Load the R package we will use.
Replace all the instances of ???. These are answers on your moodle quiz.
Run all the individual code chunks to make sure the answers in this file correspond with your quiz answers
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Save a plot to be your preview plot
Question: t-test
- The data this quiz is a subset of HR
- Look at the variable definitions
- Note that the variables evaluation and salary have been recoded to be represented as words instead of numbers
- Set random seed generator to 123
set.seed(123)
hr_3_tidy.csv is the name of your data subset - Read it into and assign to hr - Note: col_types = “fddfff” defines the column types factor-double-double-factor-factor-factor
hr <- read_csv("https://estanny.com/static/week13/data/hr_3_tidy.csv",
col_types = "fddfff")
use the skim to summarize the data in hr
skim(hr)
| Name | hr |
| Number of rows | 500 |
| Number of columns | 6 |
| _______________________ | |
| Column type frequency: | |
| factor | 4 |
| numeric | 2 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| gender | 0 | 1 | FALSE | 2 | fem: 253, mal: 247 |
| evaluation | 0 | 1 | FALSE | 4 | bad: 148, fai: 138, goo: 122, ver: 92 |
| salary | 0 | 1 | FALSE | 6 | lev: 98, lev: 87, lev: 87, lev: 86 |
| status | 0 | 1 | FALSE | 3 | fir: 196, pro: 172, ok: 132 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| age | 0 | 1 | 39.41 | 11.33 | 20 | 29.9 | 39.35 | 49.1 | 59.9 | ▇▇▇▇▆ |
| hours | 0 | 1 | 49.68 | 13.24 | 35 | 38.2 | 45.50 | 58.8 | 79.9 | ▇▃▃▂▂ |
The mean hours worked per week is: 49.7
Q: Is the mean number of hours worked per week 48?
specify that hours is the variable of interest
hr %>%
specify(response = hours)
Response: hours (numeric)
# A tibble: 500 x 1
hours
<dbl>
1 49.6
2 39.2
3 63.2
4 42.2
5 54.7
6 54.3
7 37.3
8 45.6
9 35.1
10 53
# … with 490 more rowshypothesize that the average hours worked is 48
hr %>%
specify(response = hours) %>%
hypothesize(null = "point", mu = 48)
Response: hours (numeric)
Null Hypothesis: point
# A tibble: 500 x 1
hours
<dbl>
1 49.6
2 39.2
3 63.2
4 42.2
5 54.7
6 54.3
7 37.3
8 45.6
9 35.1
10 53
# … with 490 more rowsgenerate 1000 replicates representing the null hypothesis
hr %>%
specify(response = hours) %>%
hypothesize(null = "point", mu = 48) %>%
generate(reps = 1000, type = "bootstrap")
Response: hours (numeric)
Null Hypothesis: point
# A tibble: 500,000 x 2
# Groups: replicate [1,000]
replicate hours
<int> <dbl>
1 1 34.5
2 1 33.6
3 1 35.6
4 1 78.2
5 1 52.7
6 1 77.0
7 1 37.1
8 1 41.9
9 1 62.7
10 1 38.8
# … with 499,990 more rowsThe output has 500,000 rows
calculate the distribution of statistics from the generated data
- Assign the output
null_t_distribution - Display
null_t_distribution
null_t_distribution <- hr %>%
specify(response = age) %>%
hypothesize(null = "point", mu = 48) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "t")
null_t_distribution
# A tibble: 1,000 x 2
replicate stat
* <int> <dbl>
1 1 0.929
2 2 0.480
3 3 -0.0136
4 4 0.435
5 5 -0.810
6 6 -1.06
7 7 -0.0470
8 8 0.809
9 9 0.986
10 10 0.199
# … with 990 more rows- null_t_distribution has 1,000 t-stats
visualize the simulated null distribution
visualize(null_t_distribution)
calculate the statistic from your observed data
- Assign the output
observed_t_statistic - Display
observed_t_statistic
observed_t_statistic <- hr %>%
specify(response = hours) %>%
hypothesize(null = "point", mu = 48) %>%
calculate(stat = "t")
observed_t_statistic
# A tibble: 1 x 1
stat
<dbl>
1 2.83get_p_value from the simulated null distribution and the observed statistic
null_t_distribution %>%
get_p_value(obs_stat = observed_t_statistic , direction = "two-sided")
# A tibble: 1 x 1
p_value
<dbl>
1 0.012shade_p_value on the simulated null distribution
null_t_distribution %>%
visualize() +
shade_p_value(obs_stat = observed_t_statistic, direction = "two-sided")
If the p-value < 0.05? yes
Does your analysis support the null hypothesis that the true mean number of hours worked was 48? no
Question: 2 sample t-test
hr_1_tidy.csv is the name of your data subset - Read it into and assign to hr_2 - Note: col_types = “fddfff” defines the column types factor-double-double-factor-factor-factor
hr_2 <- read_csv("https://estanny.com/static/week13/data/hr_1_tidy.csv",
col_types = "fddfff")
Q: Is the average number of hours worked the same for both genders
use skim to summarize the data in hr_2 by gender
hr_2 %>%
group_by(gender) %>%
skim()
| Name | Piped data |
| Number of rows | 500 |
| Number of columns | 6 |
| _______________________ | |
| Column type frequency: | |
| factor | 3 |
| numeric | 2 |
| ________________________ | |
| Group variables | gender |
Variable type: factor
| skim_variable | gender | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|---|
| evaluation | female | 0 | 1 | FALSE | 4 | fai: 81, bad: 71, ver: 57, goo: 51 |
| evaluation | male | 0 | 1 | FALSE | 4 | bad: 82, fai: 61, goo: 55, ver: 42 |
| salary | female | 0 | 1 | FALSE | 6 | lev: 54, lev: 50, lev: 44, lev: 41 |
| salary | male | 0 | 1 | FALSE | 6 | lev: 52, lev: 47, lev: 46, lev: 39 |
| status | female | 0 | 1 | FALSE | 3 | fir: 96, pro: 87, ok: 77 |
| status | male | 0 | 1 | FALSE | 3 | fir: 89, ok: 76, pro: 75 |
Variable type: numeric
| skim_variable | gender | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|---|
| age | female | 0 | 1 | 41.78 | 11.50 | 20.5 | 32.15 | 42.35 | 51.62 | 59.9 | ▆▅▇▆▇ |
| age | male | 0 | 1 | 39.32 | 11.55 | 20.2 | 28.70 | 38.55 | 49.52 | 59.7 | ▇▇▆▇▆ |
| hours | female | 0 | 1 | 50.32 | 13.23 | 35.0 | 38.38 | 47.80 | 60.40 | 79.7 | ▇▃▃▂▂ |
| hours | male | 0 | 1 | 48.24 | 12.95 | 35.0 | 37.00 | 42.40 | 57.00 | 78.1 | ▇▂▂▁▂ |
- Females worked an average of 50.3 hours per week
- Males worked an average of 48.2 hours per week
Use geom_boxplot to plot distributions of hours worked by gender
hr_2 %>%
ggplot(aes(x = gender, y = hours)) +
geom_boxplot()
hr_2 %>%
specify(response = hours, explanatory = gender)
Response: hours (numeric)
Explanatory: gender (factor)
# A tibble: 500 x 2
hours gender
<dbl> <fct>
1 36.5 female
2 55.8 female
3 35 male
4 52 female
5 35.1 male
6 36.3 female
7 40.1 female
8 42.7 female
9 66.6 male
10 35.5 male
# … with 490 more rowshr_2 %>%
specify(response = hours, explanatory = gender) %>%
hypothesize(null = "independence")
Response: hours (numeric)
Explanatory: gender (factor)
Null Hypothesis: independence
# A tibble: 500 x 2
hours gender
<dbl> <fct>
1 36.5 female
2 55.8 female
3 35 male
4 52 female
5 35.1 male
6 36.3 female
7 40.1 female
8 42.7 female
9 66.6 male
10 35.5 male
# … with 490 more rowshr_2 %>%
specify(response = hours, explanatory = gender) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute")
Response: hours (numeric)
Explanatory: gender (factor)
Null Hypothesis: independence
# A tibble: 500,000 x 3
# Groups: replicate [1,000]
hours gender replicate
<dbl> <fct> <int>
1 36.4 female 1
2 35.8 female 1
3 35.6 male 1
4 39.6 female 1
5 35.8 male 1
6 55.8 female 1
7 63.8 female 1
8 40.3 female 1
9 56.5 male 1
10 50.1 male 1
# … with 499,990 more rowsThe output has 500,000 rows
calculate the distribution of statistics from the generated data - Assign the output null_distribution_2_sample_permute - Display null_distribution_2_sample_permute
null_distribution_2_sample_permute <- hr_2 %>%
specify(response = hours, explanatory = gender) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "t", order = c("female", "male"))
null_distribution_2_sample_permute
# A tibble: 1,000 x 2
replicate stat
* <int> <dbl>
1 1 -0.208
2 2 -0.328
3 3 -2.28
4 4 0.528
5 5 1.60
6 6 0.795
7 7 1.24
8 8 -3.31
9 9 0.517
10 10 0.949
# … with 990 more rowsnull_t_distributionhas 1,000 t-stats
visualize the simulated null distribution
visualize(null_distribution_2_sample_permute)
calculate the statistic from your observed data - Assign the output observed_t_2_sample_stat - Display observed_t_2_sample_stat
observed_t_2_sample_test <- hr_2 %>%
specify(response = hours, explanatory = gender) %>%
calculate(stat = "t", order = c("female", "male"))
observed_t_2_sample_test
# A tibble: 1 x 1
stat
<dbl>
1 1.78get_p_value from the simulated null distribution and the observed statistic
null_t_distribution %>%
get_p_value(obs_stat = observed_t_2_sample_test, direction = "two-sided")
# A tibble: 1 x 1
p_value
<dbl>
1 0.08null_t_distribution %>%
visualize() +
shade_p_value(obs_stat = observed_t_2_sample_test, direction = "two-sided")
If the p-value < 0.05? yes
Does your analysis support the null hypothesis that the true mean number of hours worked by female and male employees was the same? no
Question: ANOVA
hr_2_tidy.csv is the name of your data subset - Read it into and assign to hr_anova - Note: col_types = “fddfff” defines the column types factor-double-double-factor-factor-factor
hr_anova <- read_csv("https://estanny.com/static/week13/data/hr_2_tidy.csv",
col_types = "fddfff")
Q: Is the average number of hours worked the same for all three status (fired, ok and promoted) ?
use skim to summarize the data in hr_anova by statushr_anova %>%
group_by(status) %>%
skim()
| Name | Piped data |
| Number of rows | 500 |
| Number of columns | 6 |
| _______________________ | |
| Column type frequency: | |
| factor | 3 |
| numeric | 2 |
| ________________________ | |
| Group variables | status |
Variable type: factor
| skim_variable | status | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|---|
| gender | promoted | 0 | 1 | FALSE | 2 | mal: 90, fem: 89 |
| gender | fired | 0 | 1 | FALSE | 2 | fem: 101, mal: 93 |
| gender | ok | 0 | 1 | FALSE | 2 | mal: 73, fem: 54 |
| evaluation | promoted | 0 | 1 | FALSE | 4 | goo: 70, ver: 62, fai: 24, bad: 23 |
| evaluation | fired | 0 | 1 | FALSE | 4 | bad: 78, fai: 72, goo: 25, ver: 19 |
| evaluation | ok | 0 | 1 | FALSE | 4 | bad: 53, fai: 46, ver: 15, goo: 13 |
| salary | promoted | 0 | 1 | FALSE | 6 | lev: 42, lev: 42, lev: 39, lev: 34 |
| salary | fired | 0 | 1 | FALSE | 6 | lev: 54, lev: 44, lev: 34, lev: 24 |
| salary | ok | 0 | 1 | FALSE | 6 | lev: 32, lev: 31, lev: 26, lev: 19 |
Variable type: numeric
| skim_variable | status | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|---|
| age | promoted | 0 | 1 | 40.63 | 11.25 | 20.4 | 30.75 | 41.10 | 50.25 | 59.9 | ▆▇▇▇▇ |
| age | fired | 0 | 1 | 40.03 | 11.53 | 20.3 | 29.45 | 40.40 | 50.08 | 59.9 | ▇▅▇▆▆ |
| age | ok | 0 | 1 | 38.50 | 11.98 | 20.3 | 28.15 | 38.70 | 49.45 | 59.9 | ▇▆▅▅▆ |
| hours | promoted | 0 | 1 | 59.21 | 12.66 | 35.0 | 49.75 | 58.90 | 70.65 | 79.9 | ▅▆▇▇▇ |
| hours | fired | 0 | 1 | 41.67 | 8.37 | 35.0 | 36.10 | 38.45 | 43.40 | 77.7 | ▇▂▁▁▁ |
| hours | ok | 0 | 1 | 47.35 | 10.86 | 35.0 | 37.10 | 45.70 | 54.50 | 78.9 | ▇▅▃▂▁ |
Employees that were fired worked an average of 41.7 hours per week
Employees that were ok worked an average of 47.4 hours per week
Employees that were promoted worked an average of 59.2 hours per week
hr_anova %>%
ggplot(aes(x = status, y = hours)) +
geom_boxplot()
hr_anova %>%
specify(response = hours, explanatory = status)
Response: hours (numeric)
Explanatory: status (factor)
# A tibble: 500 x 2
hours status
<dbl> <fct>
1 78.1 promoted
2 35.1 fired
3 36.9 fired
4 38.5 fired
5 36.1 fired
6 78.1 promoted
7 76 promoted
8 35.6 fired
9 35.6 ok
10 56.8 promoted
# … with 490 more rowshr_anova %>%
specify(response = hours, explanatory = status) %>%
hypothesize(null = "independence")
Response: hours (numeric)
Explanatory: status (factor)
Null Hypothesis: independence
# A tibble: 500 x 2
hours status
<dbl> <fct>
1 78.1 promoted
2 35.1 fired
3 36.9 fired
4 38.5 fired
5 36.1 fired
6 78.1 promoted
7 76 promoted
8 35.6 fired
9 35.6 ok
10 56.8 promoted
# … with 490 more rowshr_anova %>%
specify(response = hours, explanatory = status) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute")
Response: hours (numeric)
Explanatory: status (factor)
Null Hypothesis: independence
# A tibble: 500,000 x 3
# Groups: replicate [1,000]
hours status replicate
<dbl> <fct> <int>
1 41.9 promoted 1
2 36.7 fired 1
3 35 fired 1
4 58.9 fired 1
5 36.1 fired 1
6 39.4 promoted 1
7 54.3 promoted 1
8 59.2 fired 1
9 40.2 ok 1
10 35.3 promoted 1
# … with 499,990 more rowsThe output has *500,000** rows
calculate the distribution of statistics from the generated data - Assign the output null_distribution_anova - Display null_distribution_anova
null_distribution_anova <- hr_anova %>%
specify(response = hours, explanatory = gender) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "F")
null_distribution_anova
# A tibble: 1,000 x 2
replicate stat
* <int> <dbl>
1 1 0.309
2 2 0.854
3 3 0.00000101
4 4 0.288
5 5 4.26
6 6 1.80
7 7 0.381
8 8 1.40
9 9 1.39
10 10 0.398
# … with 990 more rows- null_distribution_anova has 1,000 F-stats
visualize(null_distribution_anova)
calculate the statistic from your observed data - Assign the output observed_f_sample_stat - Display observed_f_sample_stat
observed_f_sample_stat <- hr_anova %>%
specify(response = hours, explanatory = status) %>%
calculate(stat = "F")
observed_f_sample_stat
# A tibble: 1 x 1
stat
<dbl>
1 128.null_distribution_anova %>%
get_p_value(obs_stat = observed_f_sample_stat, direction = "greater")
# A tibble: 1 x 1
p_value
<dbl>
1 0null_t_distribution %>%
visualize() +
shade_p_value(obs_stat = observed_f_sample_stat, direction = "greater")
If the p-value < 0.05? yes
Does your analysis support the null hypothesis that the true means of the number of hours worked for those that were “fired”, “ok” and “promoted” were the same? no
Save the previous plot to preview.png and add to the yaml chunk at the top
ggsave(filename = "preview.png", path = here::here("_posts", "2021-05-14-hypothesis-testing"))