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 is data that consists of categories and does not have a order. This type of data does not represent quantities. Ordinal data is categorical data that have a meaningful order but they are not consistent. Lastly, interval data is the data that has order and categories and has equal intervals between them.

  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 would be intervals because with intervals there is no true zero point. Response time would be ratio because it has a zero point. Likert scale ratings of agreement is ordinal because the intervals between categories are not equal. diagnostic categories are nominal because they are categories with a specific order. Lastly, age in years would be ratio becuase it has a true zero point.

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.

A random error is the arrors that happen at anytime and there affect has a unpredictable measurement. An example of that is an error with participant attentiveness. Systematic error is the errors that happen in a predictable manner. An example of this the environment you put the participants in (to loud, to distracting).

  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?

Measurement error could not predict or detect the problem with environmental factors or external factors that no one could ever know about. A way to minimize this is to control the participants environment for time before an experimenter and during the experiment.

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).
# Using the psych package to calculate the summary statistics
library(psych)
# Reaction time and accuracy by condition
desc_stats <- describeBy(data[, c("reaction_time", "accuracy")], group = data$condition)
desc_stats
## 
##  Descriptive statistics by group 
## group: Control
##               vars  n   mean    sd median trimmed   mad    min    max  range
## reaction_time    1 30 301.40 48.54 299.68  300.42 55.38 201.67 408.45 206.78
## accuracy         2 29  85.49  9.86  85.53   85.68  8.77  61.91 105.50  43.59
##                skew kurtosis   se
## reaction_time  0.14    -0.66 8.86
## accuracy      -0.15    -0.35 1.83
## ------------------------------------------------------------ 
## group: Experimental
##               vars  n   mean    sd median trimmed   mad    min    max  range
## reaction_time    1 17 295.75 38.37 288.49  295.61 43.74 215.67 377.94 162.27
## accuracy         2 19  88.06  8.20  88.32   87.76  9.86  74.28 106.87  32.59
##               skew kurtosis   se
## reaction_time 0.00    -0.27 9.31
## accuracy      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.
# Create the 'anxiety_change' variable
data <- data %>% mutate(anxiety_change = anxiety_pre - anxiety_post)
# Calculate the mean anxiety change by condition
anxiety_change_stats <- data %>%
  group_by(condition) %>%
  summarize(mean_anxiety_change = mean(anxiety_change, na.rm = TRUE))

anxiety_change_stats
## # A tibble: 2 × 2
##   condition    mean_anxiety_change
##   <chr>                      <dbl>
## 1 Control                     3.79
## 2 Experimental                8.64

Write your answer(s) here

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? # Using the normal distribution to calculate the probability probability_450ms <- 1 - pnorm(450, mean = 350, sd = 75) probability_450ms answer: 0.09121122
    2. What is the probability that a participant will have a reaction time between 300ms and 400ms? 0.09121122
# Remove rows with missing values

Write your answer(s) here

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.
# Your code here
  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
# Your code here
  1. Filter the dataset to include only participants in the Experimental condition with reaction times faster than the overall mean reaction time.
# Your code here

Write your answer(s) here describing your data cleaning process.

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?
# 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).

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?

1: How does vaping affect cognitive performance. I would take a group of student who vape and a group who don’t and see what there attention span adn grade look like. I don’t know all outside factors, if they are sleep deprived, if they have a drinking problem, if they have a learning disability. 2: It has changed my understanding because I have learned that it is much easier to run code and have readable psychological data to present. It also make analysis much easier because having raw data can be much easier to comprehend to the common eye.

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.