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:

  1. Describe the key differences between nominal, ordinal, interval, and ratio data. Provide one example of each from psychological research.

Nominal Data categorizes mutually exclusive categories. Example, Gender. Ordinal Data categorizes data into distinct categories with a meaningful order and ranking. Example, Educational level. Interval Data orders data with equal intervals between values. Example, Temperature in Celsius & Fahrenheit. Ratio data has equal intervals between values, just like interval data. Example, Height, weight.

  1. 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 is an Interval, a score of 0 which doesn’t represent depression which means there is no true 0 point. Response time in milliseconds is Ratio, a true 0 point and meaningful ratios. Likert scale ratings of agreement is Ordinal, the internal categorizes might not be equal for the same degree. Diagnostic categories is Nominal, No fundamental order. Age in years is Ratio, a true zero point and meaningful ratios and twice the age.

Question 2: Measurement Error

Referring to Chapter 3 (Measurement Errors in Psychological Research):

  1. Explain the difference between random and systematic error, providing an example of each in the context of a memory experiment.

Random errors are not predictable and have variation in measurements that can occur in random. An example of random errors is misreading the weighing scale. Systematic errors are steady and quotable derivation the value. An example of systematic errors is thermometer that steadily reads temperature 1 or 2 degrees higher than the original temperature.

  1. 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?

Validity refers to the degree to which a test measures what it claims to measure. The measurement error affects the validity of a study of the relationship between stress and academic performance because your results will be messed up, which leads it to being inaccurate. To minimize these errors we could use reliable tools or repeat experiments to have better results.

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     19.93397

Now, perform the following computations*:

  1. Calculate the mean, median, standard deviation, minimum, and maximum for reaction time and accuracy, grouped by condition (hint: use the psych package).
describeBy(data$accuracy, data$condition, mat = TRUE, digits = 2)
##     item       group1 vars  n  mean   sd median trimmed  mad   min    max range
## X11    1      Control    1 29 85.49 9.86  85.53   85.68 8.77 61.91 105.50 43.59
## X12    2 Experimental    1 19 88.06 8.20  88.32   87.76 9.86 74.28 106.87 32.59
##      skew kurtosis   se
## X11 -0.15    -0.35 1.83
## X12  0.45    -0.45 1.88
  1. Using dplyr and piping, create a new variable anxiety_change that represents the difference between pre and post anxiety scores (pre minus post). Then calculate the mean anxiety change for each condition.
data <- data %>%
  mutate(anxiety_change = anxiety_pre - anxiety_post)

data %>%
  group_by(condition) %>%
  summarise(mean_anxiety_change = mean(anxiety_change, na.rm = TRUE))
## # A tibble: 2 × 2
##   condition    mean_anxiety_change
##   <chr>                      <dbl>
## 1 Control                     3.79
## 2 Experimental                8.64

The mean anxiety for the control group is 3.79. The mean anxiety for the experimental group is 8.64

Question 4: Probability Calculations

Using the concepts from Chapter 4 (Descriptive Statistics and Basic Probability in Psychological Research):

  1. If reaction times in a cognitive task are normally distributed with a mean of 350ms and a standard deviation of 75ms:
    1. What is the probability that a randomly selected participant will have a reaction time greater than 450ms?
    2. What is the probability that a participant will have a reaction time between 300ms and 400ms?
mean_rt <- 350  
sd_rt <- 75     

# (a) Probability of reaction time > 450ms
p_greater_450 <- 1 - pnorm(450, mean = mean_rt, sd = sd_rt)

# (b) Probability of reaction time between 300ms and 400ms
p_between_300_400 <- pnorm(400, mean = mean_rt, sd = sd_rt) - pnorm(300, mean = mean_rt, sd = sd_rt)


p_greater_450
## [1] 0.09121122

The probability that a randomly selected student will have a reaction time greater than 450ms is 0.09. The probability that a participant will have a reaction time between 300ms and 400ms is 0.49.

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:

  1. Remove all rows with missing values and create a new dataset called clean_data.
clean_data <- na.omit(data)
  1. Create a new variable performance_category that 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
mean_reaction_time <- mean(clean_data$reaction_time, na.rm = TRUE)

filtered_data <- clean_data %>%
  filter(condition == "Experimental" & reaction_time < mean_reaction_time)
  1. Filter the dataset to include only participants in the Experimental condition with reaction times faster than the overall mean reaction time.
mean_reaction_time <- mean(clean_data$reaction_time, na.rm = TRUE)

filtered_data <- clean_data %>%
  filter(condition == "Experimental" & reaction_time < mean_reaction_time)

I started with removed rows that had missing values, which created a new dataset(clean-data). Moving on created a new variable(performance_category) which classified participants based on their accuracy. 90 or above accuracy is high, between 70 and 90 was participants is medium accuracy and 70 was participants is low accuracy. Finally, I filtered the dataset to include only participants in the experimental who had faster reaction time than the mean.

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:

  1. Select the numeric variables from the dataset (reaction_time, accuracy, anxiety_pre, anxiety_post, and anxiety_change if you created it).
  2. Use the psych package’s corPlot() function to create a correlation plot.
  3. 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 <- clean_data %>%
  select(reaction_time, accuracy, anxiety_pre, anxiety_post, anxiety_change)

corPlot(cor(numeric_data, use = "pairwise.complete.obs"), 
        numbers = TRUE,  # Display correlation values
        upper = FALSE,   # Show only lower triangle
        main = "Correlation Plot of Key Variables")
## Error in plot.new(): figure margins too large

There is a strong correlation between anxiety_pre & anxiety_post. Another strong correlation is between anxiety_change and anxiety_pre. A unique relationship is between reaction time and accuracy. These correlations can advise further research in psychology. Studies can explore ways to reduce anxiety in high pressure situations.

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?

1. How does sleep schedule affect anxiety levels in teenagers? To research this, I would collect data on daily sleep time as well as self reports on anxiety levels using google forms. I would use correlation tests to see if less sleep hours is linked with higher anxiety. I could use reversion analysis. A latent measurement error that needs to be addressed could be on self reported data from the google forms. People may under or overestimate their anxiety levels or hours of sleep time. 2. Learning R for data analysis changed my viewpoint of psychological statistics as it is useful for this topic. The advantage of R is that is free and widely accessible, and it has tools for collected data. The only challenge would be to learn the code for the people who are new to the program.

Submission Instructions:

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