STATS OVERVIEW: Quantitative Research Design
Quantitative Research Design Notes
Today's Agenda
Quantitative Research
Variables
Data Collection
Sampling
Descriptive Research
Standard Scores
Data Analysis & Report Writing
The Research Process
Research Design: An outlined plan for data collection and analysis; the purpose of the study determines the design that will be used.
Six Steps of the Research Process:
Identify the topic
Review literature to narrow the problem
Develop research design
Collect data
Analyze data
Report results
Variables/Constructs
Definition: Any trait, attribute, or characteristic that varies across individuals.
Something a researcher intends to explore and understand.
Quantitative Research: Uses "Variables" (measurable traits).
Qualitative Research: Uses "Constructs" (conceptual ideas).
Defining Variables
Operationalizing (for quantitative research):
Stating its specific definition for the purpose of the intended research.
Precisely defining what the variable includes and does not include.
Stating how the variable will be identified and measured.
Example: Mental Health
Could be operationally defined as a DSM diagnosis.
Could be operationally defined by a score on a specific wellness scale.
Conceptually Defining (for qualitative research):
Assigning a dictionary-type meaning.
Example: Mental Health
Could be conceptually defined as "a person's condition regarding their psychological and emotional well-being."
Research Questions
Definition: Questions that the researcher seeks to answer.
Quantitative Research Questions:
Reflect the relationship between variables.
Are posed in the form of a question.
Qualitative Research Questions:
Are broad, open-ended questions.
Answer the "how" or "what" about a particular phenomenon.
Quantitative Research Overview
Key Characteristics:
Defining the variables.
Posing research questions or hypotheses that reflect the relationship between variables.
Collecting data in numeric values.
Conducting statistical analyses to determine whether proposed relationships exist.
Note: Understanding quantitative research does not require being an expert in advanced math; software like SPSS and JASP assist with analyses.
Variables in Quantitative Research
Purpose: To determine the relationship between variables.
All quantitative research has at least one of each of the following:
Independent Variable (IV):
Hypothesized to be the cause.
Researchers manage or manipulate the IV.
Dependent Variable (DV):
Hypothesized to be the outcome or the effect of the IV.
Relationship: The IV causes changes to the DV.
Examples for Identification (IV and DV):
Study: "Does the frequency of counseling affect counseling outcome?" ext{IV} = ext{Frequency of counseling} ext{DV} = ext{Counseling outcome}
Study: "Do different CBT techniques reduce depression?" ext{IV} = ext{Different CBT techniques} ext{DV} = ext{Depression}
Study: "Can one's success in college be predicted by income, intelligence, and race?" ext{IV} = ext{Income, Intelligence, Race} ext{DV} = ext{Success in college}
Study: "Does mindfulness have a significant relationship with client perceived empathy?" ext{IV} = ext{Mindfulness} ext{DV} = ext{Client perceived empathy}
Data Collection in Quantitative Research
First Step: Identify the targeted population.
Population: An entire unit or group; includes all units of interest in the study (e.g., all students, all clients, all employees).
Reality: Researchers usually cannot gather data from the whole population.
Solution: Use sampling strategies to draw a smaller group of individuals (a "sample") that may represent the population.
Goal: Conduct statistical analyses on the sample and then support that the findings are generalizable to the larger population.
Sampling in Counseling Research
Challenges: Counseling researchers often work with protected populations (e.g., individuals in medical, clinical, or correctional institutions; elders or minors), which limits sampling options.
Common Sampling Strategies:
Random sampling
Nonprobability sampling
Convenience sampling
Snowball sampling
Adequate Sample Size: "It depends" on the research; tools like G*Power can help determine appropriate sample size.
Sample Bias
Definition: Issues that arise from the inability to identify or gain access to a true representation of the population, often leading to underrepresenting or overrepresenting certain members.
Causes of Bias:
Inability to identify a population.
Difficulty gaining access to an identified population.
Underrepresenting or overrepresenting certain members of the population.
Volunteerism: Participants may have a personal interest or connection to the topic, which can skew results.
Addressing Sample Bias:
Reporting participants' demographic characteristics.
Discussing how certain sample biases may influence the results in the research report.
Relationship between Population, Sampling, and Statistics:
Population o Sampling o Sample o Descriptive Statistics o Inferential Statistics o Population (generalization)
Descriptive Statistics
Definition: Describe the basic features of the data in a study.
Key Components:
Frequency Distribution
Measures of Central Tendency
Variability
Scales of Measurement
Definition: Classification of what numbers mean to a particular variable.
Crucial for managing statistical software calculations.
Types of Scales:
Nominal:
Assigned to groups or categories.
Numbers serve as names or labels.
Examples: Gender (1=cisgender woman, 2=cisgender man), marital status, religion.
Ordinal:
Measurement by rank or order.
No assumed equal interval between places.
Examples: Letter grade (1=A, 2=B, 3=C…), ranking.
Interval:
Equal interval between scale points.
Arbitrary zero point (zero does not mean absence of a quantity).
Examples: Temperature, IQ test scores.
Ratio:
Possesses a true zero point (zero means the complete absence of a quantity).
Examples: Age, years of counseling experience.
Frequency Distribution
Purpose: To organize and summarize data to show how often different values or ranges of values occur.
Frequency Table: Organizes data into categories or intervals, showing absolute and relative frequencies.
Example Structure:
| Years of Experience (X) | Frequency (f) | Percentage | Cumulative Percentage |
| :-------------------- | :------------ | :--------- | :-------------------- |
| 13-15 | 1 | 10.0% | 100.00% |
| 10-12 | 0 | 0.0% | 90.0% |
| 7-9 | 1 | 10.0% | 90.0% |
| 4-6 | 5 | 50.0% | 80.0% |
| 1-3 | 3 | 30.0% | 30.0% |
| N=10 | | 100.00%| |
Graphing Frequencies:
Histogram: Bar graph showing quantities or percentages within specified ranges.
Polygon (Frequency Polygon): Line graph connecting the midpoints of the tops of the bars of a histogram.
Measures of Central Tendency
Purpose: To find a single value that best represents the center or typical value of a distribution.
Mean:
Most commonly used method of describing central tendency.
The arithmetic average of all scores.
Calculated by summing all values and dividing by the number of values.
Formula: \bar{X} = \frac{\sum X}{N}
Median:
The midpoint of an ordered list of values.
Found by listing values in rank order and identifying the point below which one-half of the scores lie.
Example 1 (odd number of scores): 2, 3, 3, 5, 7, 8, 9 (Median = 5).
Example 2 (even number of scores): 2, 3, 3, 5, 6, 7, 8, 9 (Median = (5+6)/2 = 5.5).
Mode:
Reports the most frequent score in the variable.
Most useful when studying nominal variables.
Not often a useful indicator of central tendency in a continuous distribution.
Types of Distribution
Symmetrical Distribution:
Often described as a "Bell Curve" or normal distribution.
Mean, Median, and Mode are approximately equal and located at the center.
Skewed Distribution: The "tail tells the tale" in terms of skewness.
Positive Skew (Right Skew):
The tail extends to the right (positive direction).
Mean > Median > Mode.
Indicates a few very high scores pulling the mean upwards.
Negative Skew (Left Skew):
The tail extends to the left (negative direction).
Mean < Median < Mode.
Indicates a few very low scores pulling the mean downwards.
Multimodal Distribution: Has more than one mode (peaks in frequency).
Standard Normal Distribution ("Bell Curve")
A specific type of symmetrical distribution representing many naturally occurring phenomena.
Properties:
Mean = 0, Standard Deviation (SD) = 1.
Specific percentages of data fall within certain standard deviations from the mean:
Approx. 68.2\% of data within \pm 1 SD.
Approx. 95.4\% of data within \pm 2 SD.
Approx. 99.7\% of data within \pm 3 SD.
Variability
Definition: The extent to which the scores in a distribution differ from each other; how the scores are spread out.
Homogenous Distribution: Lacking variability (scores are close together).
Heterogeneous Distribution: Having much variability (scores are spread out).
Three Frequently Used Measures of Variability:
Range
Variance
Standard Deviation
Measures of Variability
Range:
Calculated by taking the highest score and subtracting the lowest score.
Represents the distance or difference between the largest and smallest scores.
Considered unstable because it relies on only two scores.
Variance:
The average of the squared deviations from the mean.
Represents how close the scores in the distribution are to the mean (larger variance indicates more spread).
Standard Deviation (SD):
The square root of the variance.
Indicates the average difference between individual scores and the group mean.
It is in the same units as the original data, making it more interpretable than variance.
Standard Scores
Standardization: A process of converting individual raw scores in a distribution to a common scale.
Z-score
Definition: A number indicating the distance an individual raw score is above or below the mean in standard deviation units.
Purpose:
Tells how large or small an individual score is relative to other scores in the distribution.
Allows comparison of individual scores from two variables that use different scales for measurement.
Properties: When a distribution is converted to z-scores, its mean becomes 0 and its standard deviation becomes 1.
The absolute value of a z-score indicates the distance of the raw score from the mean of the distribution.
T-score
Definition: Standardized scores widely used to report performance on standardized tests and inventories (e.g., personality assessments).
Properties:
A T-score of 50 represents the mean.
A difference of 10 from the mean indicates a difference of one standard deviation.
Formula for Conversion from Z-score: T = 50 + 10z
Basic Data Analysis and Reporting
The next step after collecting and describing data involves further statistical analysis and report writing based on the research design.