Hypothesis Testing

Computer simulation based on examples from the infer package. Code for Quiz 13. - name: Nico Kellenberger url: {}

Load the R packages 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

After you check all your code chunks run then you can knit it. It won’t knit until the ??? are replaced

Save a plot to be your preview plot

Question: t-test

The data this quiz uses 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

hr_2_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

use skim to summarize the data in hr

Table 1: Data summary

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	mal: 256, fem: 244
evaluation	0	1	FALSE	4	bad: 154, fai: 142, goo: 108, ver: 96
salary	0	1	FALSE	6	lev: 95, lev: 94, lev: 87, lev: 85
status	0	1	FALSE	3	fir: 194, pro: 179, ok: 127

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
age	0	1	39.86	11.55	20.3	29.60	40.2	50.1	59.9	▇▇▇▇▇
hours	0	1	49.39	13.15	35.0	37.48	45.6	58.9	79.9	▇▃▂▂▂

Q: Is the mean number of hours worked per week 48? specify that hours is the variable of interest

Response: hours (numeric)
# A tibble: 500 x 1
   hours
   <dbl>
 1  78.1
 2  35.1
 3  36.9
 4  38.5
 5  36.1
 6  78.1
 7  76  
 8  35.6
 9  35.6
10  56.8
# ... with 490 more rows

hypothesize that the average hours worked is 48

Response: hours (numeric)
Null Hypothesis: point
# A tibble: 500 x 1
   hours
   <dbl>
 1  78.1
 2  35.1
 3  36.9
 4  38.5
 5  36.1
 6  78.1
 7  76  
 8  35.6
 9  35.6
10  56.8
# ... with 490 more rows

generate 1000 replicates representing the null hypothesis

Response: hours (numeric)
Null Hypothesis: point
# A tibble: 500,000 x 2
# Groups:   replicate [1,000]
   replicate hours
       <int> <dbl>
 1         1  39.7
 2         1  44.3
 3         1  46.8
 4         1  33.7
 5         1  39.6
 6         1  39.5
 7         1  40.5
 8         1  55.8
 9         1  72.6
10         1  35.7
# ... with 499,990 more rows

Display null_t_distribution

Response: age (numeric)
Null Hypothesis: point
# A tibble: 1,000 x 2
   replicate     stat
       <int>    <dbl>
 1         1  0.144  
 2         2 -1.72   
 3         3  0.404  
 4         4 -1.11   
 5         5  0.00894
 6         6  1.46   
 7         7 -0.905  
 8         8 -0.663  
 9         9  0.291  
10        10  3.09   
# ... with 990 more rows

visualize the simulated null distribution

calculate the statistic from your observed data

Assign the output observed_t_statistic

Display observed_t_statistic

Response: hours (numeric)
Null Hypothesis: point
# A tibble: 1 x 1
   stat
  <dbl>
1  2.37

get_p_value from the simulated null distribution and the observed statistic

# A tibble: 1 x 1
  p_value
    <dbl>
1   0.014

shade_p_value on the simulated null distribution

Is 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

Q: Is the average number of hours worked the same for both genders? use skim to summarize the data in hr_2 by gender

Table 2: Data summary

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	▇▂▂▁▂

Use geom_boxplot to plot distributions of hours worked by gender

specify the variables of interest are hours and 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 rows

hypothesize that the number of hours worked and gender are independent

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 rows

generate 1000 replicates representing the null hypothesis

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 rows

calculate the distribution of statistics from the generated data

Assign the output null_distribution_2_sample_permute

Display null_distribution_2_sample_permute

Response: hours (numeric)
Explanatory: gender (factor)
Null Hypothesis: independence
# 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 rows

visualize the simulated null distribution

calculate the statistic from your observed data

Assign the output observed_t_2_sample_stat

Display observed_t_2_sample_stat

Response: hours (numeric)
Explanatory: gender (factor)
# A tibble: 1 x 1
   stat
  <dbl>
1  1.78

get_p_value from the simulated null distribution and the observed statistic

# A tibble: 1 x 1
  p_value
    <dbl>
1   0.086

shade_p_value on the simulated null distribution

Is the p-value < 0.05? no

Does your analysis support the null hypothesis that the true mean number of hours worked by female and male employees was the same? yes

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

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 status 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 Use geom_boxplot to plot distributions of hours worked by status

specify the variables of interest are hours and 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 rows

hypothesize that the number of hours worked and status are independent

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 rows

generate 1000 replicates representing the null hypothesis

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 rows

calculate the distribution of statistics from the generated data Assign the output null_distribution_anova

Display null_distribution_anova

Response: hours (numeric)
Explanatory: status (factor)
Null Hypothesis: independence
# A tibble: 1,000 x 2
   replicate  stat
       <int> <dbl>
 1         1 0.312
 2         2 2.85 
 3         3 0.369
 4         4 0.142
 5         5 0.511
 6         6 2.73 
 7         7 1.06 
 8         8 0.171
 9         9 0.310
10        10 1.11 
# ... with 990 more rows

visualize the simulated null distribution

calculate the statistic from your observed data

Assign the output observed_f_sample_stat

Display observed_f_sample_stat

Response: hours (numeric)
Explanatory: status (factor)
# A tibble: 1 x 1
   stat
  <dbl>
1  128.

get_p_value from the simulated null distribution and the observed statistic

# A tibble: 1 x 1
  p_value
    <dbl>
1       0

shade_p_value on the simulated null distribution

Save the previous plot to preview.png and add to the yaml chunk at the top

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