Chapter 3 Midterm
3.1 Introduction
The purpose of this midterm was to examine a sleep exercise data set and clean it up and analyze it. I ran various tests such as a t-test, ANOVA and post-hoc. ## Setup & Data import
library(tidyverse)
library(readxl)
library(knitr)
library(mosaic)
library(ggplot2)
library(supernova)
library(AICcmodavg)sleep_exercise_info <- read_excel("midterm_sleep_exercise.xlsx",
sheet = "participant_info_midterm")
View(sleep_exercise_info)
sleep_exercise_data <- read_excel("midterm_sleep_exercise.xlsx",
sheet = "sleep_data_midterm")
View(sleep_exercise_data)
glimpse(sleep_exercise_info)## Rows: 100
## Columns: 4
## $ ID <chr> "P001", "P002", "P003", "P004", "P005", "P006", "P007", "P008", "P009", "P010", "P011", …
## $ Exercise_Group <chr> "NONE", "Nonee", "None", "None", "None", "None", "None", "None", "None", "None", "None",…
## $ Sex <chr> "Male", "Malee", "Female", "Female", "Male", "Female", "Male", "Female", "Male", "Female…
## $ Age <dbl> 35, 57, 26, 29, 33, 33, 32, 30, 37, 28, 30, 20, 42, 31, 33, 26, 41, 18, 28, 37, 48, 37, …## Rows: 100
## Columns: 4
## $ ID <chr> "P001", "P002", "P003", "P004", "P005", "P006", "P007", "P008", "P009", "P010", "P011"…
## $ Pre_Sleep <chr> "zzz-5.8", "Sleep-6.6", NA, "SLEEP-7.2", "score-7.4", "Sleep-6.6", "Sleep-6", "zzz-8.1…
## $ Post_Sleep <dbl> 4.7, 7.4, 6.2, 7.3, 7.4, 7.1, 6.7, 9.0, 5.1, 6.3, 6.2, 4.6, 7.6, 7.2, 4.6, 8.2, 7.6, 7…
## $ Sleep_Efficiency <dbl> 81.6, 75.7, 82.9, 83.6, 83.5, 88.5, 83.6, 73.4, 88.2, 80.4, 85.2, 82.9, 74.0, 92.0, 89…We have both data sets and are now ready to clean and analye our data.
3.2 Merge and Base Cleaning
clean_exercise_group<- sleep_exercise_info %>%
mutate(Exercise_Group = case_when(
Exercise_Group %in% c("cardio", "CARDIO", "C") ~ "Cardio",
Exercise_Group %in% c("WEIGHTS", "WEIGHTSSS", "WEIGHTZ") ~ "Weights",
Exercise_Group %in% c("CW", "C+W") ~ "Cardio+Weights",
Exercise_Group %in% c("Nonee", "NONE", "N") ~ "None",
TRUE ~ Exercise_Group
))
View(clean_exercise_group)
clean_sex_label <- sleep_exercise_info %>%
mutate(Sex = case_when(
Sex %in% c("F", "Fem", "Femalee") ~ "Female",
Sex %in% c("M", "MALE", "Mal", "Malee") ~ "Male",
TRUE ~ Sex
))
View(clean_sex_label)
exercise_group_data <- merge(clean_exercise_group, clean_sex_label)
View(exercise_group_data)
clean_sleep_data<- merge(exercise_group_data, sleep_exercise_data)
View(clean_sleep_data)I was able to clean up the data in the Exercise group and Sex column in the sleep_exercise_info data set. Now the words in those columns are standardized. I also merged both data sets together.
3.3 Create Derived Variables
clean_sleep_data <- clean_sleep_data %>%
mutate(
pre_sleep_num = as.numeric(gsub("[^0-9.]", "", Pre_Sleep))
)
clean_sleep_data <- clean_sleep_data %>%
mutate(Sleep_Difference = clean_sleep_data$Post_Sleep - clean_sleep_data$pre_sleep_num)
clean_sleep_data <- clean_sleep_data %>%
mutate(
AgeGroup2 = case_when(
Age < 40 ~ "40",
Age >= 40 ~ "40+"
)
)
clean_sleep_data %>%filter(is.na(Sleep_Difference))## ID Exercise_Group Sex Age Pre_Sleep Post_Sleep Sleep_Efficiency pre_sleep_num Sleep_Difference AgeGroup2
## 1 P003 None Female 26 <NA> 6.2 82.9 NA NA 40
## 2 P014 None Male 31 <NA> 7.2 92.0 NA NA 40
## 3 P019 None Male 28 <NA> 5.7 69.1 NA NA 40
## 4 P023 None Female 42 sleep-5 NA 81.3 5.0 NA 40+
## 5 P037 Cardio Male 35 <NA> 9.7 85.6 NA NA 40
## 6 P095 Cardio+Weights Female 29 Sleep-5.7 NA 85.0 5.7 NA 40
## 7 P099 Cardio+Weights Male 28 <NA> 8.8 88.5 NA NA 40## ID Exercise_Group Sex Age Pre_Sleep Post_Sleep Sleep_Efficiency pre_sleep_num Sleep_Difference AgeGroup2
## 1 P004 None Female 29 SLEEP-7.2 7.3 83.6 7.2 0.1 40
## 2 P005 None Male 33 score-7.4 7.4 83.5 7.4 0.0 40
## 3 P006 None Female 33 Sleep-6.6 7.1 88.5 6.6 0.5 40
## 4 P007 None Male 32 Sleep-6 6.7 83.6 6.0 0.7 40
## 5 P008 None Female 30 zzz-8.1 9.0 73.4 8.1 0.9 40
## 6 P009 None Male 37 sleep-5.5 5.1 88.2 5.5 -0.4 40
## 7 P010 None Female 28 sleep-5.7 6.3 80.4 5.7 0.6 40
## 8 P011 None Female 30 score-7 6.2 85.2 7.0 -0.8 40
## 9 P012 None Male 20 sleep-5.5 4.6 82.9 5.5 -0.9 40
## 10 P013 None Male 42 Sleep-8 7.6 74.0 8.0 -0.4 40+
## 11 P016 None Male 26 SLEEP-7.8 8.2 71.7 7.8 0.4 40
## 12 P017 None Female 41 zzz-6.7 7.6 78.5 6.7 0.9 40+
## 13 P018 None Male 18 SLEEP-7.4 7.2 73.8 7.4 -0.2 40
## 14 P021 None Male 48 zzz-6.8 7.1 78.7 6.8 0.3 40+
## 15 P024 None Female 39 score-6 5.6 76.6 6.0 -0.4 40
## 16 P026 Cardio Female 34 score-5.2 6.7 84.5 5.2 1.5 40
## 17 P027 Cardio Female 28 sleep-6.6 7.8 75.9 6.6 1.2 40
## 18 P028 Cardio Female 29 SLEEP-5.6 6.3 79.0 5.6 0.7 40
## 19 P029 Cardio Male 36 Sleep-6 6.3 87.6 6.0 0.3 40
## 20 P031 Cardio Female 42 Sleep-6.9 7.6 88.5 6.9 0.7 40+
## 21 P032 Cardio Female 18 SLEEP-6.9 7.9 87.8 6.9 1.0 40
## 22 P033 Cardio Female 38 zzz-5.9 6.6 80.9 5.9 0.7 40
## 23 P034 Cardio Female 20 score-5.2 6.0 92.8 5.2 0.8 40
## 24 P035 Cardio Male 30 SLEEP-6.7 8.0 86.4 6.7 1.3 40
## 25 P036 Cardio Female 19 zzz-5.4 5.7 88.0 5.4 0.3 40
## 26 P038 Cardio Female 34 zzz-7 8.1 79.6 7.0 1.1 40
## 27 P039 Cardio Male 39 SLEEP-5.6 6.3 81.3 5.6 0.7 40
## 28 P040 Cardio Female 39 zzz-6 8.1 79.7 6.0 2.1 40
## 29 P042 Cardio Female 28 SLEEP-5.6 7.3 81.9 5.6 1.7 40
## 30 P043 Cardio Female 43 zzz-6.9 8.2 81.3 6.9 1.3 40+
## 31 P044 Cardio Female 33 zzz-5.8 7.1 88.7 5.8 1.3 40
## 32 P046 Cardio Male 30 SLEEP-7.1 8.5 95.0 7.1 1.4 40
## 33 P047 Cardio Female 42 SLEEP-5.8 7.0 85.5 5.8 1.2 40+
## 34 P050 Cardio Male 31 zzz-6.4 8.4 101.5 6.4 2.0 40
## 35 P076 Cardio+Weights Male 37 sleep-5.7 6.5 83.9 5.7 0.8 40
## 36 P077 Cardio+Weights Female 37 score-5.9 7.3 92.4 5.9 1.4 40
## 37 P078 Cardio+Weights Female 24 score-6.6 7.2 74.5 6.6 0.6 40
## 38 P079 Cardio+Weights Male 38 SLEEP-6.6 7.4 89.0 6.6 0.8 40
## 39 P080 Cardio+Weights Male 42 Sleep-7.2 8.1 94.5 7.2 0.9 40+
## 40 P081 Cardio+Weights Female 38 Sleep-8 8.9 74.5 8.0 0.9 40
## 41 P082 Cardio+Weights Male 46 score-6.5 6.4 88.7 6.5 -0.1 40+
## 42 P083 Cardio+Weights Female 49 score-5.9 6.8 90.4 5.9 0.9 40+
## 43 P084 Cardio+Weights Female 31 sleep-8 8.4 80.2 8.0 0.4 40
## 44 P085 Cardio+Weights Male 33 score-6.2 6.9 89.9 6.2 0.7 40
## 45 P086 Cardio+Weights Female 46 SLEEP-6.2 7.4 83.1 6.2 1.2 40+
## 46 P087 Cardio+Weights Male 18 SLEEP-6.7 7.6 96.3 6.7 0.9 40
## 47 P088 Cardio+Weights Male 34 score-7.5 8.9 81.2 7.5 1.4 40
## 48 P090 Cardio+Weights Female 41 Sleep-7.2 7.6 79.9 7.2 0.4 40+
## 49 P091 Cardio+Weights Male 46 zzz-7.3 7.9 87.5 7.3 0.6 40+
## 50 P093 Cardio+Weights Female 40 Sleep-8 9.5 90.4 8.0 1.5 40+
## 51 P094 Cardio+Weights Male 35 zzz-6.1 7.2 84.4 6.1 1.1 40
## 52 P097 Cardio+Weights Male 24 SLEEP-4.4 4.7 88.9 4.4 0.3 40
## 53 P098 Cardio+Weights Female 35 score-5.9 6.9 92.6 5.9 1.0 40
## 54 P100 Cardio+Weights Male 32 zzz-6.5 7.3 84.2 6.5 0.8 40I created a new column and called it pre_sleep_num to make the Pre_Sleep column just numeric, without any of the characters. After making it numeric, I was able to create a derived variable called sleep_difference which was the scores from post_sleep minus the scores from pre_sleep. I also created a variable called Age_Group_ which conveyed whether participants were either 40 years old or younger, and 40+ years old. I also ran the is.na function to drop the rows in the Sleep_difference column
3.4 Descriptive Statistics
## min Q1 median Q3 max mean sd n missing
## -0.9 0.4 0.8 1.175 2.1 0.7240741 0.6398512 54 7## min Q1 median Q3 max mean sd n missing
## 69.1 80.2 84.2 88.5 101.5 84.25246 6.495886 61 0clean_sleep_data %>%
group_by(Exercise_Group) %>%
summarise(
mean_sleep_difference = mean(Sleep_Difference, na.rm = TRUE)
)## # A tibble: 3 × 2
## Exercise_Group mean_sleep_difference
## <chr> <dbl>
## 1 Cardio 1.12
## 2 Cardio+Weights 0.825
## 3 None 0.0867clean_sleep_data %>%
group_by(Exercise_Group) %>%
summarise(
mean_sleep_efficiency = mean(Sleep_Efficiency, na.rm = TRUE)
)## # A tibble: 3 × 2
## Exercise_Group mean_sleep_efficiency
## <chr> <dbl>
## 1 Cardio 85.6
## 2 Cardio+Weights 86.4
## 3 None 80.4| ID | Exercise_Group | Sex | Age | Pre_Sleep | Post_Sleep | Sleep_Efficiency | pre_sleep_num | Sleep_Difference | AgeGroup2 |
|---|---|---|---|---|---|---|---|---|---|
| P003 | None | Female | 26 | NA | 6.2 | 82.9 | NA | NA | 40 |
| P004 | None | Female | 29 | SLEEP-7.2 | 7.3 | 83.6 | 7.2 | 0.1 | 40 |
| P005 | None | Male | 33 | score-7.4 | 7.4 | 83.5 | 7.4 | 0.0 | 40 |
| P006 | None | Female | 33 | Sleep-6.6 | 7.1 | 88.5 | 6.6 | 0.5 | 40 |
| P007 | None | Male | 32 | Sleep-6 | 6.7 | 83.6 | 6.0 | 0.7 | 40 |
| P008 | None | Female | 30 | zzz-8.1 | 9.0 | 73.4 | 8.1 | 0.9 | 40 |
| P009 | None | Male | 37 | sleep-5.5 | 5.1 | 88.2 | 5.5 | -0.4 | 40 |
| P010 | None | Female | 28 | sleep-5.7 | 6.3 | 80.4 | 5.7 | 0.6 | 40 |
| P011 | None | Female | 30 | score-7 | 6.2 | 85.2 | 7.0 | -0.8 | 40 |
| P012 | None | Male | 20 | sleep-5.5 | 4.6 | 82.9 | 5.5 | -0.9 | 40 |
| P013 | None | Male | 42 | Sleep-8 | 7.6 | 74.0 | 8.0 | -0.4 | 40+ |
| P014 | None | Male | 31 | NA | 7.2 | 92.0 | NA | NA | 40 |
| P016 | None | Male | 26 | SLEEP-7.8 | 8.2 | 71.7 | 7.8 | 0.4 | 40 |
| P017 | None | Female | 41 | zzz-6.7 | 7.6 | 78.5 | 6.7 | 0.9 | 40+ |
| P018 | None | Male | 18 | SLEEP-7.4 | 7.2 | 73.8 | 7.4 | -0.2 | 40 |
| P019 | None | Male | 28 | NA | 5.7 | 69.1 | NA | NA | 40 |
| P021 | None | Male | 48 | zzz-6.8 | 7.1 | 78.7 | 6.8 | 0.3 | 40+ |
| P023 | None | Female | 42 | sleep-5 | NA | 81.3 | 5.0 | NA | 40+ |
| P024 | None | Female | 39 | score-6 | 5.6 | 76.6 | 6.0 | -0.4 | 40 |
| P026 | Cardio | Female | 34 | score-5.2 | 6.7 | 84.5 | 5.2 | 1.5 | 40 |
| P027 | Cardio | Female | 28 | sleep-6.6 | 7.8 | 75.9 | 6.6 | 1.2 | 40 |
| P028 | Cardio | Female | 29 | SLEEP-5.6 | 6.3 | 79.0 | 5.6 | 0.7 | 40 |
| P029 | Cardio | Male | 36 | Sleep-6 | 6.3 | 87.6 | 6.0 | 0.3 | 40 |
| P031 | Cardio | Female | 42 | Sleep-6.9 | 7.6 | 88.5 | 6.9 | 0.7 | 40+ |
| P032 | Cardio | Female | 18 | SLEEP-6.9 | 7.9 | 87.8 | 6.9 | 1.0 | 40 |
| P033 | Cardio | Female | 38 | zzz-5.9 | 6.6 | 80.9 | 5.9 | 0.7 | 40 |
| P034 | Cardio | Female | 20 | score-5.2 | 6.0 | 92.8 | 5.2 | 0.8 | 40 |
| P035 | Cardio | Male | 30 | SLEEP-6.7 | 8.0 | 86.4 | 6.7 | 1.3 | 40 |
| P036 | Cardio | Female | 19 | zzz-5.4 | 5.7 | 88.0 | 5.4 | 0.3 | 40 |
| P037 | Cardio | Male | 35 | NA | 9.7 | 85.6 | NA | NA | 40 |
| P038 | Cardio | Female | 34 | zzz-7 | 8.1 | 79.6 | 7.0 | 1.1 | 40 |
| P039 | Cardio | Male | 39 | SLEEP-5.6 | 6.3 | 81.3 | 5.6 | 0.7 | 40 |
| P040 | Cardio | Female | 39 | zzz-6 | 8.1 | 79.7 | 6.0 | 2.1 | 40 |
| P042 | Cardio | Female | 28 | SLEEP-5.6 | 7.3 | 81.9 | 5.6 | 1.7 | 40 |
| P043 | Cardio | Female | 43 | zzz-6.9 | 8.2 | 81.3 | 6.9 | 1.3 | 40+ |
| P044 | Cardio | Female | 33 | zzz-5.8 | 7.1 | 88.7 | 5.8 | 1.3 | 40 |
| P046 | Cardio | Male | 30 | SLEEP-7.1 | 8.5 | 95.0 | 7.1 | 1.4 | 40 |
| P047 | Cardio | Female | 42 | SLEEP-5.8 | 7.0 | 85.5 | 5.8 | 1.2 | 40+ |
| P050 | Cardio | Male | 31 | zzz-6.4 | 8.4 | 101.5 | 6.4 | 2.0 | 40 |
| P076 | Cardio+Weights | Male | 37 | sleep-5.7 | 6.5 | 83.9 | 5.7 | 0.8 | 40 |
| P077 | Cardio+Weights | Female | 37 | score-5.9 | 7.3 | 92.4 | 5.9 | 1.4 | 40 |
| P078 | Cardio+Weights | Female | 24 | score-6.6 | 7.2 | 74.5 | 6.6 | 0.6 | 40 |
| P079 | Cardio+Weights | Male | 38 | SLEEP-6.6 | 7.4 | 89.0 | 6.6 | 0.8 | 40 |
| P080 | Cardio+Weights | Male | 42 | Sleep-7.2 | 8.1 | 94.5 | 7.2 | 0.9 | 40+ |
| P081 | Cardio+Weights | Female | 38 | Sleep-8 | 8.9 | 74.5 | 8.0 | 0.9 | 40 |
| P082 | Cardio+Weights | Male | 46 | score-6.5 | 6.4 | 88.7 | 6.5 | -0.1 | 40+ |
| P083 | Cardio+Weights | Female | 49 | score-5.9 | 6.8 | 90.4 | 5.9 | 0.9 | 40+ |
| P084 | Cardio+Weights | Female | 31 | sleep-8 | 8.4 | 80.2 | 8.0 | 0.4 | 40 |
| P085 | Cardio+Weights | Male | 33 | score-6.2 | 6.9 | 89.9 | 6.2 | 0.7 | 40 |
| P086 | Cardio+Weights | Female | 46 | SLEEP-6.2 | 7.4 | 83.1 | 6.2 | 1.2 | 40+ |
| P087 | Cardio+Weights | Male | 18 | SLEEP-6.7 | 7.6 | 96.3 | 6.7 | 0.9 | 40 |
| P088 | Cardio+Weights | Male | 34 | score-7.5 | 8.9 | 81.2 | 7.5 | 1.4 | 40 |
| P090 | Cardio+Weights | Female | 41 | Sleep-7.2 | 7.6 | 79.9 | 7.2 | 0.4 | 40+ |
| P091 | Cardio+Weights | Male | 46 | zzz-7.3 | 7.9 | 87.5 | 7.3 | 0.6 | 40+ |
| P093 | Cardio+Weights | Female | 40 | Sleep-8 | 9.5 | 90.4 | 8.0 | 1.5 | 40+ |
| P094 | Cardio+Weights | Male | 35 | zzz-6.1 | 7.2 | 84.4 | 6.1 | 1.1 | 40 |
| P095 | Cardio+Weights | Female | 29 | Sleep-5.7 | NA | 85.0 | 5.7 | NA | 40 |
| P097 | Cardio+Weights | Male | 24 | SLEEP-4.4 | 4.7 | 88.9 | 4.4 | 0.3 | 40 |
| P098 | Cardio+Weights | Female | 35 | score-5.9 | 6.9 | 92.6 | 5.9 | 1.0 | 40 |
| P099 | Cardio+Weights | Male | 28 | NA | 8.8 | 88.5 | NA | NA | 40 |
| P100 | Cardio+Weights | Male | 32 | zzz-6.5 | 7.3 | 84.2 | 6.5 | 0.8 | 40 |
I did some descriptive statistics to look at the mean, min, max, and sd for Sleep_difference and Sleep_efficiency. I also looked at the group means by Exercise Group for Sleep_difference and Sleep_efficiency.
3.5 Visualization
ggplot(clean_sleep_data, aes(x = Exercise_Group, y = Sleep_Difference)) +
geom_boxplot() +
labs(
title = "Relationship between Sleep Difference and Exercise Group",
x = "Exercise Group",
y = "Sleep Difference"
) +
theme_minimal()
Figure 3.1: This is a box plot that shows the relationship between sleep difference and exercise group.
ggplot(clean_sleep_data, aes(x = Exercise_Group, y = Sleep_Efficiency)) +
geom_boxplot() +
labs(
title = "Relationship between Sleep Efficiency and Exercise Group",
x = "Exercise Group",
y = "Sleep Efficiency"
)
Figure 3.2: This is a boxplot that looks at the relationship between sleep efficiency and exercise group.
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## @ complete: logi TRUE
## @ validate: logi TRUEggplot(clean_sleep_data, aes(x = Sleep_Difference, y = Sleep_Efficiency)) +
geom_point() +
geom_smooth(method="lm") +
labs(
title = "Relationship between Sleep Difference and Efficiency",
x = "Sleep Difference",
y = "Sleep Efficiency"
)
Figure 3.3: This is a scatterplot to look at the relationship between sleep efficiency and sleep difference.
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## [list output truncated]
## @ complete: logi TRUE
## @ validate: logi TRUEI created 3 plots, the first 2 were box plots that showed the relationship between Sleep_difference and Exercise group, and Sleep_efficiency and Exercise group. The last one was a scatterplot to look at the relationship between Sleep_efficiency and Sleep_difference.
3.6 T-Tests
##
## Welch Two Sample t-test
##
## data: Sleep_Difference by Sex
## t = 1.7108, df = 46.409, p-value = 0.0938
## alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
## 95 percent confidence interval:
## -0.05259837 0.64926503
## sample estimates:
## mean in group Female mean in group Male
## 0.8566667 0.5583333The mean for the female group is 0.8566667, and the mean for the male group is 0.5583333. The p-value is 0.0938, making the differences not statistically significant.
##
## Welch Two Sample t-test
##
## data: Sleep_Difference by AgeGroup2
## t = 0.0070374, df = 24.033, p-value = 0.9944
## alternative hypothesis: true difference in means between group 40 and group 40+ is not equal to 0
## 95 percent confidence interval:
## -0.3838214 0.3864481
## sample estimates:
## mean in group 40 mean in group 40+
## 0.7243902 0.7230769The mean for age group 40 is 0.7243902, and the mean for group 40+ is 0.7230769. The p-value is 0.9944, making the difference not statistically significant.
I ran independent t-tests for Sleep_difference and sex, and another one for Sleep_difference by AgeGroup2.
3.7 Anovas + Post-Hocs
anova_sleep_difference<- aov(Sleep_Difference ~ Exercise_Group, data = clean_sleep_data)
summary(anova_sleep_difference)## Df Sum Sq Mean Sq F value Pr(>F)
## Exercise_Group 2 9.292 4.646 19.1 6.44e-07 ***
## Residuals 51 12.406 0.243
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 7 observations deleted due to missingness## Analysis of Variance Table (Type III SS)
## Model: Sleep_Difference ~ Exercise_Group
##
## SS df MS F PRE p
## ----- --------------- | ------ -- ----- ------ ----- -----
## Model (error reduced) | 9.292 2 4.646 19.099 .4282 .0000
## Error (from model) | 12.406 51 0.243
## ----- --------------- | ------ -- ----- ------ ----- -----
## Total (empty model) | 21.699 53 0.409## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Sleep_Difference ~ Exercise_Group, data = clean_sleep_data)
##
## $Exercise_Group
## diff lwr upr p adj
## Cardio+Weights-Cardio -0.2960526 -0.6774802 0.08537496 0.1567301
## None-Cardio -1.0343860 -1.4456196 -0.62315233 0.0000005
## None-Cardio+Weights -0.7383333 -1.1450060 -0.33166066 0.0001710
The F-value is 19.1, the df are 2 and 51, the p-value is .0000, the PRE is 42.82%. Looking at the adjusted p-values, None-Cardio and None-Cardio+Weights are the 2 groups that are statistically significant.
anova_sleep_efficiency<- aov(Sleep_Efficiency ~ Exercise_Group, data = clean_sleep_data)
summary(anova_sleep_efficiency)## Df Sum Sq Mean Sq F value Pr(>F)
## Exercise_Group 2 412.7 206.36 5.648 0.00574 **
## Residuals 58 2119.1 36.54
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Analysis of Variance Table (Type III SS)
## Model: Sleep_Efficiency ~ Exercise_Group
##
## SS df MS F PRE p
## ----- --------------- | -------- -- ------- ----- ----- -----
## Model (error reduced) | 412.718 2 206.359 5.648 .1630 .0057
## Error (from model) | 2119.074 58 36.536
## ----- --------------- | -------- -- ------- ----- ----- -----
## Total (empty model) | 2531.792 60 42.197## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Sleep_Efficiency ~ Exercise_Group, data = clean_sleep_data)
##
## $Exercise_Group
## diff lwr upr p adj
## Cardio+Weights-Cardio 0.7886364 -3.703252 5.280525 0.9065424
## None-Cardio -5.1592105 -9.816907 -0.501514 0.0265716
## None-Cardio+Weights -5.9478469 -10.501233 -1.394461 0.0073440
The F-value is 5.648, the df are 2 and 58, the p-value is 0.0057, the PRE is 16.30%. Looking at the adjusted p values, None-Cardio and None-Cardio+Weights are the 2 statistically significant groups.
I ran 2 ANOVAs, one for Sleep_difference and Exercise group, and the other for Sleep_efficiency and Exercise group. I also ran a Tukey post-hoc test for both ANOVAs.
3.8 Synthesis & Reccomendation
Considering both outcomes (Sleep Difference and Sleep Efficiency) of the anova and post-hoc tests, I would recommend cardio and weights as the exercise regimen to improve overall sleep. The reason for this is because in both the post-hoc tests we can see that cardio+weights-cardio has the smallest difference compared to the other 2 combinations in both tests. Although in the sleep efficiency ~ exercise group post-hoc test the difference between cardio+weights and none is the largest out of the 3 combinations (-5.9478469), it looks like ‘None’ is causing the difference to be large, and not cardio+weight. In the sleep difference ~ exercise group post-hoc test, none - cardio have the largest negative difference out of the the 3 combinations (-1.0343860), with none - cardio+weights having the second largest (-0.7383333), and cardio+weights - cardio having the smallest difference (-0.2960526), conveying that cardio+weight must be the exercise regimen that helps to improve overall sleep. We could also see the differences and their sizes in the plot of the Tukey post-hoc test above.
3.9 Reflection
One challenging thing for me while creating this report was trying to clean the pre_sleep column and just make it numeric, without any characters. One thing I was confident about was cleaning and merging the data, as well as conducting descriptive statistics. Next time, I would like to try to improve on cleaning specific columns like what I had to do with the pre_sleep column.