Measuring scale of variables

Sample Solution

The Primary Variable: Customer Loyalty

Based on how we would typically measure customer loyalty in a research setting, the primary variable I would focus on would likely be ordinal.

Describing Why Customer Loyalty is Ordinal and Its Impact on Data Evaluation:

• What is an Ordinal Variable? An ordinal variable is a categorical variable where the categories have a natural, ordered ranking. We know that one category is "more" or "less" than another, but the difference between the categories is not necessarily uniform or quantifiable.

• How Customer Loyalty Fits the Ordinal Definition: In our survey, we would likely ask customers to rate their level of loyalty on a scale. Common examples include:

  • A Likert scale: (1) Very Unlikely, (2) Unlikely, (3) Neutral, (4) Likely, (5) Very Likely (to recommend, repurchase, etc.)
  • A ranking scale: Rank your likelihood of switching to a competitor (1 being most likely, 5 being least likely).

Full Answer Section

• These scales provide an order. "Very Likely" indicates a higher degree of loyalty than "Likely," and "Unlikely" indicates less loyalty than "Neutral." However, the difference in loyalty between "Very Likely" and "Likely" might not be the same as the difference between "Neutral" and "Unlikely." We can't say that someone who chooses a '5' is exactly twice as loyal as someone who chooses a '2'. The intervals between the points on the scale are not necessarily equal.

• How This Affects Data Evaluation: Because our primary variable (customer loyalty as measured by a rating scale) is ordinal, the types of statistical analyses we can perform are somewhat limited compared to interval or ratio data.

  • Appropriate Analyses:
    • Frequency Distributions and Percentages: We can look at how many customers fall into each loyalty category before and after the protocol change.
    • Mode and Median: We can identify the most common loyalty level and the middle loyalty level.
    • Non-parametric Statistical Tests: To compare loyalty levels before and after the change, we would use non-parametric tests that don't assume a normal distribution or equal intervals, such as:
      • Mann-Whitney U test: To compare two independent groups (e.g., a control group that didn't experience the new protocol and a group that did).
      • Wilcoxon signed-rank test: To compare the same group of customers' loyalty levels before and after the change (if we can survey the same individuals).
      • Chi-square test: To examine if there's a significant association between the customer service protocol (a nominal variable: old vs. new) and the different levels of customer loyalty.
  • Inappropriate Analyses: We should avoid calculating a true mean (arithmetic average) or standard deviation for ordinal data, as these statistics assume equal intervals between the data points. While some researchers might calculate means for Likert scales for practical purposes, it's important to acknowledge the underlying ordinal nature of the data and interpret these means with caution. We definitely couldn't perform ratio-based calculations (e.g., saying loyalty increased by 50%).

Secondary Variables (Potential for Other Scales):

It's worth noting that we might also collect data on other variables that could be different scales:

• Customer Satisfaction with Specific Service Aspects: We might use similar rating scales (likely ordinal).
• Number of Repurchases in a Given Period: This would be a ratio variable (e.g., 0, 1, 2, 5 repurchases). It has a true zero point, and ratios are meaningful (5 repurchases is five times as many as 1). For this, we could use more powerful parametric statistical tests if the data meets the assumptions.
• Time Since Last Interaction: This could be an interval or ratio variable depending on how it's measured (e.g., days, weeks). If measured from a specific zero point (like the date of the protocol change), it's ratio. We could calculate means, standard deviations, and use parametric tests.
• Demographic Information (e.g., Region, Product Type): These would likely be nominal variables (categories with no inherent order). We would use frequency counts and chi-square tests to analyze relationships with loyalty.

In conclusion, for our primary measure of customer loyalty based on a typical survey rating scale, we would be working with an ordinal variable. This characteristic dictates that we should primarily rely on non-parametric statistical methods for comparing groups and assessing the impact of the customer service protocol change. While we might collect other types of data (nominal, interval, or ratio), the analysis of our core loyalty measure needs to respect its ordinal nature to draw valid conclusions.