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? 4000

What percentage of the time did the re sampled chi-square statistic exceed the chi-square statistic in the actual study? 12.5%

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? .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 there is a strong relationship

chisqtestGC(~relig+marijuan,data=gss02,
            graph=TRUE)
## Pearson's Chi-squared test 
## 
## Observed Counts:
##             marijuan
## relig        Legal NotLegal
##   Catholic      68      140
##   Jewish        10       10
##   Other        107       73
##   Protestant   118      319
## 
## Counts Expected by Null:
##             marijuan
## relig         Legal NotLegal
##   Catholic    74.58   133.42
##   Jewish       7.17    12.83
##   Other       64.54   115.46
##   Protestant 156.70   280.30
## 
## Contributions to the chi-square statistic:
##             marijuan
## relig        Legal NotLegal
##   Catholic    0.58     0.32
##   Jewish      1.12     0.62
##   Other      27.93    15.61
##   Protestant  9.56     5.34
## 
## 
## Chi-Square Statistic = 61.0839 
## Degrees of Freedom of the table = 3 
## P-Value = 0

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? They differ slightly

Sex and Wages

Let’s learn about a new data frame (its form the mosaicData package):

View(CPS85)
help(CPS85)

Say that we want 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 = "Who Makes More",
             xlab = "Wages")

Who seems to make more?

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.

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 7.226471

Does 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?