# Y-Scale type

## Y-scale type for histograms

To specify the y-scale type when you create the graph, click Scale, then select the type on the Y-Scale Type tab. To change the y-scale type on an existing graph, double-click the y-scale, then specify the type on the Type tab.

Frequency
The height of each bar represents the number of observations that fall within the bin.
Percent
The height of each bar represents the percentage of the sample observations that fall within the bin. A histogram with a percentage scale is sometimes called a relative frequency histogram. Use a percent scale to compare samples of different sizes.
Density
The area of each bar represents the proportion of the sample observations that fall within the bin (proportion = bar area = bin width × bar height).

Accumulate values across bins: (Frequency and percent scales only) The bar heights accumulate from left to right. The height of each bar is equal the height of the bin plus all the previous bins.

## Y-scale type for probability plots and empirical CDF plots

To specify the y-scale type when you create the graph, click Scale, then select the type on the Y-Scale Type tab. To change the y-scale type on an existing probability plot or empirical CDF plot, double-click the y-scale, then specify the type on the Type tab.

Percent

Values on the y-axis represent estimated cumulative percentages. The estimated cumulative percentage is equal to the estimated cumulative probability multiplied by 100.

Probability

Values on the y-axis represent estimated cumulative probabilities. The cumulative probability for a value x is the probability that a random observation that is taken from the population will be less than or equal to x.

Minitab uses the median rank method (also called the Benard method) to estimate the cumulative probability (r) for each observation:

In this formula, i is the rank of the observation in the sample and n is the total number of observations in the sample. For the smallest value in the sample, i = 1 and for the largest value in the sample, i = n.

Score (Probability plot only)

Values on the y-axis represent inverse cumulative probabilities.

The score values for the normal distribution and the lognormal distribution are the inverse cumulative probability of r, calculated using the standard normal distribution.

The score values for the exponential distribution and the Weibull distribution are calculated as LN(−LN(1−r)), where LN is the natural log function.

## Y-scale type for dendrograms

To specify the y-scale type when you perform a cluster analysis, select Show dendrogram, then click Customize. To change the y-scale type on an existing dendrogram, double-click the y-scale, then click the Type tab.

Similarity (default)
The height of each cluster represents the similarity. The similarity, s(ij), between two clusters i and j is given by s(ij) = 100 (1- d(ij) / d(max). If you entered the original distance matrix D for the analysis, then d(max) is the maximum value in D. If D was calculated from data, then d(max) = 2 if you selected correlation as the distance measure and 1 if you selected absolute correlation as the distance measure.
Distance
The height of each cluster represents the distance.
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