed the chi-square statistic in the actual study? 9.97%
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? If there is no relationship between sex and belief in love at first sight, then there is about a 9.97% chance of getting a X^2 Statistic less than or equal to the one we actually got. This shows that there is some evidence that there is a relationship between the two variables, but there’s still a 10% probability that the results occurred completely due to chance.
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? .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 we have strong evidence that there is a relationship between race and gun ownership because the p-value obtained from the data is so small (p=0).
Is there a relationship between religion and the support or opposition of capital punishment in the US?
religCappun <- xtabs(~relig+cappun,data=gss02); religCappun## cappun
## relig Favor Oppose
## Catholic 232 95
## Jewish 12 13
## Other 183 103
## Protestant 466 197rowPerc(religCappun)## cappun
## relig Favor Oppose Total
## Catholic 70.95 29.05 100.00
## Jewish 48.00 52.00 100.00
## Other 63.99 36.01 100.00
## Protestant 70.29 29.71 100.00chisqtestGC(~relig+cappun,data=gss02)## Pearson's Chi-squared test
##
## Observed Counts:
## cappun
## relig Favor Oppose
## Catholic 232 95
## Jewish 12 13
## Other 183 103
## Protestant 466 197
##
## Counts Expected by Null:
## cappun
## relig Favor Oppose
## Catholic 224.45 102.55
## Jewish 17.16 7.84
## Other 196.31 89.69
## Protestant 455.08 207.92
##
## Contributions to the chi-square statistic:
## cappun
## relig Favor Oppose
## Catholic 0.25 0.56
## Jewish 1.55 3.40
## Other 0.90 1.97
## Protestant 0.26 0.57
##
##
## Chi-Square Statistic = 9.4698
## Degrees of Freedom of the table = 3
## P-Value = 0.0237What’s the test statistic? 9.4698
About how big should it be if the Null is correct? 3
What is the p-value? 0.0237
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 there is strong evidence that there is a relationship between religious orientation and whether one supports or opposes capital punishment. According to the percentage chart of the two variables, it seems Catholics and Protestants are more likely to favor capital punishment, while Jewish people are more likely to oppose capital punishment.
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 from both functions are the same; 0.1546.
Sex and Wages
Let’s learn about a new data frame (its form 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)## sex min Q1 median Q3 max mean sd n missing
## 1 F 1.75 4.75 6.80 10 44.50 7.878857 4.720113 245 0
## 2 M 1.00 6.00 8.93 13 26.29 9.994913 5.285854 289 0Complete the chunk below to get a density plot to answer the same question, graphically:
densityplot( ~ wage | sex, data = CPS85,
main = "Do women or men make higher wages?",
xlab = "Wages (US dollars per hour)")
Who seems to make more? Men seem to make higher wages because their density plot is less condensed into the $8-10 range than women and extends into the higher wages. Also, according to favstats(), men make higher wages both according to their mean and median ($9.99 and $8.93, respectively, versus $7.87 and $6.80, respectively for women).
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 ype 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 ypes of work.
In the code chunk below, produce some graphical output to help see whether men and women choose different ypes of work.
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.
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?