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Techniques for presenting data may vary depending on the technical background of the target audience.

*The Importance of Credible Data*

Lake monitoring programs must ensure that data released to the public are absolutely accurate. Misinformation can occur when data are too hastily or sloppily collected, stored, analyzed, or presented. When this happens, the credibility and hence, the utility of the monitoring program is thrown into question.

To ensure that collected data are credible and defensible, program managers must carefully plan and maintain a quality assurance

program. Approved data collection methods must be established and followed;
data must be stored and documented according to specific quality assurance
protocols; incoming data must be constantly reviewed; and staff time should
be committed in advance to c onduct concise, clear, accurate analyses and
presentations of data.

*Presenting the Data*

Some citizen monitoring programs issue annual reports at the end of the sampling season. Others rely on regularly-issued newsletters or bulletins. Whatever the format, it is always important to keep in mind the interest, background, and level of technical understanding of the target audience.

Three rules apply when presenting data.

It is not enough to simply list the data when preparing a summary report. Instead, the author of the report should use an appropriate combination of graphs, summary statistics, maps, and narra tive interpretation. Some common options for pr esenting the data are discussed below.

*Graphs*

Choosing a graphic format that will best transfer information about the monitoring data requires careful thought. Three basic types of graphs are often used to present monitoring information:

The bar graph uses column bars of varying lengths to compare data. This graph places special emphasis on individual values in the data set rather than overall trends.

The pie graph compares parts to the whole. In a pie graph, each value in the data set is represented by a wedge in a circular pie. The pie as a whole equals 100 percent of the total values in the data set. The size of any individual wedge, therefore, corresponds to the percentage that the value represents to the total.

The line graph effectively shows changes (or trends) over a period of time or space. Unlike bar graphs, it does not place emphasis on the individual values in the data set.

Listed below are some basic rules when creating graphs.

*Summary Statistics*

Summary statistics are useful for conveying information about a data set. These statistics should succinctly, yet efficiently, transfer facts about the measured variable.

Textbook statistics assume that if a parameter is measured a large number of times under a common universe of circumstances, the measurement values will be distributed at random around an average value. If the relative frequency of these values are plotte d against value magnitude, the result will be the familiar Gaussian (normal or bell-shaped) curve. The specific shape of this curve is defined by two statistics, the mean (or average) of the data set values and the standard deviation.

The mean is a statistic that describes the central tendency of the data set. Standard deviation describes the variability or spread of the data around the mean. Traditionally, the mean and standard deviation are the statistics used to summarize a set of l ake data.

In practical application, however, the mean and standard deviation are not always the appropriate summary statistics to use because lake data do not usually follow textbook patterns of normal distribution around an average value. Instead, the data are fre quently skewed in one direction or the other.

This skewness occurs because there are many important factors that influence lake conditions, including the changing seasons, weather condi tions, and activity in the lake and watershed. As a result, the parameters used to describe lake conditions are con stantly in a state of flux.

Thus, skewness can usually be expected, especially when measuring the
parameters that characterize an algal condition (Secchi disk transpar ency,
chlorophyll *a*, and total phosphorus concentration). Chlorophyll
*a*
concentration, for example, m ay go through several cycles each year. It
may be low in the spring, high during a mid-summer algae bloom, and low
again in the fall.

*Robust Statistics*

Whenever there is an irregular or uncertain pattern of data values for a lake parameter, robust summary statistics should be used. A robust statistic conveys information under a variety of conditions. It is not overly influenced by data values at the extr emes of the data distribution.

*Median *and *interquartile range* are robust statistics that
describe central tendency and spread around the median, respectively. Both
these summary statistics are unaffected by extreme points. Consequently,
they are usually more appropriate f or summarizing lake data than the traditional
mean and standard devia tions.

Both the median and interquartile ranges are based on order statistics. They are derived by ordering data values from high to low. The median is simply the middle value of the data set. The interquartile range is the difference between the value at the 75 percent level and the value at the 25 percent level.

*The Box Plot*

The box plot is a convenient method of presenting lake data based on the robust order statistics. In one simple graphic, the box plot can provide information on:

A box plot is constructed using the following steps:

1. Order the data from lowest to highest.

2. Plot the lowest and highest values on the graph as short horizontal lines. These are the extreme values of the data set and repre sent the data range.

3. Determine the 75 percent value and 25 percent value of the data set. These values define the interquartile range and are represented by the location of the top and bottom lines of the box.

4. The horizontal length of the lines that define the top and bottom lines of the box (the box width) can be used as a relative indica tion of the size of the data set. For example, the box width that describes a lake data set of 20 values can be displayed twice as wide as a lake with a data set of 10 values. Alternatively, the width may be set as proportional to the square root of the sample size. Any proportional scheme can be used as long as it is consistently applied.

5. Close the box by drawing vertical lines that connect to the ends of the horizontal lines.

6. Plot the median as a dashed line in the box.

Klettbach Lake was sampled on the 1st and 15th of the month from May 15 to October 15. The lake depth at the sampling station was 30 feet. At one sampling site over the deepest part of the lake, personnel:

Secchi disk transparency is a parameter that interests. Data are easily understandable and can be presented by a modified bar graph. The horizontal axis presents the sampling dates and the vertical axis represents the lake's water column. Minia ture Secchi disks extend down from the surface to the actual Secchi disk reading.

General trends in Secchi disk measurements can be noted in this data presentation, but the graphic emphasis is on the individual reading on each sampling date.

*Chlorophyll a*

Chlorophyll *a* is usually best presented in a traditional bar
graph. By examining this data presentation, personnel can observe when
chlorophyll *a* concentrations were high and low during the sampling
season.

The horizontal axis presents the sampling dates. The vertical axis is
a scale of chlorophyll *a* values. Like the Secchi disk graph, general
trends can be noted, but the graphic emphasis is on the chlorophyll *a*
concentration on each sampling d ate.

**Total Phosphorus**

The total phosphorus graph displays the surface and bottom data together. By examining this double bar graph, personnell can observe when phosphorus concentrations were high and low in each zone. In addition, they can compare surface and bottom concentrat ions on each sampling date.

The horizontal axis presents the sampling dates. The vertical axis is a scale of total phosphorus values. As with the other bar graphs, general trends in measurements can be noted, but the graphic emphasis is on phos phorus concentrations measured on each sampling date.

*Data Interpretation*

In addition to displaying graphs, box plots, and summary statistics, the report author must provide interpretation of what the data presentations mean. The interpretation process begins with a data analysis by an experienced limnologist. The report author then has the critical job of putting technical analysis into terms that can be understood by personnell. Toward this end, data interpretation is often best presented in the context of an explanation of how the lake functions during a seasonal cycle.

Although time-consuming, a thoughtful explanation by the report author rewards personnell with greater insight and understanding of their lake.

Examples of observations and reasonable conclusions based on the data from Klettbach Lake may include the following:

and relatively low in the summer. Phosphorus concentrations near the lake bottom were generally moderate in May, June, and October. Concentrations increased during the summer, reaching a maximum on September 1.

*The reduction of water transparency on June 15 may be due to algae,
but it may also be due to increased water turbidity from a spring rain.
A check of the field data sheet can often explain sudden variations in
data magnitude.*

**Trophic State**

Secchi disk transparency, chlorophyll* a*, and total phosphorus
are often used to define the degree of eutrophication, or trophic status
of a lake. The concept of trophic status is based on the fact that changes
in nutrient levels (measured by total phosphorus) causes changes in algal
biomass (measured by chlorophyll* a*) which in turn causes changes
in lake clarity (measured by Secchi disk transparency).

A trophic state index is a convenient way to quantify this relationship. One popular index was developed by Dr. Robert Carlson of Kent State University. His index uses a log transformation of Secchi disk values as a measure of algal biomass on a scale fro m 0 - 110.

Each increase of ten units on the scale represents a doubling of algal
biomass. Because chlorophyll *a* and total phosphorus are usually
closely correlated to Secchi disk measurements, these parameters can also
be assigned trophic state index values.

The Carlson trophic state index is useful for comparing lakes within a region and for assessing changes in trophic status over time. Thus it is often valuable to include an analysis of trophic state index values in summary reports of a monitoring program.

The program manager must be aware, however, that the Carlson trophic state index was developed for use with lakes that have few rooted aquatic plants and little non-algal turbidity. Use of the index with lakes that do not have these characteristics is not appropriate.

TSI = 60 - 14.41 ln Secchi disk (meters)

TSI = 9.81 ln Chlorophyll *a* (µg/L) + 30.6

TSI = 14.42 ln Total phosphorus (µg/L) + 4.15

*where:*

TSI = Carlson trophic state index

ln = natural logarithm

The formulas for calculating the Carlson trophic state index values
for Secchi disk, chlorophyll* a*, and total phosphorus are presented
below. Also presented is a table that lists the trophic state values and
the corre sponding measurements of the t hree parameters. Ranges of trophic
state index values are often grouped into trophic state classifications.
The range between 40 and 50 is usually associated with mesotrophy (moderate
productivity). Index values greater than 50 are associated with eutrophy
(high productivity). Values less than 40 are associated with oligotrophy
(low productivity).

Presented below are Carlson trophic state index values for Volun teer Lake. Summer averages (June 15 - September 1) are used in the calcula tions. As seen from the TSI values, Klettbach Lake can be classified somewhere near the border of mesotrophy and eu trophy.

Secchi Disk

Average Summer Secchi disk = 5.9 feet = 1.8 meters

TSI = 60 - 14.41 (ln Secchi disk (meters))

TSI = 60 - (14.41) (0.59)

TSI = 51.5

Total Phosphorus

Average Summer Surface Total Phosphorus = 19.6 µg/L

TSI = 14.42 (ln Total phosphorus (µg/L)) + 4.15

TSI = (14.42) (2.98) = 4.15

TSI = 47.1

Chlorophyll *a*

Average Summer Chlorophyll *a* = 17.2 µg/L

TSI = (9.81) (ln Chlorophyll *a* (µg/L)) + 30.6

TSI = (9.81) (2.84) + 30.6

TSI = 58.5

Reporting the results of these activities can be relatively straightfor ward. The rough aquatic plant map drawn by personnell can be cleaned -up and reproduced (see below).

Estimates of the percent composition of the different plant types at each transect station are best displayed by using a pie graph. Relative density information can also be incorporated into the graph. Identified plants can be listed along with a sketch a nd a short description.

Temperature and oxygen profiles were measured at one sampling site located
over the deepest part of the lake on April 15 and July 15. Using a temperature/oxygen
meter, personnell recorded readings at five-foot intervals from the surface
to the lake bottom . A data table of the results is presented below.

Results of the temperature and dissolved oxygen measurements (profiles)
can be presented together on the same line graph (page 117). The horizontal
axis displays a range of values that can be read both as dis solved oxygen
units (mg/L) and temperature uni ts (°C). The vertical axis represents
the water column of the lake with the surface at the graph's top and the
lake bottom at the graph's bottom.