Consumers are asked to rate the attractiveness of four...

Consumers are asked to rate the attractiveness of four potential dashboard surface textures on an interval scale ( $1=$ least attractive, $10=$ most attractive). Use MegaStat or another software package to perform a Friedman test to see whether the median ratings of surfaces differ at $\alpha=.05$, using age as the blocking factor. $$ \begin{array}{|c|c|c|c|c|c|} \hline & \text { Shiny } & \text { Satin } & \text { Pebbled } & \text { Pattern } & \text { Embossed } \\ \hline \text { Youth (Under 21) } & 6.7 & 6.6 & 5.5 & 4.3 & 4.4 \\ \hline \text { Adult (21 to 39) } & 5.5 & 5.3 & 6.2 & 5.9 & 6.2 \\ \hline \text { Middle-Age (40 to 61) } & 4.5 & 5.1 & 6.7 & 5.5 & 5.4 \\ \hline \text { Senior (62 and over) } & 3.9 & 4.5 & 6.1 & 4.1 & 4.9 \\ \hline \end{array} $$

Consumers are asked to rate the attractiveness of four potential dashboard surface textures on an interval scale ( $1=$ least attractive, $10=$ most attractive). Use MegaStat or another software package to perform a Friedman test to see whether the median ratings of surfaces differ at $\alpha=.05$, using age as the blocking factor.
$$
\begin{array}{|c|c|c|c|c|c|}
\hline & \text { Shiny } & \text { Satin } & \text { Pebbled } & \text { Pattern } & \text { Embossed } \\
\hline \text { Youth (Under 21) } & 6.7 & 6.6 & 5.5 & 4.3 & 4.4 \\
\hline \text { Adult (21 to 39) } & 5.5 & 5.3 & 6.2 & 5.9 & 6.2 \\
\hline \text { Middle-Age (40 to 61) } & 4.5 & 5.1 & 6.7 & 5.5 & 5.4 \\
\hline \text { Senior (62 and over) } & 3.9 & 4.5 & 6.1 & 4.1 & 4.9 \\
\hline
\end{array}
$$

Key Concepts

Blocking in Experimental Design

Blocking is a technique used in experimental design to control for potential variability from nuisance variables by grouping similar experimental units together. By using a blocking factor, such as age in this context, the analysis reduces the impact of extraneous variability on the results, thereby increasing the sensitivity of the test to detect actual treatment differences.

Interval Scale Data

Interval scale data represent a level of measurement where the differences between values are meaningful, and the intervals between points are equal. Such data provide a basis for a wide range of statistical analyses, including both parametric and nonparametric tests, when assumptions for parametric tests are not fully met.

Nonparametric Statistical Methods

Nonparametric methods do not rely on the data following a specific probability distribution, making them versatile when standard parametric assumptions (such as normality) are violated. These methods are based on ranks or medians and are often employed in the analysis of ordinal data or non-normally distributed interval data, providing an alternative approach to measure differences across groups.

Friedman Test

The Friedman test is a nonparametric statistical test used to detect differences in treatments across multiple test attempts. It is particularly useful when data are collected in a repeated measures design or when the assumptions of parametric tests (like normality) are not met. The test compares the ranks of the data within each block and assesses whether there are systematic differences between the treatments.

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