LESSON 3: GRAPHING QUANTITATIVE VARIABLES

QUANTITATIVE VARIABLE

- Variables measured on a numeric scale

Example: height, weight, response time, subjective rating of pain, temperature, score on an exam

STEM DISPLAYS

arranged as a column to the left of the bars; represents the tens digits (e.g. 3 stem = 30 to 39)

LEAF DISPLAYS

- Numbers to the right represent the ones digits

- Every leaf in the graph, therefore, stands for the result of adding the leaf to 10 times its stem.

Purpose: to clarify the shape of the distribution; the precise numbers can be determined by examining the leaves

STEM AND LEAF DISPLAYS

- Best-suited for small to moderate amounts of data (up to 200 observations)

- We can make our figure even more revealing by splitting each stem into 2 parts

- Splitting depends on the exact form of your data: if rows get too long with single stems, you can try splitting them into 2 or more parts

- they are placed back to back along a common column of stems: "Back-to-back stem and leaf display"

- Easy to graph when:

- data are whole numbers

- All numbers are positive

- Data with decimals can be rounded to 2-digit accuracy

Test Anxiety Questionnaire

(Scores range from 10 - 50)

Low: 10 - 19

Moderate: 20 - 35

High: over 35

HISTOGRAMS

- Used for displaying the shape of the

distribution of a quantitative variable.

- It groups data into class intervals (bins) and represents the frequency (or relative frequency) of data within each interval using adjacent bars.

- Best-suited for large amounts of data

- can also be used when the scores

are measured on a more continuous scale, such as the length of time (in milliseconds) required to perform a task.

When to Use It:

- Best-suited for large data sets (typically more than 20-30 observations).

- Useful for identifying distribution shape, such as normality, skewness, or multimodality.

- Can be used for both discrete and continuous quantitative variables.

class frequencies

- In a histogram, are represented by bars.

- Height of each bar corresponds to its class frequency.

FREQUENCY POLYGONS

- Same purpose as histograms, but are

especially helpful for comparing two or more distributions.

- Also a good choice for displaying cumulative frequency distributions (or trends in grouped data)

- are useful for comparing distributions

- Achieved by overlaying the frequency polygons drawn for different data sets

- Also possible to plot two cumulative frequency distributions in the same graph.

- Shows data distribution

- X-axis: class midpoints,

- Y-axis: frequencies

- Always uses straight line segments

- Comparing grouped frequency data

Cumulative Frequency

- Y-axis values represent cumulative frequency: not the individual class frequency

- Helps to visually identify medians, quartiles, and percentiles.

- The final point always shows the total number of observations.

PERCENTILES

- are based on cumulative frequency, indicating the value below which a given percentage of data falls.

- indicates the score below which

a given percentage of scores fall.

- Commonly used in standardization tables of psychological tests and measures

- Describe a person's standing compared with the set of individuals on which the test or measure was initially researched

- Quick method of expressing a person's score relative to those of others.

Example:

- 90th percentile = the score is greater than or equal to 90% of the distribution.

- Neuroticism score is 90th percentile = person is more neurotic than about 90% of people

BOX PLOTS

- Box-and-Whiskers Plot

- Provide a visual summary of a distribution's central tendency and spread.

- Highlight the median, quartiles, and potential outliers.

positive skew

Longer whisker on the top

negative skew

Longer whisker on the bottom

positively skewed

If mean > median

LINE GRAPH

- Are appropriate only when both the X- and Y-axes display ordered (not qualitative) variables

- Generally better than bar charts when comparing changes over time

- Shows trends over time

- Both axes are ordered variables

- Can be smooth or segmented

- Time-series data