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 categories or labels without any order or ranking, Ordinal Data have a meaningful order or ranking, but the intervals between the values may not be equal. Interval can be categorized, ranked and the interval between the values are equal but there’s no zero. Ratio can be categorized,ranked and the interval between values are equal and there is a zero point, meaning the zero represents the absence of the measure quantity. Ordinal data example, a questionnaire on depression, Interval Data Example, test scores of a examination. Ratio data example is an self reported behavior report rating the frequency of certain behaviors and nominal data example can be gender female or male or different types of mental health disorders.

  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

Nominal data without any inherent order or ranking labels or categories with no order because they are purely descriptive, they dont have any quantitative or numeric value, Ordinal is categorized with a specific order or ranking but the intervals are not equal because the distance between the categories are uneven or unknown. Interval data equals distance between values no true zero because zero is an arbitrary point and not a complete absence of the variable. Ratio Data has equal intervals and a true zero because the quantity is being measured.

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 sampling relies on chance, while systematic relies on a fixed rule. Random error mainly affects precision based on the same measurement under the equivalent circumstances, data affected by systematic error are biased, and this type of error can not be reduced or eliminated by taking repeated measures. Systematic example can be an thermometer resulting in results being to high that can be eliminated. Random example can be a coin toss because the results can be heads or tails, being unsure of what the results will be obtained.

  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?

Construct validity refers to whether the study is actually measuring the concept it intends to measures for example if the participants misunderstand the questions on a test survey or if it dont captures the main concept in all forms the construct validity of the study is compromised and the conclusions drawn from the study can be misleading. measuring errors could introduce confounding variables or ocscure the true relationship stress and academic performance.

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).
data.frames(1:6) reaction_times (271.9762,288.4911,377.9354,303.5254,385.7532)
mean(reaction_times) 
median(reaction_times)
sd(reaction_times)
## Error in parse(text = input): <text>:1:18: unexpected symbol
## 1: data.frames(1:6) reaction_times
##                      ^
  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.

311.75 and 302.5 indicates no outliner

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?
pt(75,df)
pt(1,df)-pt(-1,df)




---

## 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`.
## Error in parse(text = input): <text>:12:7: unexpected symbol
## 11: ### Question 5: Data Cleaning with dplyr
## 12: Using the
##           ^
# 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
medium (y), 
## Error in parse(text = input): <text>:1:11: unexpected ','
## 1: medium (y),
##               ^
  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?

How does social media use affect adolescents mental health over a three month period? The data could lead to the different types of mental health diagnosis, gender and age which can allow researchers to analyze the correlations of variables, which can be systematic procedures used to observed, describe ans predict and explained ensuring the data collection is objective and reliable to understand. Using R has showed me how to organized code, data and input codes to identify data calculation. .


Submission Instructions:

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