STAT 20: Introduction to Probability and Statistics

- Concept Questions
- Data Pipelines
*Break*- Worksheet - Digital
- Lab 3.1: Flights

What will this line of code return?

Respond at `pollev.com`

.

`01:00`

In R, this evaluation happens element-wise when operating on vectors.

`[1] TRUE TRUE FALSE`

`[1] FALSE FALSE TRUE`

`[1] TRUE TRUE FALSE`

Which observations will be included in the following data frame?

Please respond at `pollev.com`

.

`01:00`

- What are students’ perceptions of the chance that there is a new COVID variant that disrupts instruction in Spring 2023?

Do you think students in their first semester would be *more* likely or *less* likely to think we would remain in remote learning for the entire semester?

Answer at `pollev.com`

.

Which data frame will have fewer rows?

How do we extract the average of these students’ chance that class will be disrupted by a new COVID variant?

How do we extract the average of these students’ chance that class will be disrupted by a new COVID variant?

How do we extract the average of these students’ chance that class will be disrupted by a new COVID variant?

Most claims about data start with a *raw* data set, undergo many subsetting, aggregating, and cleaning operations, then return a *data product*.

Let’s look at three equivalent ways to build a pipeline

**Cons**

- Must be read from inside out 👎
- Hard to keep track of arguments 👎

**Pros**

- All in one line of code 👍
- Only refer to one data frame 👍

**Cons**

- Have to repeat data frame names 👎
- Creates unnecessary objects 👎

**Pros**

- Stores intermediate objects 👍
- Can be read top to bottom 👍

**Cons**

- 🤷

**Pros**

- Can be read like an english paragraph 👍
- Only type the data once 👍
- No leftovers objects 👍

It’s good practice to understand the output of each line of code by *breaking the pipe*.

What are the dimensions (rows x columns) of the data frames output at each stage of this pipe?

`01:00`

Do you think first year students would be more likely or less likely to think we would remain in remote learning for the entire semester?

Which commands are needed to help answer this question?

`new_COVID_variant`

Aside: *density plot*

`new_COVID_variant`

```
summarize(class_survey,
mean = mean(new_COVID_variant),
med = median(new_COVID_variant),
iqr = IQR(new_COVID_variant),
sd = sd(new_COVID_variant))
```

```
# A tibble: 1 × 4
mean med iqr sd
<dbl> <dbl> <dbl> <dbl>
1 0.368 0.3 0.35 0.468
```

The distribution of probabilities of **all** students is right-skewed with a mean probability of 0.37 and a median probability of 0.3, an IQR of 0.35 and a SD of 0.47.

How can we focus our analysis on just first year students?

**General goal**: Identify whether the *value* in a variable meets a *condition*.

Here: Is the value in

`new_COVID_variant`

equal to`"I'm in my first year."`

?

**Our Tool, Comparison operators**: A collection of operators that compare two values / vectors and return `TRUE`

or `FALSE`

.

`[1] FALSE`

`[1] TRUE`

`[1] FALSE`

`==`

evaluates equality,`!=`

evaluates inequality.

```
# A tibble: 619 × 3
year new_COVID_variant first_year
<chr> <dbl> <lgl>
1 I'm in my second year. 0.25 FALSE
2 This is my first semester! 0.1 FALSE
3 This is my first semester! 0 FALSE
4 I'm in my second year. 0.2 FALSE
5 I'm in my first year. 0.9 TRUE
6 I'm in my second year. 0.2 FALSE
7 I'm in my second year. 0.4 FALSE
8 I'm in my second year. 0 FALSE
9 I'm in my second year. 0.2 FALSE
10 I'm in my first year. 0.3 TRUE
# ℹ 609 more rows
```

```
# A tibble: 245 × 3
year new_COVID_variant first_year
<chr> <dbl> <lgl>
1 I'm in my first year. 0.9 TRUE
2 I'm in my first year. 0.3 TRUE
3 I'm in my first year. 0.6 TRUE
4 I'm in my first year. 0.3 TRUE
5 I'm in my first year. 0.3 TRUE
6 I'm in my first year. 0.1 TRUE
7 I'm in my first year. 0.7 TRUE
8 I'm in my first year. 0.2 TRUE
9 I'm in my first year. 0.5 TRUE
10 I'm in my first year. 0.5 TRUE
# ℹ 235 more rows
```

`new_COVID_variant`

with statisticsStatistics from *all* students

```
summarize(class_survey,
mean = mean(new_COVID_variant),
med = median(new_COVID_variant),
iqr = IQR(new_COVID_variant),
sd = sd(new_COVID_variant))
```

```
# A tibble: 1 × 4
mean med iqr sd
<dbl> <dbl> <dbl> <dbl>
1 0.368 0.3 0.35 0.468
```

Statistics from *first year* students

`new_COVID_variant`

with graphicsHistogram for *all* students

Histograms from *first year* and non-first year students

What is the mean probability of

`new_COVID_variant`

for students who were very confident that we could engineer our way out of the effects of climate change (6 or above on`climate_change`

)?

```
# A tibble: 619 × 3
year new_COVID_variant first_year
<chr> <dbl> <lgl>
1 I'm in my second year. 0.25 FALSE
2 This is my first semester! 0.1 FALSE
3 This is my first semester! 0 FALSE
4 I'm in my second year. 0.2 FALSE
5 I'm in my first year. 0.9 TRUE
6 I'm in my second year. 0.2 FALSE
7 I'm in my second year. 0.4 FALSE
8 I'm in my second year. 0 FALSE
9 I'm in my second year. 0.2 FALSE
10 I'm in my first year. 0.3 TRUE
# ℹ 609 more rows
```

```
# A tibble: 1 × 1
`mean(new_COVID_variant)`
<dbl>
1 0.368
```

What is the mean probability of

`new_COVID_variant`

forfirst-yearstudents who were very confident that we could engineer our way out of the effects of climate change (6 or above on`climate_change`

)?

```
# A tibble: 1 × 1
`mean(new_COVID_variant)`
<dbl>
1 0.370
```

`filter()`

separated by commas.What else can logical vectors be used for?

What is will this line of code return?

Respond at `pollev.com`

.

Logical vectors have a dual representation as `TRUE`

`FALSE`

and `1`

, `0`

, so you can do math on logicals accordingly.

Taking the mean of a logical vector is equivalent to find the proportion of rows that are

`TRUE`

(i.e. the proportion of rows that meet the condition).

`25:00`