# Boxplots

We provide boxplots to summarize the distributions of species occurrence along the major topographic gradients of elevation and slope. For each gradient, we divided data into north-facing or south-facing occurrences for comparison of different aspects. Occurrence data come from Denali’s plant and soil inventories and landscape scale vegetation monitoring program (which includes over 85,000 plant occurrences at 5,900 sites!).

NOTE: In graphs where we present information about aspects (such as north-facing and south-facing slopes, we have not included occurrences in flat sites (where the slope angle was < 5˚) because flat locations don’t have an aspect – they are flat. For example, in boxplots shown in the Interpreting the Boxplots section below, we omit 28 occurrences of Boschniakia rossica because sites where located were flat or gently sloping.

## Parts of a Boxplot

Median: The median represents the middle of the data values – 50% of the values are above the median and 50% of the values are below. For example, with the dataset of values 1, 2, 3, 4, 5, 6, 7, 8, 9, the value of 5 is the median because 1 – 4 are below it and 6 – 9 are above. Note that with this dataset, the average (or mean) value would also be 5, but with most environmental data, the average very rarely equals the median.

Range: The box represents the range of the middle 50% of values. Using the example dataset above, the box would extend across the values 3 through 7, because 5 of the observations (or about 50% of them) are contained in that range (3, 4, 5, 6, 7). The half-box above the median (the 75% quartile) represents 25% of the values above the median, while the lower half-box (the 25% quartile) represents 25% of the values below the median.

Whiskers: The whiskers represent the approximate location of the 10th and 90th percentile values in the dataset. Any points beyond the whiskers represent outlier values. Outliers have a specific statistical definition (outside 1.5 times the interquartile range), but can be interpreted as species occurrences at sites that are highly unusual for that species.

## Interpreting the Boxplots

As an example, let’s interpret the boxplots provided for northern groundcone (Boschniakia rossica).

## Looking first at the boxplot set showing the distribution of B. rossica’s elevational occurrence, we see that this species reaches higher median and maximum elevations on warmer (south-facing) slopes than on colder (north-facing) ones. Note also that the boxplots indicate the number of B. rossica occurrences recorded on north- and south-facing slopes; in this case 16 and 20 respectively (n = number of occurrences). So for occurrences on north-facing slopes, the median elevation was 520m, thus there were ~ 8 occurrences both above and below this elevation. By comparing the box and whisker span of the two boxplots in this set, we see that this species was generally found at lower elevations on north-facing slopes because the median of the south-facing slope occurrences is around 650m. Also note that the overall range of elevations where B. rossica occurred was greater on south-facing slopes as compared to north-facing ones and that both its highest and lowest elevation occurrence were on south-facing slopes.

Looking next to the boxplot set showing the distribution of B. rossica’s slope angle occurrence, note first that we measure the inclination of a plot or occurrence site in degrees so that a vertical cliff would have a slope of 90˚. These boxplots show that B. rossica was typically found growing on slightly steeper locations on south-facing slopes (median of 18˚ on south-facing slopes vs. a median of 16˚ on north-facing slopes). We can also see an unusual (outlier) occurrence of this species growing on a 36˚ south-facing slope. Occurrences of B. rossica on south-facing slopes had a greater range of slope angles overall than locations on north-facing slopes, but the middle 50% of occurrences (the box) exhibited a wider range on north-facing slopes.

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