Chi-Square Analysis
Chi square analysis is a way of comparing categorical responses from two or more different groups (Ryan & Eck, Unk.). This comparison can help reveal whether there is a relationship between the two different groups, and also whether real-world results are in line with anticipated results. Chi square analysis is what is known as a nonparametic test. "Parametric and nonparametric statistical procedures test hypotheses involving different assumptions. Parametric statistics test hypotheses based on the assumption that the samples come from populations that are normally distributed. Also, parametric statistical tests assume that there is homogeneity of variance (variances within groups are the same). The level of measurement for parametric tests is assumed to be interval or at least ordinal. Nonparametric statistical procedures test hypotheses that do not require normal distribution or variance assumptions about the populations from which the samples were drawn and are designed for ordinal or nominal data" (Key, 1997). In other words, chi square analysis permits one to examine data even outside of an expected normal curve distribution. Furthermore, it allows a person to compare observed values with expected values.
One real life application for a chi-square test comes in the business world. It makes sense that heavy down jackets would sell more in cold weather areas than in warm weather areas. However, lightweight layering pieces might do equally well in both locations. A national chain clothing store could compare sales of lightweight longsleeve shirts between geographic areas to determine if geographic area impacts the sales of those shirts. This would tell the chain which locations should stock those shirts, and which locations should not. Moreover, it would provide more information for the company than just overall sales numbers, because it would allow for the comparison of more than one factor at a time.
Inappropriate Use of Statistics
There are a number of ways that statistics can be used inappropriately. Though not an exhaustive list, some of the ways that statistics can be misused is by: failing to provide a context for the statistics, selective use or omission of statistics, using misleading charts or graphics, using selective surveys, confusing or misleading use of statistical terms, using statistical differences that are not significant, interchanging different definitions of average, and rounding (Bolton, 2010). When people use a statistic without providing adequate information behind the statistic, it can lead the audience to a conclusion that simply is not supported by the research. Furthermore, statistics can be impacted by the researcher. "Statistics based on polls can be faulty if the poll is constructed in such a way as to encourage a particular answer" (Korn, 2013).
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