The ranking test is a sensory analysis method used to establish a preference order among multiple samples. It is particularly useful when judges are required to rank products from most to least preferred without ties.
To statistically analyze the results of such tests, the non-parametric Friedman test is a robust option. It determines whether there are statistically significant differences between the evaluated treatments, considering the variability among judges (Meilgaard et al., 2016).
To evaluate whether there are significant differences in the preference of treatments formulated with different ratios using the Friedman test, and if so, to identify which treatments differ significantly using a post-hoc analysis.
In this example, a sensory ranking test was conducted with 60 panelists who evaluated four beverage formulations based on varying proportions of two ingredients: mango pulp and passion fruit extract. The treatment ratios were: 75:25, 50:50, 25:75, and 0:100. Each panelist ranked the four samples from 1 (most preferred) to 4 (least preferred), with no ties allowed.
print(data)## # A tibble: 240 × 3
## Sujeto Tratamiento Valor
## <dbl> <chr> <dbl>
## 1 1 75:25 1
## 2 1 50:50 4
## 3 1 25:75 3
## 4 1 0:100 2
## 5 2 75:25 1
## 6 2 50:50 3
## 7 2 25:75 4
## 8 2 0:100 2
## 9 3 75:25 1
## 10 3 50:50 3
## # ℹ 230 more rows# Apply Friedman test
friedman_result <- with(data, friedman(trt = Tratamiento, judge = Sujeto, evaluation = Valor))
# Display results
friedman_result## $statistics
## Chisq Df p.chisq F DFerror p.F t.value LSD
## 93.26 3 0 63.43486 177 0 1.973457 19.53736
##
## $parameters
## test name.t ntr alpha
## Friedman Tratamiento 4 0.05
##
## $means
## Valor rankSum std r Min Max Q25 Q50 Q75
## 0:100 2.200000 132 0.6587096 60 1 4 2 2 2
## 25:75 3.233333 194 0.8102451 60 1 4 3 3 4
## 50:50 3.250000 195 0.7945791 60 1 4 3 3 4
## 75:25 1.316667 79 0.8535403 60 1 4 1 1 1
##
## $comparison
## NULL
##
## $groups
## Sum of ranks groups
## 50:50 195 a
## 25:75 194 a
## 0:100 132 b
## 75:25 79 c
##
## attr(,"class")
## [1] "group"The Friedman test checks whether the medians of the rankings assigned to the treatments differ significantly. If the p-value is less than the significance level (usually 0.05), the null hypothesis that all treatments are equally preferred is rejected.
If the Friedman test indicates significant differences, a multiple comparison of average ranks is performed to identify which treatments differ from each other.
Based on the results, it is possible to draw conclusions about which treatment(s) were significantly preferred by the judges. This information is essential to guide reformulation, product selection, or acceptance decisions during product development.