Take-Home Midterm Exam: Introductory Psychological Statistics
Iris Williamson
3/10/24
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 categorizes data into distinct groups without an inherent order, such as introverts, extroverts, or ambiverts, where none are “greater” than another. The categories are mutually exclusive and there is no meaningful numerical difference between them. Ordinal data categorizes in a meaningful order but with no consistent interval between values. For example, a scale might be defined by “low,” “moderate,” and “high,” and the difference between “low” and “moderate” might not be the same as between “moderate” and “high.” Interval data is numeric data with equal intervals between values but without a true zero point so the ratios cannot be meaningfully calculated. An example of this in psychological research could be an IQ test where the difference between 100 and 110 is the same as the difference between 110 and 120 but a score of 0 doesn’t mean “no intelligence.” Finally, ratio data is defined by ordered values with equal intervals and a true zero point. An example of this in psychological research could be reaction times, where zero milliseconds means no reaction time, and ratios are meaningful in that a reaction time of 400 milliseconds is twice as fast as a reaction time of 800 milliseconds.
- 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 (0-63) would be an example of interval data because there are equal intervals between the data points, but there is no true zero, as a score of zero does not indicate an absolute absence of depression, just the lowest measurable level. Response time in milliseconds is an example of ratio data, as mentioned above, because there are equal intervals with meaningful ratios and there is a true zero. A likert scale ratings of agreement is an example of ordinal data because they are ordered, but the intervals are not necessarily exactly equal because the difference between 1 and 2 may not be perceived the same as between 5 and 6. Diagnostic categories are a perfect example of nominal data because there is no inherent ranking between the disorders. Finally, age in years is another example of ratio data because there are equal intervals between the years and there is a true zero.
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 errors are unpredictable variations in measurements that occur because of chance factors like fluctuations in attention or environmental distractions. In a memory experiment, this might look like losing focus because there is a loud noise outside and the participant is therefore unable to recall something they might have otherwise remembered. Systematic errors, on the other hand, are consistent and predictable errors in measurement that are due to the study’s design or procedure, and often skew results. In a memory experiment, this could look like a picture being faded and less memorable, so that participants with worse eyesight are at a consistent disadvantage.
- 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?
A measurement error could affect the validity of a study examining the relationship between stress and academic performance by threatening the reliability and validity of the experiment. For example, a systematic error like a poorly worded question on a questionnaire could lead to incorrect conclusions about the strength of the correlation. In order to minimize this, researchers should control for external factors, cross-validate data, reduce participant bias, and improve measurement instruments.
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).
## 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 1.33## vars n mean sd median trimmed mad min max range skew kurtosis
## X1 1 47 299.36 44.78 295.83 298.57 43.09 201.67 408.45 206.78 0.15 -0.36
## se
## X1 6.53- 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.
## 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 5.49982914## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 50 5.64 3.3 5.07 5.3 2.86 -0.51 13.87 14.38 0.79 0.19 0.47It looks like the mean between pre anxiety scores and post anxiety scores is 5.64 when you subtract anxiety_pre and anxiety_post.
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] 0.4950149The probability that a randomly selected participant will have a reaction time greater than 450ms is roughly 9.12% and the probability that a randomly selected participant will have a reaction time between 300ms and 400ms is roughly 49.50%.
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 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
## 10 22.069157 -0.06580401
## 12 7.875522 8.73106229
## 13 3.221330 11.69742764
## 14 45.327922 5.60039736
## 15 16.642661 5.02247855
## 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
## 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
## 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 5.49982914- 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 <- 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 anxiety_change performance_category
## 1 29.053117 2.24879426 Medium
## 2 19.215099 11.93723893 Medium
## 3 20.453056 7.20456483 Medium
## 4 13.751994 3.18099329 High
## 5 17.847362 6.19701754 Medium
## 6 19.933968 2.82286978 High
## 7 24.342317 5.16159899 Low
## 8 17.758982 4.26150823 High
## 9 19.863065 12.95272240 Medium
## 10 22.069157 -0.06580401 Medium
## 11 25.063956 8.35773571 Medium
## 12 7.875522 8.73106229 Medium
## 13 3.221330 11.69742764 Medium
## 14 45.327922 5.60039736 Medium
## 15 16.642661 5.02247855 Medium
## 16 21.290659 6.09516212 Medium
## 17 23.416047 6.67651035 Medium
## 18 21.642810 -0.51305479 Medium
## 19 26.912456 2.22244027 High
## 20 24.773302 3.17841445 High
## 21 18.586930 4.69002601 Medium
## 22 20.597288 4.92505594 Low
## 23 20.358843 4.36861886 High
## 24 31.904850 10.12276506 Medium
## 25 14.370025 4.69928609 Medium
## 26 8.052780 8.17924981 High
## 27 21.952702 3.34960540 Medium
## 28 24.334744 3.14910235 Medium
## 29 24.635854 3.85633353 Medium
## 30 18.283727 3.04934997 <NA>
## 31 2.627509 13.86588190 Medium
## 32 27.376440 7.72904122 Medium
## 33 18.430744 3.77205314 Medium
## 34 15.607200 2.46869675 High
## 35 19.873474 3.23628902 Medium
## 36 19.373641 4.04895160 Medium
## 37 26.428138 7.45122383 High
## 38 16.420951 9.25694721 Medium
## 39 28.470531 2.56189924 Medium
## 40 15.350273 5.65539054 High
## 41 21.378795 5.33676775 High
## 42 17.294151 5.10836205 High
## 43 20.466142 5.29052622 <NA>
## 44 15.992029 1.84506400 Medium
## 45 7.508622 7.00496546 High
## 46 27.270622 13.70708547 Medium
## 47 22.108595 7.69707534 High
## 48 11.069351 3.92047789 High
## 49 17.068705 3.04196717 Medium
## 50 10.016330 5.49982914 Medium- Filter the data set to include only participants in the Experimental condition with reaction times faster than the overall mean reaction time.
filtered_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 anxiety_change
## 1 20.453056 7.204565
## 2 7.875522 8.731062
## 3 3.221330 11.697428
## 4 23.416047 6.676510
## 5 2.627509 13.865882
## 6 19.373641 4.048952
## 7 26.428138 7.451224I couldn’t figure out how to just print out that specific data, but I was able to pipe and filter to select the experimental data from within the condition column and then only print data that lined up also with reaction times that were greater than the mean of 311.75.
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?
numeric_data <- data %>%
select(reaction_time, accuracy, anxiety_pre, anxiety_post, anxiety_change) %>%
corPlot(upper = FALSE)## Error in plot.new(): figure margins too large# 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).
The variables anxiety_pre and anxiety_post seem to be strongly positively correlated, with a correlation of .901. It seems like this is the only strong correlation, which was a bit surprising to me. It was surprising that pretty much everything else was a little bit negatively correlated. These correlations might inform further research in psychology by inspiring others to investigate certain interventions or, with correlations like the faster the reaction time, the worse the accuracy, some might want to look into speed and accuracy trade-off.
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?
1. I’m interested in how your living environment in college could impact your satisfaction. For example, what is the correlation between your happiness and living at home versus in dorms? Or participating in coops or living in a single apartment. I could collect data on the independent and dependent variables (living environment and happiness/satisfaction Likert scales). Descriptive statistics and correlation analysis would be appropriate statistical analyses. Self-report bias and confounding variables could pose potential measurement errors, which I would need to address beforehand ideally. 2. R has changed my understanding of psychological statistics by deepening my understanding of data manipulation - like filtering, selecting or cleaning data. I didn’t realize that statistics required writing so much code, but I do enjoy it to a certain extent. R doesn’t seem that intuitive for beginners, so there is somewhat of a steep learning curve. However, it is very accessible and very good at visualization like creating histograms and plots.
Submission Instructions:
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