```{r setup, include=FALSE, message = FALSE} knitr::opts_chunk$set(echo = TRUE, comment = "",warning = FALSE, message = FALSE) library(rmarkdown) ``` Before you start the lab, add the code that will load any other packages you might need into this code chunk. ```{r, message = FALSE} ``` ## Scenario 1: Sex Bias Sex bias stems from a perceived mismatch from an expected role or characteristics based on sex. Studies have shown that men and women have unconscious sex biases against women in traditionally male-dominated fields (such as the sciences) or characteristics (such as leadership qualities). These biases often cause equally qualified women to be seen as [less likable](https://www.youtube.com/watch?v=hK0Q8b6QhDo) or [less qualified](https://blogs.scientificamerican.com/unofficial-prognosis/study-shows-gender-bias-in-science-is-real-heres-why-it-matters/) than the men. (These links are to descriptions of two well-known studies, but there are plenty of other good resources). Researchers are interested if this sex bias exists in traditionally female-dominated jobs as well, such as teaching. Students are asked to watch a video of an animated classroom and rate the professor. Each student is randomly assigned to either of two animations; the videos are exactly the same except for the sex of the professor drawn. You have been asked to analyze the data for the researchers to determine if the female-identifying professor is rated more poorly, on a 1 to 7 scale (with 7 being the best), than the male-identifying professor. 1.1. State the general research question and then the statistical research question. > General research question: > Statistical research question: 1.2. State the parameter(s) of interest in the study. Replace all placeholders, including brackets. > [parameter1 symbol] = [parameter] of [variable] in [population + group1] > [parameter2 symbol] = [parameter] of [variable] in [population + group2] 1.3. What is your null value? Use mathematical notation to write your answer. Explain why this null value is appropriate in context of the study. > [symbol] = [value] > Insert explanation here 1.4. State your null and alternative hypotheses, both symbolically and verbally. You may need one of these symbols for the alternative: $<, >, \neq$. You will need to replace the entire placeholder we supplied, including [ ]s. > $H_0$: [parameter1] - [parameter2] = [null value] > Insert verbal null hypothesis here > $H_1$: [parameter1] - [parameter2] [alternative symbol] [null value] > Insert verbal alternative hypothesis here 1.5. Calculate the relevant summary statistics. Annotate your code using `#` to describe what each line of code is doing. Enter your values in the table below. ```{r} bias <- read.csv("prof_ratings.csv", header=TRUE) # reads in the csv file names(bias) df_stats(______ ~ ______, data = ______) # annotate here mean(______ ~ ______, data = ______) # annotate here var(______ ~ ______, data = ______) # annotate here ``` Symbols | Female | Male ----------|-----------|----------- $n$ | | $\bar{x}$ | | $s^2$ | | 1.6. Using the descriptive statistics you calculated in 1.5, calculate your observed difference in means. You should edit the subscripts to make them informative, replacing the entire placeholder we supplied, including [ ]s. > $\bar{x}_{[population1]} - \bar{x}_{[population2]}$ = [calculated value]
```{r setup, include=FALSE, message = FALSE}
knitr::opts_chunk$set(echo = TRUE, comment = "",warning = FALSE, message = FALSE)
library(rmarkdown)
```
Before you start the lab, add the code that will load any other packages you might need into this code chunk.
```{r, message = FALSE}
```
## Scenario 1: Sex Bias
Sex bias stems from a perceived mismatch from an expected role or characteristics based on sex. Studies have shown that men and women have unconscious sex biases against women in traditionally male-dominated fields (such as the sciences) or characteristics (such as leadership qualities). These biases often cause equally qualified women to be seen as [less likable](https://www.youtube.com/watch?v=hK0Q8b6QhDo) or [less qualified](https://blogs.scientificamerican.com/unofficial-prognosis/study-shows-gender-bias-in-science-is-real-heres-why-it-matters/) than the men. (These links are to descriptions of two well-known studies, but there are plenty of other good resources).
Researchers are interested if this sex bias exists in traditionally female-dominated jobs as well, such as teaching. Students are asked to watch a video of an animated classroom and rate the professor. Each student is randomly assigned to either of two animations; the videos are exactly the same except for the sex of the professor drawn. You have been asked to analyze the data for the researchers to determine if the female-identifying professor is rated more poorly, on a 1 to 7 scale (with 7 being the best), than the male-identifying professor.
1.1. State the general research question and then the statistical research question.
> General research question:
> Statistical research question:
1.2. State the parameter(s) of interest in the study. Replace all placeholders, including brackets.
> [parameter1 symbol] = [parameter] of [variable] in [population + group1]
> [parameter2 symbol] = [parameter] of [variable] in [population + group2]
1.3. What is your null value? Use mathematical notation to write your answer. Explain why this null value is appropriate in context of the study.
> [symbol] = [value]
> Insert explanation here
1.4. State your null and alternative hypotheses, both symbolically and verbally. You may need one of these symbols for the alternative: $<, >, \neq$. You will need to replace the entire placeholder we supplied, including [ ]s.
> $H_0$: [parameter1] - [parameter2] = [null value]
> Insert verbal null hypothesis here
> $H_1$: [parameter1] - [parameter2] [alternative symbol] [null value]
> Insert verbal alternative hypothesis here
1.5. Calculate the relevant summary statistics. Annotate your code using `#` to describe what each line of code is doing. Enter your values in the table below.
```{r}
bias <- read.csv("prof_ratings.csv", header=TRUE) # reads in the csv file
names(bias)
df_stats(______ ~ ______, data = ______) # annotate here
mean(______ ~ ______, data = ______) # annotate here
var(______ ~ ______, data = ______) # annotate here
```
Symbols | Female | Male
----------|-----------|-----------
$n$ | |
$\bar{x}$ | |
$s^2$ | |
1.6. Using the descriptive statistics you calculated in 1.5, calculate your observed difference in means. You should edit the subscripts to make them informative, replacing the entire placeholder we supplied, including [ ]s.
> $\bar{x}_{[population1]} - \bar{x}_{[population2]}$ = [calculated value]
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