Question

3. Explain how histograms are used to examine data.

4. Describe "Simpson's Paradox".

Answer 1

3] Histograms It is often useful to look at the distribution of the data, or the frequency with which certain values fall between pre-set bins of specified sizes. The defining property of a histogram is: The area of each bar is proportional to the frequency.

To make a histogram, follow these steps:

On the vertical axis, place frequencies. Label this axis "Frequency".

On the horizontal axis, place the lower value of each interval. ...

Draw a bar extending from the lower value of each interval to the lower value of the next interval.

4] Simpson's paradox, or the Yule–Simpson effect, is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined. It is sometimes given the descriptive title reversal paradox or amalgamation paradox.

in statistics, an effect that occurs when the marginal association between two categorical variables is qualitatively different from the partial association between the same two variables after controlling for one or more other variables. Simpson’s paradoxis important for three critical reasons. First, people often expect statistical relationships to be immutable. They often are not. The relationship between two variables might increase, decrease, or even change direction depending on the set of variables being controlled. Second, Simpson’s paradox is not simply an obscure phenomenon of interest only to a small group of statisticians. Simpson’s paradox is actually one of a large class of association paradoxes. Third, Simpson’s paradox reminds researchers that causal inferences, particularly in nonexperimental studies, can be hazardous. Uncontrolled and even unobserved variables that would eliminate or reverse the association observed between two variables might exist.