Take-Home Midterm Exam: Introductory Psychological Statistics
Nicholas Barnard
22 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.
Nominal data is categorical data with no inherent order like gender. This allows for counting and frequency analysis. Ordinal data is categorical data with a meaningful order but unequal intervals like education levels. This allows for comparisons but not arithmetic operations. Interval data is numerical data with equal intervals but no true zero point such as IQ scores. Ratio data is numerical data with equal intervals and a true zero point such as weight. While interval and ratio data both permit arithmetic operations, ratio data is the only one that allows for meaningful 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
Scores on a depression inventory are an example of interval data. This is due to the scores being numerical data but not having a true point of zero. Response time is an example of ratio data due to it being numerical with a true zero point. The likert scale is an example of ordinal data because the scores can be compared as greater or less than each other but doesn’t have a definitive difference. Diagnostic categories such as ADHD and anxiety are examples of nominal data due to being able to be categorized but not having an inherent order or scale of measurement. Age in years is an example of ratio data due to having a true zero point.
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.
Random error comes from unpredictable variables that reduces reliability but doesn’t create bias in the results, such as someone getting distracted for a moment when takinnng a memory test. Systematic errors are predictable and consistent variables that can create bias towards a certain direction in an experiments results. For example, an experimenter giving certain participants a more difficult list of things to memorize than other participants.
- 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?
Measurement error could create more deviation in the study’s results, making the study less reliable and therefore less valid as a result. Researchers can minimize these errors by making sure that they are conducting the test as unbiased as possible and that their equipment is working properly.
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
conditiondata <- data %>%
group_by(condition) %>%
summarize(
mean_rt = mean(reaction_time, na.rm = TRUE),
mean_acc = mean(accuracy, na.rm = TRUE),
median_rt = median(reaction_time, na.rm = TRUE),
median_acc = median(accuracy, na.rm = TRUE),
sd_rt = sd(reaction_time, na.rm = TRUE),
sd_acc = sd(accuracy, na.rm = TRUE),
min_rt = min(reaction_time, na.rm = TRUE),
min_acc = min(accuracy, na.rm = TRUE),
max_rt = max(reaction_time, na.rm = TRUE),
max_acc = max(accuracy, na.rm = TRUE) )
print(conditiondata)## # A tibble: 2 × 11
## condition mean_rt mean_acc median_rt median_acc sd_rt sd_acc min_rt min_acc
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Control 301. 85.5 300. 85.5 48.5 9.86 202. 61.9
## 2 Experimental 296. 88.1 288. 88.3 38.4 8.20 216. 74.3
## # ℹ 2 more variables: max_rt <dbl>, max_acc <dbl>- 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
maindata <- data%>%
mutate(anxiety_change = anxiety_pre - anxiety_post)
controlgroup <- maindata %>%
filter(condition == "Control")
mean(controlgroup$anxiety_change)## [1] 3.794972## participant_id reaction_time accuracy gender condition anxiety_pre
## 1 1 271.9762 87.53319 Female Control 31.30191
## 2 4 303.5254 98.68602 Male Control 16.93299
## 3 5 306.4644 82.74229 Female Control 24.04438
## 4 6 385.7532 100.16471 Female Control 22.75684
## 5 7 323.0458 69.51247 Female Control 29.50392
## 6 8 236.7469 90.84614 Male Control 22.02049
## 7 10 277.7169 87.15942 Female Control 22.00335
## 8 14 305.5341 74.81425 Female Control 50.92832
## 9 16 NA 88.03529 Female Control 27.38582
## 10 18 201.6691 85.53004 Male Control 21.12975
## 11 19 335.0678 94.22267 Female Control 29.13490
## 12 20 276.3604 105.50085 Male Control 27.95172
## 13 21 246.6088 80.08969 Female Control 23.27696
## 14 22 289.1013 61.90831 Male Control 25.52234
## 15 23 248.6998 95.05739 Male Control 24.72746
## 16 25 268.7480 78.11991 Female Control 19.06931
## 17 27 341.8894 82.15227 Male Control 25.30231
## 18 28 307.6687 72.79282 Male Control 27.48385
## 19 29 243.0932 86.81303 Female Control 28.49219
## 20 30 362.6907 NA Male Control 21.33308
## 21 33 344.7563 81.29340 Female Control 22.20280
## 22 34 343.9067 91.44377 Male Control 18.07590
## 23 35 341.0791 82.79513 Female Control 23.10976
## 24 39 284.7019 81.74068 Female Control 31.03243
## 25 41 265.2647 94.93504 Male Control 26.71556
## 26 42 289.6041 90.48397 Female Control 22.40251
## 27 43 236.7302 NA Male Control 25.75667
## 28 44 408.4478 78.72094 Female Control 17.83709
## 29 45 360.3981 98.60652 Male Control 14.51359
## 30 49 338.9983 82.64300 Female Control 20.11067
## 31 50 295.8315 74.73579 Female Control 15.51616
## anxiety_post anxiety_change
## 1 29.053117 2.24879426
## 2 13.751994 3.18099329
## 3 17.847362 6.19701754
## 4 19.933968 2.82286978
## 5 24.342317 5.16159899
## 6 17.758982 4.26150823
## 7 22.069157 -0.06580401
## 8 45.327922 5.60039736
## 9 21.290659 6.09516212
## 10 21.642810 -0.51305479
## 11 26.912456 2.22244027
## 12 24.773302 3.17841445
## 13 18.586930 4.69002601
## 14 20.597288 4.92505594
## 15 20.358843 4.36861886
## 16 14.370025 4.69928609
## 17 21.952702 3.34960540
## 18 24.334744 3.14910235
## 19 24.635854 3.85633353
## 20 18.283727 3.04934997
## 21 18.430744 3.77205314
## 22 15.607200 2.46869675
## 23 19.873474 3.23628902
## 24 28.470531 2.56189924
## 25 21.378795 5.33676775
## 26 17.294151 5.10836205
## 27 20.466142 5.29052622
## 28 15.992029 1.84506400
## 29 7.508622 7.00496546
## 30 17.068705 3.04196717
## 31 10.016330 5.49982914experimentalgroup <- maindata %>%
filter(condition == "Experimental")
mean(experimentalgroup$anxiety_change) ## [1] 8.642833## participant_id reaction_time accuracy gender condition anxiety_pre
## 1 2 288.4911 84.71453 Female Experimental 31.15234
## 2 3 377.9354 84.57130 Female Experimental 27.65762
## 3 9 NA 86.23854 Female Experimental 32.81579
## 4 11 NA 88.79639 Female Experimental 33.42169
## 5 12 317.9907 79.97677 Male Experimental 16.60658
## 6 13 320.0386 81.66793 Male Experimental 14.91876
## 7 15 272.2079 74.28209 Female Experimental 21.66514
## 8 17 324.8925 89.48210 Female Experimental 30.09256
## 9 24 263.5554 77.90799 Male Experimental 42.02762
## 10 26 215.6653 95.25571 Female Experimental 16.23203
## 11 31 321.3232 85.05764 Male Experimental 16.49339
## 12 32 285.2464 88.85280 Female Experimental 35.10548
## 13 36 334.4320 88.31782 Female Experimental 23.42259
## 14 37 327.6959 95.96839 Female Experimental 33.87936
## 15 38 296.9044 89.35181 Female Experimental 25.67790
## 16 40 280.9764 96.48808 Male Experimental 21.00566
## 17 46 243.8446 78.99740 Male Experimental 40.97771
## 18 47 279.8558 106.87333 Male Experimental 29.80567
## 19 48 276.6672 100.32611 Female Experimental 14.98983
## anxiety_post anxiety_change
## 1 19.215099 11.937239
## 2 20.453056 7.204565
## 3 19.863065 12.952722
## 4 25.063956 8.357736
## 5 7.875522 8.731062
## 6 3.221330 11.697428
## 7 16.642661 5.022479
## 8 23.416047 6.676510
## 9 31.904850 10.122765
## 10 8.052780 8.179250
## 11 2.627509 13.865882
## 12 27.376440 7.729041
## 13 19.373641 4.048952
## 14 26.428138 7.451224
## 15 16.420951 9.256947
## 16 15.350273 5.655391
## 17 27.270622 13.707085
## 18 22.108595 7.697075
## 19 11.069351 3.920478For the control group reaction time had a mean of 301.4, a median of 299.7, standard deviation of 48.5, minimum of 201.7, and maximum of 408.5. Accuracy for the control group had a mean of 85.5, median of 85.5, standard deviation of 9.9, minimum of 61.9, and maximum of 105.5. For the experimental group reaction time had a mean of 295.8, median of 288.5, standard deviation of 38.4, minimum of 215.7, and maximum of 377.9. Accuracy for the experimental group had a mean of 88.1, median of 88.3, standard deviation of 8.2, minimum of 74.3, and maximum of 106.9. The mean anxiety change for the control group was 3.8 and for the experimental group was 8.6.
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?
## [1] 0.09121122## [1] 0.4950149A reaction time greater than 450ms has a probability of 9%. Having a reaction time between 300ms and 400ms has a probability of 50%.
Part 3: Data Cleaning and Manipulation
Question 5: Data Cleaning with dplyr
Using the data set created in Part 2, perform the following data cleaning and manipulation tasks:
- Remove all rows with missing values and create a new data set 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 %>%
mutate(performance_category = ifelse(accuracy >= 90, "High", ifelse(accuracy >= 70, "Medium", "Low")))## 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## 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- Filter the data set to include only participants in the Experimental condition with reaction times faster than the overall mean reaction time.
## participant_id reaction_time accuracy gender condition anxiety_pre
## 1 3 377.9354 84.57130 Female Experimental 27.65762
## 2 4 303.5254 98.68602 Male Control 16.93299
## 3 5 306.4644 82.74229 Female Control 24.04438
## 4 6 385.7532 100.16471 Female Control 22.75684
## 5 7 323.0458 69.51247 Female Control 29.50392
## 6 12 317.9907 79.97677 Male Experimental 16.60658
## 7 13 320.0386 81.66793 Male Experimental 14.91876
## 8 14 305.5341 74.81425 Female Control 50.92832
## 9 17 324.8925 89.48210 Female Experimental 30.09256
## 10 19 335.0678 94.22267 Female Control 29.13490
## 11 27 341.8894 82.15227 Male Control 25.30231
## 12 28 307.6687 72.79282 Male Control 27.48385
## 13 31 321.3232 85.05764 Male Experimental 16.49339
## 14 33 344.7563 81.29340 Female Control 22.20280
## 15 34 343.9067 91.44377 Male Control 18.07590
## 16 35 341.0791 82.79513 Female Control 23.10976
## 17 36 334.4320 88.31782 Female Experimental 23.42259
## 18 37 327.6959 95.96839 Female Experimental 33.87936
## 19 44 408.4478 78.72094 Female Control 17.83709
## 20 45 360.3981 98.60652 Male Control 14.51359
## 21 49 338.9983 82.64300 Female Control 20.11067
## anxiety_post
## 1 20.453056
## 2 13.751994
## 3 17.847362
## 4 19.933968
## 5 24.342317
## 6 7.875522
## 7 3.221330
## 8 45.327922
## 9 23.416047
## 10 26.912456
## 11 21.952702
## 12 24.334744
## 13 2.627509
## 14 18.430744
## 15 15.607200
## 16 19.873474
## 17 19.373641
## 18 26.428138
## 19 15.992029
## 20 7.508622
## 21 17.068705## 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 10.016330I used na.omit() to remove any rows that contained NA values. Then I used mutate() to create a new column called performance_category and imbedded an ifelse statement inside another ifelse statement to label each row of data as high, medium, or low based on their accuracy. Finally I used filter() to show the rows that had reaction times greater than the overall mean reaction time.
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 data set created in Part 2. Include the following steps:
- Select the numeric variables from the data set (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 data set that selects only the numeric variable (reaction_time, accuracy, anxiety_pre, anxiety_post, and anxiety_change if you created it).
cordata <- maindata %>%
select(reaction_time, accuracy, anxiety_pre, anxiety_post, anxiety_change)
corPlot(cordata)## Error in plot.new(): figure margins too large
There is a strong positive correlation between anxiety_pre and anxiety_post. There is a surprisingly weak positive correlation between anxiety_pre and anxiety_change, which could inform further psychological research that there may be methods to reduce stress that are more effective in an individual with higher stress levels.
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?
I’m interested in how stress has changed from older generations. Data collection that comes to mind includes the levels of stress felt by different age groups, the different sources of stress, and how people relieve stress. I would likely need to address measurement errors mainly based on human error such as how honest each person who I collect data from would be or how mine and other researcher’s personal bias would affect how we view the data. Learning R for data analysis has helped me understand how many ways you can compare data to derive different answers and theories. Using R has the advantage of being flexible in it’s applications for processing data, but it may take more time for someone to learn to use it compared to other statistical software.
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.