**Interpretation**

The points plotted in a Q–Q plot are always non-decreasing when viewed from left to right. If the two distributions being compared are identical, the Q–Q plot follows the 45° line *y* = *x*. If the two distributions agree after linearly transforming the values in one of the distributions, then the Q–Q plot follows some line, but not necessarily the line *y* = *x*. If the general trend of the Q–Q plot is flatter than the line *y* = *x*, the distribution plotted on the horizontal axis is more dispersed than the distribution plotted on the vertical axis. Conversely, if the general trend of the Q–Q plot is steeper than the line *y* = *x*, the distribution plotted on the vertical axis is more dispersed than the distribution plotted on the horizontal axis. Q–Q plots are often arced, or "S" shaped, indicating that one of the distributions is more skewed than the other, or that one of the distributions has heavier tails than the other.

Although a Q–Q plot is based on quantiles, in a standard Q–Q plot it is not possible to determine which point in the Q–Q plot determines a given quantile. For example, it is not possible to determine the median of either of the two distributions being compared by inspecting the Q–Q plot. Some Q–Q plots indicate the deciles to make determinations such as this possible.

The slope and position of a linear regression between the quantiles gives a measure of the relative location and relative scale of the samples. If the median of the distribution plotted on the horizontal axis is 0, the intercept of a regression line is a measure of location, and the slope is a measure of scale. The distance between medians is another measure of relative location reflected in a Q–Q plot. The "probability plot correlation coefficient" is the correlation coefficient between the paired sample quantiles. The closer the correlation coefficient is to one, the closer the distributions are to being shifted, scaled versions of each other. For distributions with a single shape parameter, the probability plot correlation coefficient plot (PPCC plot) provides a method for estimating the shape parameter – one simply computes the correlation coefficient for different values of the shape parameter, and uses the one with the best fit, just as if one were comparing distributions of different types.

Another common use of Q–Q plots is to compare the distribution of a sample to a theoretical distribution, such as the standard normal distribution *N*(0,1), as in a normal probability plot. As in the case when comparing two samples of data, one orders the data (formally, computes the order statistics), then plots them against certain quantiles of the theoretical distribution.

Read more about this topic: Q-Q Plot

### Other articles related to "interpretation, interpretations":

**Interpretation**s

... An

**interpretation**of a formal system is the assignment of meanings to the symbols, and truth values to the sentences of a formal system ... The study of

**interpretations**is called formal semantics ... Giving an

**interpretation**is synonymous with constructing a model ...

**Interpretation**: Claimants To The "One Mighty and Strong"

... nineteenth century, a number of individuals have proposed a third

**interpretation**of the prophecy that Smith predicted the coming of "One Mighty and Strong", and that such a person has been identified ... This

**interpretation**assumes a much broader role of the One Mighty and Strong, extending throughout the church and beyond the confines of Jackson County, Missouri ...

**Interpretation**

... Heritage

**interpretation**is the communication of information about, or the explanation of, the nature, origin, and purpose of historical, natural, or cultural resources, objects, sites and ... Heritage

**interpretation**may be performed at dedicated

**interpretation**centres or at museums, historic sites, parks, art galleries, nature centres, zoos, aquaria, botanical gardens ... The thematic approach to heritage

**interpretation**advocated by University of Idaho professor Sam Ham, the National Association for

**Interpretation**, the ...

**Interpretation**- "Tilden's Principles" of

**Interpretation**

... In his 1957 book, "Interpreting Our Heritage", Freeman Tilden defined six principles of

**interpretation**... Any

**interpretation**that does not somehow relate what is being displayed or described to something within the personality or experience of the visitor will be sterile ... Information, as such, is not

**Interpretation**...

... issues that fall into two broad disciplines statutory

**interpretation**and Constitutional law ... Statutory

**interpretation**is the process of interpreting and applying legislation to the facts of a given case ... Constitutional law is the body of law that governs the

**interpretation**of the United States Constitution and covers areas of law such as the relationship between ...