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Graphical Representations

  • July 15, 2023
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Univariate Analysis - Analysis of a single variable is called Univariate Analysis.

Graphs using which we can visualize single variables are:

  • Bar Plot
  • Index Plot
  • Dot Plot
  • Strip Plot
  • Violin Plot
  • Stem & Leaf Plot
  • Candle Plot
  • Pie Chart
  • Time Series Plots
  • Histogram
  • Density Plot
  • Boxplot or Box & Whisker Plot
  • Q-Q Plot or
  • Quantile - Quantile Plot

graphical representation

 


Graphical Representations

For univariate analysis, the histogram, box plot, and Q-Q plot are the most often used plots.

Histogram

Another name for a histogram is a Frequency Distribution Plot.

The histogram's main use is to show the distribution's shape.

histogram

Histograms are used to detect the existence of outliers as a secondary purpose.

histogram


Box Plot is also called as Box and Whisker Plot

  • Box Plot gives the 5 point summary, namely, Min, Max, Q1 / First Quartile, Q3 / Third Quartile, Median / Q2 / Second Quartile
  • Middle 50% of data is located in the Inter Quartile Range (IQR) = Q3 - Q1
  • Formula used to identify outliers is Q1 - 1.5 (IQR) on the lower side and Q3 + 1.5 (IQR) on the upper side
  • Primary Purpose of Boxplot is to identify the existence of outliers
  • Secondary Purpose of Boxplot is to identify the shape of distribution

box-plot


Q-Q plot is also called Quantile Quantile Plot

  • Q-Q plot is used to check whether the data are normally distributed or not. If data are non-normal then we resort to transformation techniques to make the data normal
  • The line in the Q-Q plot connects from Q1 to Q3
  • X-axis contains the standardized values of the random variable
  • Y-axis contains random values, which are not standardized
  • If the data points fall along the line then data are considered to be Normally Distributed

Q-Q Plot


Bivariate Analysis

Analysing two variables is known as bivariate analysis.

To determine whether two variables are correlated, use a scatter plot.

The primary purpose of the Scatter Plot is to determine the following:

  • Direction - Whether the direction is Positive or Negative or No Correlation
    bivariate analysis
  • Strength - Whether the strength is Strong or Moderate or Weak
    bivariate analysis
  • Check whether the relationship is Linear or Nonlinear
    bivariate analysis

Finding out if the relationship is linear or non-linear is the Scatter Plot's secondary goal.

bivariate secondary analysis

  • Determining strength using a scatter plot is subjective
  • Objectively evaluate strength using Correlation Coefficient (r)
  • Correlation coefficient value ranges from +1 to -1
  • Covariance is also used to track the correlation between 2 variables
  • However, Correlation Coefficient normalizes the data in correlation calculations whereas Covariance does not normalize the data in correlation calculation
  • |r| > 0.85 implies that there is a strong correlation between the variables
  • |r| < = 0.4 implies that there is a weak correlation
  • |r| > 0.4 & |r|< = 0.85 implies that there is a moderate correlation

Multivariate Analysis

The two main plots to perform Multivariate analysis are:

  • Pair Plot
  • Interaction Plot

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