# Calculate an appropriate measure of association

Running head: QUESTION 18.5 RESPONSE 1

QUESTION 18.5 RESPONSE 6

A research team conducted a study of soft-drink preferences among residents in a test market prior to an advertising campaign for a new cola product. Of the participants, 130 are teenagers and 130 are adults. The researchers secured the following results:

Cola Noncola

Teenagers 50 80

Calculate an appropriate measure of association, and decide how to present the results. How might this information affect the advertising strategy?

The first factor to consider would be to determine the null hypothesis (actual age of the consumer and soft drink preference). The null hypothesis: H0= There is no relationship between the soft-drink preference and the age of the consumer.

The statistical test:

Critical values of Chi-Square (Formulas taken from pages 490 and 491, Cooper and Schindler, 2014)

a= 0.05

d.f. (degrees of freedom) = 1

χ2 critical value = 3.841

Chi-Square Test: Cola, Non-Cola

Expected counts are printed below observed counts

Chi-Square contributions are printed below expected counts

Cola Non-Cola Total

Teens 50 80 130

70.00 60.00

5.714 6.667

70.00 60.00

5.714 6.667

Total 140 120 260

Chi-Sq = 24.762, DF = 1, P-Value = 0.000

Interpreting the test

The calculated chi-square value of 24.762 is larger than the critical value of 3.841 which means the null hypothesis (H) must be rejected. The alternative hypothesis does not specify the type of association, so close attention to the data is required to interpret the information provided by the test. The alternative hypothesis (Ha) is accepted, there is a relationship between the soft-drink preference and the age (teenage and adult, exact age not considered) of the consumer.

The distribution of the statistic X2 is  chi-square  with (r-1)(c-1) degrees of freedom, where r represents the number of rows in the two-way table and c represents the number of columns. The distribution is denoted (df), where df is the number of degrees of freedom.

The chi-square distribution is defined for all positive values. The P-value for the chi-square test is P ( >X²), the probability of observing a value at least as extreme as the test statistic for a chi-square distribution with (r-1)(c-1) degrees of freedom (Anonymous, 2018).

According to Lani (2018), “There are a number of important considerations when using the Chi-Square statistic to evaluate a cross-tabulation”.  When Chi-Square value is calculated, “it is extremely sensitive to sample size – when the sample size is too large (~500), any small difference will appear statistically significant” (Lani, 2018).  The total sample size is within range (260); therefore, differences in calculations are negligible.

Presenting the results

The proper technique for associating this study is chi-square because we are

comparing two binary variables (one is teenagers or adults and the other is no cola or cola).

Adults prefer cola over no cola products (chi-square, p< .001), and teenagers prefer non-cola over cola products. This information may be useful in the advertisement strategy by proposing that promotional campaigns of cola products should focus more on adult individuals rather than teenagers. The chi-square test is applied in a two way table having one or two variables. In chi-square test the count in every cell is compared to the expected count as supposition of having no association between a table’s rows and columns.

“There is no all -round technique for explicit data. Some get severely affected by shape and number of cells; while others are sensitive to sample size or marginal,” (Schindler & Cooper, 2011, p. 515). The results demonstrate that adults consume more cola than teenagers. Marketing relies on the companies producing non-cola or cola products. It is also an important factor to know if the cola company is trying to keep their current customers, or focusing their marketing strategies for new younger customers to their products. The key is based on demographics. Only 130 of each group was surveyed, but if the company were to determine the total number of teenagers to adults, the figures would probably conclude that there are more teenagers than adults. Proverbs 24:14 states, “So [shall] the knowledge of wisdom [be] unto thy soul: when thou hast found [it], then there shall be a reward, and thy expectation shall not be cut off”. What is God trying to covey in this message; simply put, there can be numerous connotations. The expectations may be great, but knowledge and wisdom are food for the soul. The research team probably assumed teenagers were more likely to consume cola beverages, but data clearly indicated adults consume more cola beverages overall.

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