Variables and Interpreting Graphs

Operationalizing Variables

Variables are anything that can change or vary (e.g., age, gender, aggression, anxiety).

• What you’re measuring

• Defining them - conceptual (what it means) vs. operational (how it’s measured)

• Type of measurement

Construct

Variables that cannot be directly observed; traits, emotions, attitudes

Type of Measurement

1. Self-report: Interviews or questionnaires, people report their beliefs, behaviour, history, etc. (has social desirability bias)

2. Video-recordings: hint for stress cues like nail biting, fidgeting, or expressions

3. Behavioural: observing behaviours, either lab induced or naturally occurring

4. Physiological: assessment of bodily states, brain imaging, or heart rate monitors

How do you choose?

Previous research, methodological (new tech), feasibility (resource limitation)

Reliability

Consistency

True score - the "real" score on the variable (a person truly has an anxiety level of 50)

Obtained score - the score the measure gives (they score 55 because they were especially stressed that day)

Measurement error - difference between true score and obtained score

We want measurement error as small as possible by using reliable, valid measures.

To assess the reliability of report measures:

1. Test-retest - If I give the same measurement twice with time in between, will I get a similar result?

2. Parallel-forms - If there are different forms of the measure, do they all measure the same thing? Scores on two different version of test = same score = high parallel

3. Internal consistency - Do all the questions on a scale measure the same thing?

• Split-half: Compare scores from the first half of the questionnaire with the second half.

• Cronbach's alpha (α): Measures how well all the questions are related to each other.

  • Higher α = better internal consistency

To assess the reliability of observational measures:

Interrater reliability

• How consistent the results are with two/more researchers observing the participant

Validity

Accuracy

1. Face Validity - does the measure look like it’s measuring what it’s meant for

2. Content Validity - measure all the important components/parts of the construct

3. Criterion Validity - Convergent: does it correlate with similar measures. Predictive: does it predict future expected outcomes

4. Discriminant/divergent Validity - does not correlate with unrelated measures.

Example: A depression questionnaire should:

• Correlate with other depression tests (good convergent validity).

• Not strongly correlate with math ability because they measure different things.

Types of Data

Categorical - each value represents a discrete category where order does not matter (tiger = 1, lion = 2…)

Numerical - each value represents either a real number (age) or a place on a scale/continuum, where order does matter

Categorical Graphs

Pie chart (for simple data = 1), bar graph compares a series of categories as bars (for complex data)

Numerical Graphs

• Histogram shows the distribution (bell curve), visual sense of the data; the mean, range, skew, possible outliers

1. Discrete - finite number of values (dice), binned

2. Continuous - infinite number of values (height), logged

• Scatterplot

  • Used for two continuous variables, shows relationship

• Line Graph

• Time Series (changes over time)

Y-Axis

• The dependent measure or the variable you're most interested in

• Should have a reasonable range

• Too broad, you can't see the difference (flat line)

• Too limited, large top and bottoms/skyrocketing

X-Axis

• Consistent range/scale

• You can exaggerate small changes by zooming in

Truncating an Axis

Restricting range to maximize differences (exaggerate differences)

Example:

Scores are 90 and 95, but the graph starts at 89, making the difference look huge.

Expanding an Axis

Using too broad a range to minimize differences (hide differences)

Example:

Scores are 60 and 90, but the graph goes to 1,000, making the difference look tiny.

Ignoring Conventions

Values should go from small to large

Example:

Years are shown out of order, like 2024, 2022, 2023.

Comparing non-equivalent data

Two different Y-axis on same graph

Example:

Comparing temperature and sales using two different y-axes