The control group had a standard deviation of 7.78 on the pretest. Does this standard deviation represent nominal, ordinal, or interval scale data?
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To determine the scale of measurement for the standard deviation, we need to understand the characteristics of nominal, ordinal, and interval scales.
1. Nominal scale: In nominal scale, variables are categorical and can only be classified into distinct categories without any inherent order or numerical meaning. Examples include gender, blood type, or categorical variables like color. Standard deviation cannot be calculated for nominal scale data because there are no numerical values assigned to the categories.
2. Ordinal scale: In an ordinal scale, variables have distinct categories with an inherent order or rank, but the differences between the categories are not equal or measurable. Examples include rating scales like "strongly agree," "agree," "neutral," "disagree," and "strongly disagree." Standard deviation can be calculated for data on an ordinal scale, but it may not be meaningful due to the lack of equal intervals between categories.
3. Interval scale: In an interval scale, variables have distinct categories with an inherent order or rank, and the differences between categories are equal and measurable. Examples include temperature measured in Celsius or Fahrenheit or time measured in minutes or hours. Standard deviation is often calculated and meaningful for data on an interval scale.
Based on the given information that the standard deviation is 7.78, which measures the dispersion or spread of data, we can conclude that the data in the control group is measured on an interval scale.