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Visualizing Data

• Presenter: Adlyn Perez-Figueroa

• Course: Psy3010

Lecture Outline

• Topics discussed in this lecture include:

  • Visualizing Qualitative Data

  • Frequency Tables

  • Pie Charts

  • Bar Charts

  • Line Graphs (qualitative)

  • Visualizing Quantitative Data

  • Line Graph (quantitative)

  • Stem and Leaf Plot

  • Box Plots

  • Histogram

  • Distributions

Visualizing Qualitative Data (Nominal/Ordinal)

• Emphasis on presenting and interpreting qualitative data.

Frequency Tables

• When to use:

  • For a quick breakdown of the sample characteristics.

  • Helpful when analyzing multiple variables, particularly demographic data.

• Data Types:

  • Applicable for nominal and ordinal data.

Example Frequency Table Data

• Religious Affiliation:

  • Atheist/Agnostic: 75 (27.6%)

  • Unaffiliated: 70 (25.7%)

  • Roman Catholic: 36 (13.2%)

  • Mainline Protestant: 29 (10.7%)

  • Pagan: 19 (7.0%)

  • Buddhist: 11 (4.0%)

  • Evangelical: 10 (3.7%)

  • Other: 9 (3.3%)

• Sex Assigned at Birth:

  • Female: 177 (65.3%)

  • Male: 94 (34.7%)

• Sexual Orientation:

  • Bisexual: 135 (49.6%)

  • Lesbian/Gay: 51 (18.8%)

  • Pansexual: 42 (15.4%)

  • Asexual: 17 (6.3%)

  • Queer/No Label: 15 (5.5%)

  • Questioning: 8 (2.9%)

  • Heterosexual: 4 (1.5%)

Frequency Tables: Key Terms

• Frequency (count):

  • The total number of occurrences per category.

  • Example: If you have 10 apples and 9 oranges, these are the frequencies.

  • Frequencies are often denoted by “N,” which indicates count.

• Relative Frequency:

  • The percentage or proportion of occurrences in each category.

  • Example:

  • Percentage: 39.0%

  • Proportion: 0.39

Analyzing Data by Demographics

• Population of Color (POC):

  • 23% Non-Religious, 69% Religious, 57% Spiritual.

• White Population:

  • 77% Non-Religious, 31% Religious, 43% Spiritual.

Patterns in Data

• The importance of recognizing and explaining observable patterns in frequency tables.

Lesson # 1

• Key takeaway: Data tells a story.

Visualizing Qualitative Data - Charts

Pie Charts

• When to use:

  • Ideal for presenting a simple visual representation of variables.

  • Best for a limited number of variables.

• Data Types:

  • Suitable for nominal or ordinal data.

Example of Incorrect Pie Chart Usage

• Notes on how a pie chart should not look or be used (visual misrepresentation).

Bar Charts

• When to use:

  • Useful for presenting the counts categorized visually.

  • Functions similarly to a frequency table but displayed graphically.

  • Best used when dealing with fewer variables.

• Data Types:

  • Generally suitable for nominal or ordinal data.

Structural Aspects of Bar Charts

• Y-axis: Represents frequencies.

• X-axis: Represents categories.

• Horizontal variants exist and can apply comparisons across groups.

Example of Incorrect Bar Chart Usage

• Notes on how a bar chart should not be visualized or arranged (examples provided).

Line Graphs

• When to use:

  • Appropriate for ordinal data (ordered data); can also represent nominal data.

  • Excellent for illustrating changes over time (years, months).

  • Functions as a more detailed version of a bar chart by connecting points.

  • Applicable for both qualitative and quantitative data.

Example of a Line Graph (Qualitative)

• Depicts interaction plots for enjoyment across various food condiments.

  • Mean levels of enjoyment illustrate measured interactions.

Visualizing Quantitative Data (Interval/Ratio)

• Transitioning into quantitative data representations.

Line Graphs (Quantitative)

• Example of military suicide rates from the DoD report (2023) across service branches.

• Questions raised regarding which branch has the highest rates of suicide and reasons for disparities.

Historical Data Representation

• Graph depicting veteran suicide deaths from 2001 to 2021 showcases trends over time.

Lesson # 2

• Key takeaway: Utilize your knowledge and experience to interpret what data signifies.

Histograms

• When to use:

  • Suitable for visualizing distributions from large datasets.

  • Groups data into intervals for simplification and visualization.

  • Best applied to ratio or interval data.

• Y-axis: Can represent either proportions or frequencies (counts).

Histogram Concepts

• Bin Size:

  • Defined as the width of each interval.

  • Smaller bin sizes result in more detailed representations akin to pixels.

Normal Distribution (Bell Curve)

• Definition:

  • A bell-shaped curve representing normalized data that is symmetrical around the mean.

  • Characterized by a single peak in the center, tapering off at the extremes.

• Common Examples of Normal Distribution:

  • Human height and weight distributions.

  • Data typically conforms within certain bounds (e.g., most individuals fall between 5-6 feet).

• Standard Normal Distribution Characteristics:

  • 68% of data lies within one standard deviation from the mean.

  • 95% within two standard deviations.

  • 99.7% within three standard deviations.

Terms Related to Normal Distribution

• Normal curve / Bell curve / Normal distribution / Standard normal distribution:

  • All terms refer to the same statistical representation.

  • “Normally distributed” describes a dataset that follows this bell-shaped pattern.

• Implication:

  • Statistical tests function optimally with normally distributed data, increasing the accuracy of results.

Distributions

• Understanding various types of distributions:

  • Unimodal: One peak (normal distribution is a subtype).

  • Bimodal: Two peaks, indicating potential combined variations between two populations.

  • Multimodal: Three or more peaks, further indicating diverse datasets.

  • Skew: Describes the direction of asymmetry in the data distribution.

  • Skew Left: Tail of the distribution shifts leftward.

  • Skew Right: Tail shifts rightward.