Take-Home Midterm Exam: Introductory Psychological Statistics
Cole Jara
16 March, 2025
Replace “Your Name” with your actual name.
Instructions
Please complete this exam on your own. Include your R code, interpretations, and answers within this document.
Part 1: Types of Data and Measurement Errors
Question 1: Data Types in Psychological Research
Read Chapter 2 (Types of Data Psychologists Collect) and answer the following:
- Describe the key differences between nominal, ordinal, interval, and ratio data. Provide one example of each from psychological research.
Write your answer(s) here nominal data are data categories that do not have any order or number value attached to them. Ordinal data are categories with a set order however the intervals between these categories are not equal. Interval data are represented with number values and the intervals between these values are equal, yet there is no point for true zero. Ratio data has a point for true zero and number values with equal intervals which creates ratios.
- For each of the following variables, identify the appropriate level
of measurement (nominal, ordinal, interval, or ratio) and explain your
reasoning:
- Scores on a depression inventory (0-63)
- Response time in milliseconds
- Likert scale ratings of agreement (1-7)
- Diagnostic categories (e.g., ADHD, anxiety disorder, no diagnosis)
- Age in years
Write your answer(s) here - Scores on a depression inventory (0-63) = ordinal data - Response time in milliseconds = Ratio Data - Likert scale ratings of agreement (1-7) = ordinal data - Diagnostic categories (e.g., ADHD, anxiety disorder, no diagnosis) = nominal data - Age in years = ratio data
Question 2: Measurement Error
Referring to Chapter 3 (Measurement Errors in Psychological Research):
- Explain the difference between random and systematic error, providing an example of each in the context of a memory experiment.
Write your answer(s) here random error are entirely unpredictable and can damage the accuracy of the data although not significantly enough to make it invalid.For example, if a study is being done that involves memory, there can be unintended distractions that can effect one of the participants memory such as someone tapping their finger or a noise being heard outside. Systematic errors however, can affect the outcome of the data heavily and can damage the validity of a study.They also are predictable and avoidable errors in contrast to random errors. An example of this could be used in the same memory experiment. Perhaps there is a broken air conditioner in the room that the memory experiment takes place, causing a constant distracting buzzing noise being hear by all the participants. This could have been avoided with more caution and vigilance as opposed to a random noise outside.
- How might measurement error affect the validity of a study examining the relationship between stress and academic performance? What steps could researchers take to minimize these errors?
Write your answer(s) here An error may cause the data to be skewed and as a result, incorrect. There may be random errors affecting this specific study which are quite hard to avoid such as some individuals being more prone to stress affecting their performance while others are not. There are some individuals who may received heightened focus during times of stress and unfortunately there is not much to do about this. There are however ways to prevent systematic errors within this study such as screening the participants beforehand about their current stress levels to prevent bringing in someone with already high amounts of stress which would skew the data.
Part 2: Descriptive Statistics and Basic Probability
Question 3: Descriptive Analysis
The code below creates a simulated dataset for a psychological experiment. Run the below code chunk without making any changes:
# Create a simulated dataset
set.seed(123) # For reproducibility
# Number of participants
n <- 50
# Create the data frame
data <- data.frame(
participant_id = 1:n,
reaction_time = rnorm(n, mean = 300, sd = 50),
accuracy = rnorm(n, mean = 85, sd = 10),
gender = sample(c("Male", "Female"), n, replace = TRUE),
condition = sample(c("Control", "Experimental"), n, replace = TRUE),
anxiety_pre = rnorm(n, mean = 25, sd = 8),
anxiety_post = NA # We'll fill this in based on condition
)
# Make the experimental condition reduce anxiety more than control
data$anxiety_post <- ifelse(
data$condition == "Experimental",
data$anxiety_pre - rnorm(n, mean = 8, sd = 3), # Larger reduction
data$anxiety_pre - rnorm(n, mean = 3, sd = 2) # Smaller reduction
)
# Ensure anxiety doesn't go below 0
data$anxiety_post <- pmax(data$anxiety_post, 0)
# Add some missing values for realism
data$reaction_time[sample(1:n, 3)] <- NA
data$accuracy[sample(1:n, 2)] <- NA
# View the first few rows of the dataset
head(data)## participant_id reaction_time accuracy gender condition anxiety_pre
## 1 1 271.9762 87.53319 Female Control 31.30191
## 2 2 288.4911 84.71453 Female Experimental 31.15234
## 3 3 377.9354 84.57130 Female Experimental 27.65762
## 4 4 303.5254 98.68602 Male Control 16.93299
## 5 5 306.4644 82.74229 Female Control 24.04438
## 6 6 385.7532 100.16471 Female Control 22.75684
## anxiety_post
## 1 29.05312
## 2 19.21510
## 3 20.45306
## 4 13.75199
## 5 17.84736
## 6 19.93397Now, perform the following computations*:
- Calculate the mean, median, standard deviation, minimum, and maximum for reaction time and accuracy, grouped by condition (hint: use the psych package).
# Your code here
summary_stats <- data %>%
group_by(data$condition) %>%
summarize(
mean_reaction_time = mean(data$reaction_time, na.rm = TRUE),
median_reaction_time = median(data$reaction_time, na.rm = TRUE),
sd_reaction_time = sd(data$reaction_time, na.rm = TRUE),
min_reaction_time = min(data$reaction_time, na.rm = TRUE),
max_reaction_time = max(data$reaction_time, na.rm = TRUE),
mean_accuracy = mean(data$accuracy, na.rm = TRUE),
median_accuracy = median(data$accuracy, na.rm = TRUE),
sd_accuracy = sd(data$accuracy, na.rm = TRUE),
min_accuracy = min(data$accuracy, na.rm = TRUE),
max_accuracy = max(data$accuracy, na.rm = TRUE)
)
print(summary_stats)## # A tibble: 2 × 11
## `data$condition` mean_reaction_time median_reaction_time sd_reaction_time
## <chr> <dbl> <dbl> <dbl>
## 1 Control 299. 296. 44.8
## 2 Experimental 299. 296. 44.8
## # ℹ 7 more variables: min_reaction_time <dbl>, max_reaction_time <dbl>,
## # mean_accuracy <dbl>, median_accuracy <dbl>, sd_accuracy <dbl>,
## # min_accuracy <dbl>, max_accuracy <dbl>##
## Descriptive statistics by group
## group: Control
## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 30 301.4 48.54 299.68 300.42 55.38 201.67 408.45 206.78 0.14 -0.66
## se
## X1 8.86
## ------------------------------------------------------------
## group: Experimental
## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 17 295.75 38.37 288.49 295.61 43.74 215.67 377.94 162.27 0 -0.27
## se
## X1 9.31##
## Descriptive statistics by group
## group: 61.9083112435919
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 61.91 NA 61.91 61.91 0 61.91 61.91 0 NA NA NA
## ------------------------------------------------------------
## group: 69.5124719576978
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 69.51 NA 69.51 69.51 0 69.51 69.51 0 NA NA NA
## ------------------------------------------------------------
## group: 72.7928228774546
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 72.79 NA 72.79 72.79 0 72.79 72.79 0 NA NA NA
## ------------------------------------------------------------
## group: 74.2820877352442
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 74.28 NA 74.28 74.28 0 74.28 74.28 0 NA NA NA
## ------------------------------------------------------------
## group: 74.7357909969322
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 74.74 NA 74.74 74.74 0 74.74 74.74 0 NA NA NA
## ------------------------------------------------------------
## group: 74.8142461689291
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 74.81 NA 74.81 74.81 0 74.81 74.81 0 NA NA NA
## ------------------------------------------------------------
## group: 77.9079923741761
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 77.91 NA 77.91 77.91 0 77.91 77.91 0 NA NA NA
## ------------------------------------------------------------
## group: 78.1199138353264
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 78.12 NA 78.12 78.12 0 78.12 78.12 0 NA NA NA
## ------------------------------------------------------------
## group: 78.7209392396063
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 78.72 NA 78.72 78.72 0 78.72 78.72 0 NA NA NA
## ------------------------------------------------------------
## group: 78.9974041285287
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 79 NA 79 79 0 79 79 0 NA NA NA
## ------------------------------------------------------------
## group: 79.976765468907
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 79.98 NA 79.98 79.98 0 79.98 79.98 0 NA NA NA
## ------------------------------------------------------------
## group: 80.0896883394346
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 80.09 NA 80.09 80.09 0 80.09 80.09 0 NA NA NA
## ------------------------------------------------------------
## group: 81.2933996820759
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 81.29 NA 81.29 81.29 0 81.29 81.29 0 NA NA NA
## ------------------------------------------------------------
## group: 81.6679261633058
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 81.67 NA 81.67 81.67 0 81.67 81.67 0 NA NA NA
## ------------------------------------------------------------
## group: 81.7406841446877
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 81.74 NA 81.74 81.74 0 81.74 81.74 0 NA NA NA
## ------------------------------------------------------------
## group: 82.1522699294899
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 82.15 NA 82.15 82.15 0 82.15 82.15 0 NA NA NA
## ------------------------------------------------------------
## group: 82.6429964089952
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 82.64 NA 82.64 82.64 0 82.64 82.64 0 NA NA NA
## ------------------------------------------------------------
## group: 82.7422901434073
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 82.74 NA 82.74 82.74 0 82.74 82.74 0 NA NA NA
## ------------------------------------------------------------
## group: 82.7951343818125
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 82.8 NA 82.8 82.8 0 82.8 82.8 0 NA NA NA
## ------------------------------------------------------------
## group: 84.5712954270868
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 84.57 NA 84.57 84.57 0 84.57 84.57 0 NA NA NA
## ------------------------------------------------------------
## group: 84.714532446513
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 84.71 NA 84.71 84.71 0 84.71 84.71 0 NA NA NA
## ------------------------------------------------------------
## group: 85.0576418589989
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 85.06 NA 85.06 85.06 0 85.06 85.06 0 NA NA NA
## ------------------------------------------------------------
## group: 85.530042267305
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 85.53 NA 85.53 85.53 0 85.53 85.53 0 NA NA NA
## ------------------------------------------------------------
## group: 86.2385424384461
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 86.24 NA 86.24 86.24 0 86.24 86.24 0 NA NA NA
## ------------------------------------------------------------
## group: 86.8130347974915
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 86.81 NA 86.81 86.81 0 86.81 86.81 0 NA NA NA
## ------------------------------------------------------------
## group: 87.1594156874397
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 87.16 NA 87.16 87.16 0 87.16 87.16 0 NA NA NA
## ------------------------------------------------------------
## group: 87.5331851399475
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 87.53 NA 87.53 87.53 0 87.53 87.53 0 NA NA NA
## ------------------------------------------------------------
## group: 88.0352864140426
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 88.04 NA 88.04 88.04 0 88.04 88.04 0 NA NA NA
## ------------------------------------------------------------
## group: 88.317819639157
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 88.32 NA 88.32 88.32 0 88.32 88.32 0 NA NA NA
## ------------------------------------------------------------
## group: 88.7963948275988
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 88.8 NA 88.8 88.8 0 88.8 88.8 0 NA NA NA
## ------------------------------------------------------------
## group: 88.8528040112633
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 88.85 NA 88.85 88.85 0 88.85 88.85 0 NA NA NA
## ------------------------------------------------------------
## group: 89.351814908338
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 89.35 NA 89.35 89.35 0 89.35 89.35 0 NA NA NA
## ------------------------------------------------------------
## group: 89.4820977862943
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 89.48 NA 89.48 89.48 0 89.48 89.48 0 NA NA NA
## ------------------------------------------------------------
## group: 90.4839695950807
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 90.48 NA 90.48 90.48 0 90.48 90.48 0 NA NA NA
## ------------------------------------------------------------
## group: 90.8461374963607
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 90.85 NA 90.85 90.85 0 90.85 90.85 0 NA NA NA
## ------------------------------------------------------------
## group: 91.4437654851883
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 91.44 NA 91.44 91.44 0 91.44 91.44 0 NA NA NA
## ------------------------------------------------------------
## group: 94.2226746787974
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 94.22 NA 94.22 94.22 0 94.22 94.22 0 NA NA NA
## ------------------------------------------------------------
## group: 94.9350385596212
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 94.94 NA 94.94 94.94 0 94.94 94.94 0 NA NA NA
## ------------------------------------------------------------
## group: 95.0573852446226
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 95.06 NA 95.06 95.06 0 95.06 95.06 0 NA NA NA
## ------------------------------------------------------------
## group: 95.255713696967
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 95.26 NA 95.26 95.26 0 95.26 95.26 0 NA NA NA
## ------------------------------------------------------------
## group: 95.9683901314935
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 95.97 NA 95.97 95.97 0 95.97 95.97 0 NA NA NA
## ------------------------------------------------------------
## group: 96.4880761845109
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 96.49 NA 96.49 96.49 0 96.49 96.49 0 NA NA NA
## ------------------------------------------------------------
## group: 98.6065244853001
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 98.61 NA 98.61 98.61 0 98.61 98.61 0 NA NA NA
## ------------------------------------------------------------
## group: 98.6860228401446
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 98.69 NA 98.69 98.69 0 98.69 98.69 0 NA NA NA
## ------------------------------------------------------------
## group: 100.164706044295
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 100.16 NA 100.16 100.16 0 100.16 100.16 0 NA NA NA
## ------------------------------------------------------------
## group: 100.326106261852
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 100.33 NA 100.33 100.33 0 100.33 100.33 0 NA NA NA
## ------------------------------------------------------------
## group: 105.500846856271
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 105.5 NA 105.5 105.5 0 105.5 105.5 0 NA NA NA
## ------------------------------------------------------------
## group: 106.873329930166
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1 106.87 NA 106.87 106.87 0 106.87 106.87 0 NA NA NA- Using dplyr and piping, create a new variable
anxiety_changethat represents the difference between pre and post anxiety scores (pre minus post). Then calculate the mean anxiety change for each condition.
# Your code here
mean_anxiety_change <- data %>%
mutate(anxiety_change = data$anxiety_pre - data$anxiety_post) %>%
group_by(condition) %>%
summarise(mean_anxiety_change = mean(anxiety_change, na.rm = TRUE))
print(mean_anxiety_change)## # A tibble: 2 × 2
## condition mean_anxiety_change
## <chr> <dbl>
## 1 Control 3.79
## 2 Experimental 8.64Write your answer(s) here mean anxiety change for
control = 3.794972
mean anxiety change for experimental = 8.642833
Question 4: Probability Calculations
Using the concepts from Chapter 4 (Descriptive Statistics and Basic Probability in Psychological Research):
- If reaction times in a cognitive task are normally distributed with
a mean of 350ms and a standard deviation of 75ms:
- What is the probability that a randomly selected participant will have a reaction time greater than 450ms?
- What is the probability that a participant will have a reaction time between 300ms and 400ms?
# Your code here
prob_greater_than_450 <- 1 - pnorm(450, mean = 350, sd = 75)
print(prob_greater_than_450)## [1] 0.09121122prob_between_300_and_400 <- pnorm(400, mean = 350, sd=75) - pnorm(300, mean =350, sd =75)
print(prob_between_300_and_400)## [1] 0.4950149Write your answer(s) here a = 0.09121122 probability b = 0.4950149 probability
Part 3: Data Cleaning and Manipulation
Question 5: Data Cleaning with dplyr
Using the dataset created in Part 2, perform the following data cleaning and manipulation tasks:
- Remove all rows with missing values and create a new dataset called
clean_data.
## participant_id reaction_time accuracy gender condition anxiety_pre
## 1 1 271.9762 87.53319 Female Control 31.30191
## 2 2 288.4911 84.71453 Female Experimental 31.15234
## 3 3 377.9354 84.57130 Female Experimental 27.65762
## 4 4 303.5254 98.68602 Male Control 16.93299
## 5 5 306.4644 82.74229 Female Control 24.04438
## 6 6 385.7532 100.16471 Female Control 22.75684
## 7 7 323.0458 69.51247 Female Control 29.50392
## 8 8 236.7469 90.84614 Male Control 22.02049
## 10 10 277.7169 87.15942 Female Control 22.00335
## 12 12 317.9907 79.97677 Male Experimental 16.60658
## 13 13 320.0386 81.66793 Male Experimental 14.91876
## 14 14 305.5341 74.81425 Female Control 50.92832
## 15 15 272.2079 74.28209 Female Experimental 21.66514
## 17 17 324.8925 89.48210 Female Experimental 30.09256
## 18 18 201.6691 85.53004 Male Control 21.12975
## 19 19 335.0678 94.22267 Female Control 29.13490
## 20 20 276.3604 105.50085 Male Control 27.95172
## 21 21 246.6088 80.08969 Female Control 23.27696
## 22 22 289.1013 61.90831 Male Control 25.52234
## 23 23 248.6998 95.05739 Male Control 24.72746
## 24 24 263.5554 77.90799 Male Experimental 42.02762
## 25 25 268.7480 78.11991 Female Control 19.06931
## 26 26 215.6653 95.25571 Female Experimental 16.23203
## 27 27 341.8894 82.15227 Male Control 25.30231
## 28 28 307.6687 72.79282 Male Control 27.48385
## 29 29 243.0932 86.81303 Female Control 28.49219
## 31 31 321.3232 85.05764 Male Experimental 16.49339
## 32 32 285.2464 88.85280 Female Experimental 35.10548
## 33 33 344.7563 81.29340 Female Control 22.20280
## 34 34 343.9067 91.44377 Male Control 18.07590
## 35 35 341.0791 82.79513 Female Control 23.10976
## 36 36 334.4320 88.31782 Female Experimental 23.42259
## 37 37 327.6959 95.96839 Female Experimental 33.87936
## 38 38 296.9044 89.35181 Female Experimental 25.67790
## 39 39 284.7019 81.74068 Female Control 31.03243
## 40 40 280.9764 96.48808 Male Experimental 21.00566
## 41 41 265.2647 94.93504 Male Control 26.71556
## 42 42 289.6041 90.48397 Female Control 22.40251
## 44 44 408.4478 78.72094 Female Control 17.83709
## 45 45 360.3981 98.60652 Male Control 14.51359
## 46 46 243.8446 78.99740 Male Experimental 40.97771
## 47 47 279.8558 106.87333 Male Experimental 29.80567
## 48 48 276.6672 100.32611 Female Experimental 14.98983
## 49 49 338.9983 82.64300 Female Control 20.11067
## 50 50 295.8315 74.73579 Female Control 15.51616
## anxiety_post
## 1 29.053117
## 2 19.215099
## 3 20.453056
## 4 13.751994
## 5 17.847362
## 6 19.933968
## 7 24.342317
## 8 17.758982
## 10 22.069157
## 12 7.875522
## 13 3.221330
## 14 45.327922
## 15 16.642661
## 17 23.416047
## 18 21.642810
## 19 26.912456
## 20 24.773302
## 21 18.586930
## 22 20.597288
## 23 20.358843
## 24 31.904850
## 25 14.370025
## 26 8.052780
## 27 21.952702
## 28 24.334744
## 29 24.635854
## 31 2.627509
## 32 27.376440
## 33 18.430744
## 34 15.607200
## 35 19.873474
## 36 19.373641
## 37 26.428138
## 38 16.420951
## 39 28.470531
## 40 15.350273
## 41 21.378795
## 42 17.294151
## 44 15.992029
## 45 7.508622
## 46 27.270622
## 47 22.108595
## 48 11.069351
## 49 17.068705
## 50 10.016330- Create a new variable
performance_categorythat categorizes participants based on their accuracy:- “High” if accuracy is greater than or equal to 90
- “Medium” if accuracy is between 70 and 90
- “Low” if accuracy is less than 70
# Your code here
clean_data <- clean_data %>%
mutate(performance_category = case_when(
accuracy >= 90 ~ "High",
accuracy >= 70 & accuracy < 90 ~ "Medium",
accuracy < 70 ~ "Low"
))
print(clean_data)## participant_id reaction_time accuracy gender condition anxiety_pre
## 1 1 271.9762 87.53319 Female Control 31.30191
## 2 2 288.4911 84.71453 Female Experimental 31.15234
## 3 3 377.9354 84.57130 Female Experimental 27.65762
## 4 4 303.5254 98.68602 Male Control 16.93299
## 5 5 306.4644 82.74229 Female Control 24.04438
## 6 6 385.7532 100.16471 Female Control 22.75684
## 7 7 323.0458 69.51247 Female Control 29.50392
## 8 8 236.7469 90.84614 Male Control 22.02049
## 10 10 277.7169 87.15942 Female Control 22.00335
## 12 12 317.9907 79.97677 Male Experimental 16.60658
## 13 13 320.0386 81.66793 Male Experimental 14.91876
## 14 14 305.5341 74.81425 Female Control 50.92832
## 15 15 272.2079 74.28209 Female Experimental 21.66514
## 17 17 324.8925 89.48210 Female Experimental 30.09256
## 18 18 201.6691 85.53004 Male Control 21.12975
## 19 19 335.0678 94.22267 Female Control 29.13490
## 20 20 276.3604 105.50085 Male Control 27.95172
## 21 21 246.6088 80.08969 Female Control 23.27696
## 22 22 289.1013 61.90831 Male Control 25.52234
## 23 23 248.6998 95.05739 Male Control 24.72746
## 24 24 263.5554 77.90799 Male Experimental 42.02762
## 25 25 268.7480 78.11991 Female Control 19.06931
## 26 26 215.6653 95.25571 Female Experimental 16.23203
## 27 27 341.8894 82.15227 Male Control 25.30231
## 28 28 307.6687 72.79282 Male Control 27.48385
## 29 29 243.0932 86.81303 Female Control 28.49219
## 31 31 321.3232 85.05764 Male Experimental 16.49339
## 32 32 285.2464 88.85280 Female Experimental 35.10548
## 33 33 344.7563 81.29340 Female Control 22.20280
## 34 34 343.9067 91.44377 Male Control 18.07590
## 35 35 341.0791 82.79513 Female Control 23.10976
## 36 36 334.4320 88.31782 Female Experimental 23.42259
## 37 37 327.6959 95.96839 Female Experimental 33.87936
## 38 38 296.9044 89.35181 Female Experimental 25.67790
## 39 39 284.7019 81.74068 Female Control 31.03243
## 40 40 280.9764 96.48808 Male Experimental 21.00566
## 41 41 265.2647 94.93504 Male Control 26.71556
## 42 42 289.6041 90.48397 Female Control 22.40251
## 44 44 408.4478 78.72094 Female Control 17.83709
## 45 45 360.3981 98.60652 Male Control 14.51359
## 46 46 243.8446 78.99740 Male Experimental 40.97771
## 47 47 279.8558 106.87333 Male Experimental 29.80567
## 48 48 276.6672 100.32611 Female Experimental 14.98983
## 49 49 338.9983 82.64300 Female Control 20.11067
## 50 50 295.8315 74.73579 Female Control 15.51616
## anxiety_post performance_category
## 1 29.053117 Medium
## 2 19.215099 Medium
## 3 20.453056 Medium
## 4 13.751994 High
## 5 17.847362 Medium
## 6 19.933968 High
## 7 24.342317 Low
## 8 17.758982 High
## 10 22.069157 Medium
## 12 7.875522 Medium
## 13 3.221330 Medium
## 14 45.327922 Medium
## 15 16.642661 Medium
## 17 23.416047 Medium
## 18 21.642810 Medium
## 19 26.912456 High
## 20 24.773302 High
## 21 18.586930 Medium
## 22 20.597288 Low
## 23 20.358843 High
## 24 31.904850 Medium
## 25 14.370025 Medium
## 26 8.052780 High
## 27 21.952702 Medium
## 28 24.334744 Medium
## 29 24.635854 Medium
## 31 2.627509 Medium
## 32 27.376440 Medium
## 33 18.430744 Medium
## 34 15.607200 High
## 35 19.873474 Medium
## 36 19.373641 Medium
## 37 26.428138 High
## 38 16.420951 Medium
## 39 28.470531 Medium
## 40 15.350273 High
## 41 21.378795 High
## 42 17.294151 High
## 44 15.992029 Medium
## 45 7.508622 High
## 46 27.270622 Medium
## 47 22.108595 High
## 48 11.069351 High
## 49 17.068705 Medium
## 50 10.016330 Medium- Filter the dataset to include only participants in the Experimental condition with reaction times faster than the overall mean reaction time.
# Your code here
overall_mean_reaction_time <- mean(clean_data$reaction_time, na.rm = TRUE)
filtered_data <- clean_data %>%
filter(condition == "Experimental" & reaction_time < overall_mean_reaction_time)
print(filtered_data)## participant_id reaction_time accuracy gender condition anxiety_pre
## 1 2 288.4911 84.71453 Female Experimental 31.15234
## 2 15 272.2079 74.28209 Female Experimental 21.66514
## 3 24 263.5554 77.90799 Male Experimental 42.02762
## 4 26 215.6653 95.25571 Female Experimental 16.23203
## 5 32 285.2464 88.85280 Female Experimental 35.10548
## 6 38 296.9044 89.35181 Female Experimental 25.67790
## 7 40 280.9764 96.48808 Male Experimental 21.00566
## 8 46 243.8446 78.99740 Male Experimental 40.97771
## 9 47 279.8558 106.87333 Male Experimental 29.80567
## 10 48 276.6672 100.32611 Female Experimental 14.98983
## anxiety_post performance_category
## 1 19.21510 Medium
## 2 16.64266 Medium
## 3 31.90485 Medium
## 4 8.05278 High
## 5 27.37644 Medium
## 6 16.42095 Medium
## 7 15.35027 High
## 8 27.27062 Medium
## 9 22.10860 High
## 10 11.06935 HighWrite your answer(s) here describing your data cleaning process. first I knew that I could use na.omit function in order to clean the original data set. I then went to creating the performance category variable by adding conditionals using the function case_when by inputting the required values for medium, high and low. I then went and calculated the overall mean reaction time of the cleaned data. After that I created filtered data filtering by experimental with reaction time greater than the overall mean reaction time.I used the filter function for this bit.
Part 4: Visualization and Correlation Analysis
Question 6: Correlation Analysis with the psych Package
Using the psych package, create a correlation plot for the simulated dataset created in Part 2. Include the following steps:
- Select the numeric variables from the dataset (reaction_time, accuracy, anxiety_pre, anxiety_post, and anxiety_change if you created it).
- Use the psych package’s
corPlot()function to create a correlation plot. - Interpret the resulting plot by addressing:
- Which variables appear to be strongly correlated?
- Are there any surprising relationships?
- How might these correlations inform further research in psychology?
# Your code here. Hint: first, with dplyr create a new dataset that selects only the numeric variable (reaction_time, accuracy, anxiety_pre, anxiety_post, and anxiety_change if you created it).
numeric_data <- data %>%
select(reaction_time, accuracy, anxiety_pre, anxiety_post)
print(numeric_data)## reaction_time accuracy anxiety_pre anxiety_post
## 1 271.9762 87.53319 31.30191 29.053117
## 2 288.4911 84.71453 31.15234 19.215099
## 3 377.9354 84.57130 27.65762 20.453056
## 4 303.5254 98.68602 16.93299 13.751994
## 5 306.4644 82.74229 24.04438 17.847362
## 6 385.7532 100.16471 22.75684 19.933968
## 7 323.0458 69.51247 29.50392 24.342317
## 8 236.7469 90.84614 22.02049 17.758982
## 9 NA 86.23854 32.81579 19.863065
## 10 277.7169 87.15942 22.00335 22.069157
## 11 NA 88.79639 33.42169 25.063956
## 12 317.9907 79.97677 16.60658 7.875522
## 13 320.0386 81.66793 14.91876 3.221330
## 14 305.5341 74.81425 50.92832 45.327922
## 15 272.2079 74.28209 21.66514 16.642661
## 16 NA 88.03529 27.38582 21.290659
## 17 324.8925 89.48210 30.09256 23.416047
## 18 201.6691 85.53004 21.12975 21.642810
## 19 335.0678 94.22267 29.13490 26.912456
## 20 276.3604 105.50085 27.95172 24.773302
## 21 246.6088 80.08969 23.27696 18.586930
## 22 289.1013 61.90831 25.52234 20.597288
## 23 248.6998 95.05739 24.72746 20.358843
## 24 263.5554 77.90799 42.02762 31.904850
## 25 268.7480 78.11991 19.06931 14.370025
## 26 215.6653 95.25571 16.23203 8.052780
## 27 341.8894 82.15227 25.30231 21.952702
## 28 307.6687 72.79282 27.48385 24.334744
## 29 243.0932 86.81303 28.49219 24.635854
## 30 362.6907 NA 21.33308 18.283727
## 31 321.3232 85.05764 16.49339 2.627509
## 32 285.2464 88.85280 35.10548 27.376440
## 33 344.7563 81.29340 22.20280 18.430744
## 34 343.9067 91.44377 18.07590 15.607200
## 35 341.0791 82.79513 23.10976 19.873474
## 36 334.4320 88.31782 23.42259 19.373641
## 37 327.6959 95.96839 33.87936 26.428138
## 38 296.9044 89.35181 25.67790 16.420951
## 39 284.7019 81.74068 31.03243 28.470531
## 40 280.9764 96.48808 21.00566 15.350273
## 41 265.2647 94.93504 26.71556 21.378795
## 42 289.6041 90.48397 22.40251 17.294151
## 43 236.7302 NA 25.75667 20.466142
## 44 408.4478 78.72094 17.83709 15.992029
## 45 360.3981 98.60652 14.51359 7.508622
## 46 243.8446 78.99740 40.97771 27.270622
## 47 279.8558 106.87333 29.80567 22.108595
## 48 276.6672 100.32611 14.98983 11.069351
## 49 338.9983 82.64300 20.11067 17.068705
## 50 295.8315 74.73579 15.51616 10.016330## Error in plot.new(): figure margins too large
Write your answer(s) here anxiety pre and post are quite heavily correlated with each other.I was surprised to see that anxiety pre and reaction time were just as negatively correlated as anxiety pre and accuracy.Although none of the negative correlations were all too strong in the end. the relationship between pre and post could be looked into even further to see how pre anxiety affects our educational aptitude as well as our anxiety after the fact. —
Part 5: Reflection and Application
Question 7: Reflection
Reflect on how the statistical concepts and R techniques covered in this course apply to psychological research:
Describe a specific research question in psychology that interests you. What type of data would you collect, what statistical analyses would be appropriate, and what potential measurement errors might you need to address?
How has learning R for data analysis changed your understanding of psychological statistics? What do you see as the biggest advantages and challenges of using R compared to other statistical software?
Write your answer(s) here 1.I am interested in how lack of sleep would affect someones academic performance. I know that they are most likely related but I would be curious just to see how severe the effects of lack of sleep are in this regard. I would collect data about age, hours of sleep and study time as well as others pieces of information. I would need to ensure that I collect the amount of hours that the student studies as well as their grades in order to ensure that I am acknowledging that some students will stay up late studying which causes their lack of sleep, while others will stay up late doing other activities that will not benefit academic performance. I would like to get students who are around the same level in order to prevent outliers.
2.R has allowed me to see that the actual organization of the data is not the difficult aspect of conducting a study, it is ensuring that there will be the least number of errors as humanely possible. There are things that you simply have no control over when conducting a psychological study which is the hardest thing to get under control. I think that R is definately quite advanced in its assorting of data however it can be very intimidating and frustrating to use as someone who does not like coding.
Submission Instructions:
Ensure to knit your document to HTML format, checking that all content is correctly displayed before submission. Publish your assignment to RPubs and submit the URL to canvas.