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.
  • The Similarity between Nominal and Ordinal is that they both have to do with the order of things. However Nominal has no inherent order, while Ordinal does have meaning behind its order but has unequal intervals. Interval and ratio dta permit arithmetic operations.
  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
  • Ratio: (Age in years, response time in milliseconds)
  • Nominal: ( Diagnostic categories)
  • Interval:( Scores on depression inventory)
  • Ordinal:( Likert Scale ratings of agreement)

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.
  • The difference between systematic Error and random error is that random error is unpredictable and can be reduced by increasing sample size. Versus systematic error is consistent but has biases results.
  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?
  • This might affect the measurement of the study because validity is the accuracy of measurements. I think the most important step researchers could take to minimize errors could be to check the consistency of the data and using reliable 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     19.93397

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).
# Your code here

#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.
'''{r_anxiety-change, error = TRUE, message = FALSE, warning = FALSE}
anxiety_change_stats <- data %>%
  mutate(anxiety_change = anxiety_pre - anxiety_post) %>%  # Create the new variable anxiety_change
  group_by(condition) %>%                                  # Group the data by condition
  summarise(mean_anxiety_change = mean(anxiety_change, na.rm = TRUE))  # Calculate the mean change (ignoring NA values)
print(anxiety_change_stats)
## Error in parse(text = input): <text>:4:3: unexpected INCOMPLETE_STRING
## 8:   summarise(mean_anxiety_change = mean(anxiety_change, na.rm = TRUE))  # Calculate the mean change (ignoring NA values)
## 9: print(anxiety_change_stats)
##      ^

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?
    2. What is the probability that a participant will have a reaction time between 300ms and 400ms?
pnorm(mean=350ms, sd =1)
## Error in parse(text = input): <text>:2:15: unexpected symbol
## 1: 
## 2: pnorm(mean=350ms
##                  ^

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.
remove_outliers(missing_values)
## Error in remove_outliers(missing_values): could not find function "remove_outliers"
  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
performance_catergory (high_accuarcy)
## Error in performance_catergory(high_accuarcy): could not find function "performance_catergory"
  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. I would like to research on how social media affects self esteem in young adults. I would also use despcriptive statistics and take the means, mins and maxs of test such as self esteem scores, time spent on social media etc.

-2.I think it helps see it from a very numerical perspective. I think the biggest Challenge is not being able to see the plots or data right away. However I do think it is easier to manipulate the data and you get to control more on how its presented.


Submission Instructions:

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