Replace “Your Name” with your actual name.
Please complete this exam on your own. Include your R code, interpretations, and answers within this document.
Read Chapter 2 (Types of Data Psychologists Collect) and answer the following:
Write your answer(s) here Nominal, consists of categories that are mutually exclusive with no order. Example: gender Ordinal, ordered categories with unequal intervals. Example: scale ratings Interval: categories with equal intervals, no true zero. Example: temperature in celsius Ratio: order4ed categories with equal intervals and a true zero. Example: reaction time
Write your answer(s) here - Scores on a depression inventory (0-63) -> Interval: Measured on a scale with equal intervals between the values, meaning the difference between any two scores is consistent. There is also no true zero point. - Response time in milliseconds -> Ratio: Response time is a continuous variable with a true zero point. - Likert scale ratings of agreement (1-7) -> Ordinal: Likert scale ratings represent an ordered set of categories. Intervals between categories are not guaranteed to be equal, which means it is ordinal data. - Diagnostic categories (e.g., ADHD, anxiety disorder, no diagnosis) -> Nominal: Qualitative categories that have no inherent order or ranking. Categories represent different conditions or states, but there is no meaningful ordering between them. - Age in years -> Ratio: Age is continuous variable with a true zero point. Has equal intervals between values. ### Question 2: Measurement Error Referring to Chapter 3 (Measurement Errors in Psychological Research):
Write your answer(s) here Random error is unpredictable and occurs due to chance, like a participant’s fluctuating attention in a memory experiment. Systematic error is consistent and due to flaws in the experiment, such as presenting words too quickly, affecting all participants similarly.
Write your answer(s) here Measurement error can affect the study by giving incorrect data, which may lead to wrong conclusions about the link between stress and academic performance. To reduce these errors, researchers should use reliable tools, make instructions clear, have a larger sample size, and use objective measurements when possible.
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*:
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 48 86.5 9.23 86.53 86.52 8.65 61.91 106.87 44.97 -0.05 -0.06 1.33anxiety_change that represents the difference between pre
and post anxiety scores (pre minus post). Then calculate the mean
anxiety change for each condition.## 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 19.93397## 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
## 9 9 NA 86.23854 Female Experimental 32.81579
## 10 10 277.7169 87.15942 Female Control 22.00335
## 11 11 NA 88.79639 Female Experimental 33.42169
## 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
## 16 16 NA 88.03529 Female Control 27.38582
## 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
## 30 30 362.6907 NA Male Control 21.33308
## 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
## 43 43 236.7302 NA Male Control 25.75667
## 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 anxiety_change
## 1 29.053117 2.24879426
## 2 19.215099 11.93723893
## 3 20.453056 7.20456483
## 4 13.751994 3.18099329
## 5 17.847362 6.19701754
## 6 19.933968 2.82286978
## 7 24.342317 5.16159899
## 8 17.758982 4.26150823
## 9 19.863065 12.95272240
## 10 22.069157 -0.06580401
## 11 25.063956 8.35773571
## 12 7.875522 8.73106229
## 13 3.221330 11.69742764
## 14 45.327922 5.60039736
## 15 16.642661 5.02247855
## 16 21.290659 6.09516212
## 17 23.416047 6.67651035
## 18 21.642810 -0.51305479
## 19 26.912456 2.22244027
## 20 24.773302 3.17841445
## 21 18.586930 4.69002601
## 22 20.597288 4.92505594
## 23 20.358843 4.36861886
## 24 31.904850 10.12276506
## 25 14.370025 4.69928609
## 26 8.052780 8.17924981
## 27 21.952702 3.34960540
## 28 24.334744 3.14910235
## 29 24.635854 3.85633353
## 30 18.283727 3.04934997
## 31 2.627509 13.86588190
## 32 27.376440 7.72904122
## 33 18.430744 3.77205314
## 34 15.607200 2.46869675
## 35 19.873474 3.23628902
## 36 19.373641 4.04895160
## 37 26.428138 7.45122383
## 38 16.420951 9.25694721
## 39 28.470531 2.56189924
## 40 15.350273 5.65539054
## 41 21.378795 5.33676775
## 42 17.294151 5.10836205
## 43 20.466142 5.29052622
## 44 15.992029 1.84506400
## 45 7.508622 7.00496546
## 46 27.270622 13.70708547
## 47 22.108595 7.69707534
## 48 11.069351 3.92047789
## 49 17.068705 3.04196717
## 50 10.016330 5.49982914Write your answer(s) here The mean between pre anxiety and post anxiety scores is 5.64 when you subtract pre anxiety and post anxiety.
Using the concepts from Chapter 4 (Descriptive Statistics and Basic Probability in Psychological Research):
## [1] 0.09121122## [1] 0.4950149Write your answer(s) here The probability that a randomly selected participant will have a reaction time greater than 450 ms is 9.12% and the probability that a randomly selected participant will have a reaction time between 300ms and 400ms is 49.50%
Using the dataset created in Part 2, perform the following data cleaning and manipulation tasks:
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 10.016330performance_category that
categorizes participants based on their accuracy:
clean_data <- 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
## 9 9 NA 86.23854 Female Experimental 32.81579
## 10 10 277.7169 87.15942 Female Control 22.00335
## 11 11 NA 88.79639 Female Experimental 33.42169
## 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
## 16 16 NA 88.03529 Female Control 27.38582
## 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
## 30 30 362.6907 NA Male Control 21.33308
## 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
## 43 43 236.7302 NA Male Control 25.75667
## 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
## 9 19.863065 Medium
## 10 22.069157 Medium
## 11 25.063956 Medium
## 12 7.875522 Medium
## 13 3.221330 Medium
## 14 45.327922 Medium
## 15 16.642661 Medium
## 16 21.290659 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
## 30 18.283727 <NA>
## 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
## 43 20.466142 <NA>
## 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 Mediumfiltered_data <-data %>%
filter(reaction_time > 311.75 & condition == "Experimental")
print(filtered_data)## participant_id reaction_time accuracy gender condition anxiety_pre
## 1 3 377.9354 84.57130 Female Experimental 27.65762
## 2 12 317.9907 79.97677 Male Experimental 16.60658
## 3 13 320.0386 81.66793 Male Experimental 14.91876
## 4 17 324.8925 89.48210 Female Experimental 30.09256
## 5 31 321.3232 85.05764 Male Experimental 16.49339
## 6 36 334.4320 88.31782 Female Experimental 23.42259
## 7 37 327.6959 95.96839 Female Experimental 33.87936
## anxiety_post
## 1 20.453056
## 2 7.875522
## 3 3.221330
## 4 23.416047
## 5 2.627509
## 6 19.373641
## 7 26.428138Write your answer(s) here describing your data cleaning process. Able to pipe and filter to the experimental data drom the condition column and then print data lined up with reaction times that were greater than the mean of 311.75.
Using the psych package, create a correlation plot for the simulated dataset created in Part 2. Include the following steps:
corPlot()
function to create a correlation plot.library(psych)
corPlot(cor(reaction_time))
**Write your answer(s) here**
---
## 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:
1. 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?
2. 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**
A research question I'm interested in is: How does sleep deprivation affect reaction time and accuracy in attention tasks? I would collect data on sleep duration, reaction times, and accuracy. Descriptive statistics and paired-samples t-tests would help compare performance before and after sleep deprivation. Measurement errors might include self-report bias in sleep duration and other factors like mood or motivation affecting performance.
Learning R has improved my understanding of statistics by showing how to manipulate data and automate analyses. R offers flexibility and power for complex analyses, but its steep learning curve and need for coding skills can be challenging compared to easier-to-use software like SPSS.
---
#### Submission Instructions:
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