STAT1201 Module 2 VISUALISING DISTRIBUTIONS DOT PLOTS . The three features that can be described from a dot plot: the location or centre of the distribution, the spread of the distribution, and any deviation from the general pattern · Side-by-side dot plots can be used to explore relationships between a quantitative and categorical variable. . Paired data means there are two measurements for each subject. · We can only analyse independent samples HISTOGRAMS · An alternative to dot plots for large samples is to make a histogram. . We start by breaking the range of the values into a number of bins or classes. . We tally the counts of values falling in each bin and then make the plot by drawing rectangles whose bases are the bin intervals and whose heights are the counts. · Proportion = count / total . The direction of the skewness is the direction that the tail of values is pointing . The peak of a distribution is the mode and distributions with just one peak a unimodal distribution. A distribution with two modes, is called bimodal. If there are more than two, then it's called multimodal. . The histogram is an example of a plot that estimates the density of a distribution. However it's not very good at it because it's not smooth and can change dramatically as you change the width of the bins. A solution to this is to use kernel density estimators. This is where you put a kernel of density estimate centred on each data value and then all their densities together. . The width of the kernels is referred to as the bandwidth of the density estimate CATEGORICAL VARIABLES . To get the sample proportions, we tally up all of the observations in each of the categories and divide each count by the total number of observations. · A proportion can always be expressed as a percentage . To display the distribution of a categorical variable we make a bar chart of the proportions VISUALISING CONTINUOUS DATA . Dot plots are a simple tool which are particularly useful for showing details and for comparing groups. However, they are perhaps less useful when you have a lot of points. An alternative is to plot a summary of the data instead. · Dot plots and density curves are also useful for comparing distributions between groups · A histogram is useful for showing the shape of the distribution. Histograms are a useful tool for the density of a distribution, especially for large data sets. · Categorical data can be summarised using percentages or proportions . Bar charts are used to visualize the distribution of counts or proportions for a categorical variable QUANTILES . The five-number summary for a sample is a list of the minimum, the first quartile, the median, the third quartile, and the maximum.
. The distance between Q1 and Q3, the interquartile range is IQR = Q3 - Q1. It's the range of values covered by the middle