Visualizing Data: Part 2 Study Notes

Visualizing Data: Part 2

Adlyn Perez-Figueroa
PSY3010

Histograms

• Histograms can have different shapes.
• There are specific terms and statistics used to describe a histogram’s shape, which indicate whether that shape significantly deviates from a normal distribution.

Kurtosis

• Kurtosis: Refers to the height and width of a distribution’s peak.
  • Leptokurtic: A distribution's peak is higher and narrower than the standard normal distribution.
  • Platykurtic: A distribution's peak is lower and wider than the standard normal distribution.
  • Mesokurtic: A distribution's peak that is similar to a normal distribution.

Measuring Kurtosis

• Kurtosis can be quantitatively assessed using various statistical programs.
• Typical cutoff points for kurtosis are -2 and +2.
  • A distribution with a kurtosis of -2 or lower is considered platykurtic (indicating it is too flat).
  • A distribution with a kurtosis of +2 or higher is defined as leptokurtic (indicating it is too high and narrow).

Measuring Skewness

• Skewness can also be measured in statistical programs to determine the direction of skewness.
  • A negative value indicates the data is skewed left.
  • A positive value indicates the data is skewed right.

Range of Skewness Values

• Values between -0.5 and +0.5 indicate the distribution is approximately symmetric.
• Values below -0.5 or above +0.5 are considered moderately skewed.
• Values below -1 or above +1 are classified as severely skewed.

Measuring Normality: Q-Q Plot

• A Q-Q Plot (Quantile-Quantile Plot) is an analytical tool used to assess if a dataset approximates a normal distribution.
  • Data observations are represented as dots on a diagonal line; if data dots align closely with this diagonal line, the data is considered normally distributed.
  • If the dots diverge from the diagonal, the data may be skewed or exhibit other deviations from normality.

Examples of Q-Q Plots

• Normal Q-Q Plot: Represents normally distributed data:

  • Scaled values are shown along both axes ranging from -3 to +2.

• Q-Q Plot of Left-Skewed Distribution:

  • The data points indicate a left skew, with values illustrated showing skewness towards lower quantiles.

• Q-Q Plot of Right-Skewed Distribution:

  • Similarly showcasing right skewness, illustrated data points deviate towards higher quantiles.

Box Plot

• When to Use: A box plot is ideal for providing a simple visual summary of a dataset that conveys more specific detail.
• Best Used With: Moderate to larger sample sizes (20+).
• Data Types: Effective for ratio or interval data.
• Comparison of Box Plots: Multiple box plots can be displayed side-by-side for comparison of different datasets.

Box Plot Features

• Structure:
  • The box contains the interquartile range encompassing 50% of the sample data.
  • The line in the middle of the box represents the median of the dataset.
  • The “whiskers” indicate the minimum and maximum values.
  • Q1 (Lower Quartile): 25% of the data falls below this point.
  • Q3 (Upper Quartile): 75% of the data is below this threshold.

Box Plot Interpretation

• If the median line is not centered within the box, it indicates that the data is skewed.

Box Plot with Outliers

• Outliers are defined as excessively large or small values that do not conform to the sampled data.
• Outliers are visually represented as dots that are positioned beyond the whiskers of the box plot.

Violin Plots

• Violin Plots: These integrate elements of box plots and histogram distributions into a single visualization, effectively presenting data distributions.
• They are commonly employed in neuroimaging research.
• Data Types: Suitable for displaying ratio and interval data, akin to box plots.

Structure of Violin Plot

• The central feature is the box plot, while the sides illustrate histogram distributions shaped as curves, thus providing a comprehensive view of the data distribution.