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Summary
The measures of central tendency are part of descriptive statistics that provide a basic summary of data. They help a researcher locate the center of the distribution and include the mean, median, and mode (Cooksey, 2020). They can also be called measures of location. The mean is the average value within the distribution and is the most commonly used measure of central tendency. It can indicate the average cups of coffee the typical student drinks to stay awake. Hair et al. (2020) state that the mean is best calculated when the data scale is either interval or ratio. Generally, the data will show some central tendency, with most responses distributed close to the mean. It is considered a robust measure of central tendency as it is fairly insensitive to data values being added or deleted.
The median is represented by the mid-point of data that has been arranged in an ascending or descending order. For example, if a sample of students is interviewed to determine their coffee-drinking patterns, a researcher might find that the median number of cups of coffee consumed is 3. The number of cups of coffee consumed above and below this number would be the same since the median number is in the exact middle of the distribution. Hays (2018) states that if the number of data observations is even, the median is generally considered to be the average of the two middle values. If there is an odd number of observations, the median is the middle value. The median is especially useful as a measure of central tendency for ordinal data and for data that are skewed to either the right or the left.
The mode is the value that appears in the distribution most often. For instance, in week students may drink an average of 4 cups of coffee each day, which is the mean, while the number of cups most students drink is 3, which is the mode. The mode is the value that represents the highest peak in the distribution’s graph. It is especially useful as a measure for data that have been somehow grouped into categories.
Differences Between Sample Statistics and Population Parameters
Sample statistics constitute a part of inferential statistics, which help to decide about a population based on a sample, which is a subset of the population. For example, if an analyst seeks to investigate the average cups of Starbucks coffee students consume daily, there would be no need to interview all the students. Assuming a school has 1000 students, collecting data from all the students will be time-consuming, expensive, and virtually impossible. Instead, a sample of 100 students can be considered sufficiently large to provide accurate information about the coffee-drinking habits of all 1000 students. According to Hair et al. (2020) population parameters are variables or measurements that define an entire population as opposed to sample statistics that are computed directly from a sample. In circumstances where the actual population parameters cannot be established, for example, from a continent, sample statistics are used to make inferences about the population.
Features of Chi-Square Analysis
The Chi-square test is best applied when data is measured using an ordinal or nominal scale. The analysis is categorized under the nonparametric statistics that do not need assumptions to be made that the data is normally distributed. According to Kushwaha (2017), chi-square analysis compares responses’ observed frequencies (counts) with the expected frequencies. The Chi-square test is applied to determine whether or not observed data is distributed as expected, assuming that the variables are unrelated.
The Chi-square test is univariate, meaning it does not consider relationships among multiple variables simultaneously. It can also be designed to test for a statistically significant relationship between nominal and ordinal variables organized in a bivariate table (Hair et al., 2020). In this case, the test is applied to assess whether two variables are independent. Under bivariate analysis, cross-tabulation is applied to examine relationships and report findings for two variables.
Uses of ANOVA versus Chi-Square Test
The Chi-square test is applied in the ranking data for two factors that are thought to be important. For instance, in selecting a coffee brand, coffee taste and brand name can be applied through a chi-square test to determine whether Starbucks coffee drinkers and Maxwell House drinkers ranked these factors the same or differently.
ANOVA to determine the statistical difference between three or more means. If data is collected on the actual count of the number of cups of coffee a typical Starbucks consumer drinks at a particular time versus the Maxwell House consumer, it constitutes ratio data. ANOVA can be applied to determine whether there are differences in the mean number of cups consumed. In addition, one-way ANOVA can be applied in comparing light, medium, and heavy drinkers of Starbucks coffee on their attitude toward a particular Starbucks advertising campaign. The sole independent variable is the consumption of Starbucks coffee; however, it is divided into three levels, making ANOVA the appropriate test to use. It can be used further in a case with multiple independent factors (Johnson & Wichern, 2019). The many factors create the possibility of an interaction effect, which involves acting together to affect dependent variable group means.
References
Cooksey, R. W. (2020). Illustrating statistical procedures: Finding meaning in quantitative data. Springer.
Hair, J. F., Ortinau, D. J., & Harrison, D. L. (2020). Essentials of marketing research. 5th ed. Mcgraw-Hill Education.
Hays, W. L. (2018). Statistics. Wadsworth/Thomson Learning.
Johnson, R. A., & Wichern, D. W. (2019). Applied multivariate statistical analysis. Pearson.
Kushwaha, K. S. (2017). Inferential statistics. New India Publishing Agency.
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