Business Research Methods Lecture 6 by Selim Bora
Graphs • The distribution of a variable tells us what values it takes and how often it takes these values. • To see what data say, start with graphs. Pie chart and bar graphs are two illustrative types. • Pie charts show how a whole is divided into parts, where wedges within the circle represent the parts, with the angle spanned by each wedge in proportion to the size of that part. • The bar graph make it clear to compare different values, where the height of each bar shows percentage of each part.
Categorical and Quantitative Variables • A categorical variable places an individual into one of several groups or categories. • A quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense. • To display distributions of a categorical variable, use a pie chart or a bar graph. • Pie charts always show the parts of some whole, but bar graphs can compare any set of numbers measured in the same units. • Pictogram is a bar graph in which pictures replace the bars, however the proportion of the images must exactly be equal to the proportion of the values, therefore tricky.
Change Over Time: Line Graphs • To show how a quantitative variable changes over time, use a line graph. • A line graph of a variable plots each observation against time at which it was measured. • Always put time on the horizontal scale of your plot and the variable you are measuring on the vertical scale. • Connect the data points by lines to display the change over time. • Line graphs could be stretched or squeezed to create a particular impression.
Seasonal Variation, Seasonal Adjustment • Look for an overall pattern. • A trend is a long-term upward or downward movement over time. • Look for striking deviations(sharp increases or decreases) from the overall pattern. • A pattern that repeats itself at known regular intervals of time is called seasonal variation. • Many series of regular measurements over time are seasonally adjusted. • That is, the expected seasonal variation is removed before the data are published.
Histograms • The most common graph of a distribution of a quantitative variable is a histogram. • Divide the range of the data into classes of equal width. • Count the number of individuals in each class. • Draw the histogram. • Mark on the horizontal axis the scale for the variable whose distribution you are displaying. • The vertical axis contains the scale of counts. • Each bar represents a class. • The base of the bar covers the class, and the bar height is the class count. • There’s no space between the bars unless a class is empty, so that its bar height is zero.
Interpreting Histograms • In any graph of data, look for an overall pattern and also for striking deviations from that pattern. • An outlier in any graph of data is an individual observation that falls outside the overall pattern of the graph. • To describe the overall pattern of a distribution: • Give the center and the spread.(Chapter 12) • See if the distribution has a simple shape that you can describe in a few words.
Symmetric and Skewed Distributions • A distribution is symmetric if the right and left sides of the histogram are approximately mirror images of each other. • A distribution is skewed to the right if the right side of the histogram(containing the half of the observations with larger values) extends much farther out than the left side. It is skewed to the left if the left side of the histogram extends much farther out than the right side.
Stemplots • To make a stemplot: • Separate each observation into a stem consisting of all but the final(rightmost) digit and a leaf, the final digit. • Stems may have as many digits as needed, but each leaf contains only a single digit. • Write the stems in a vertical column with the smallest at the top,, and draw a vertical line at the right of this column. • Write each leaf in the row to the right of its stem, in increasing order out from the stem. • We usually favor stemplots when we have a small number of observations and histograms for larger data sets.