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o Near the bottom, use the pull-down menu and select “Excel Add-Ins” and click ... Using one-way ANOVA in MS Excel ... Add standard error bars to the graph.
Typology: Lecture notes
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o o Select the “ Analysis ToolPak ” and click “ OK ”.
Introduction : When your observations fall into two or more categories of continuous or even discrete variables, you may be interested in asking if the groups differ from each other. Is fish diversity higher in phosphorus-enriched ponds than in low-phosphorus ponds? Does the abundance of forest-floor plants differ between clear-cut, tornado-damaged, and control plots of forest? Questions of this nature are answered using analysis of variance (ANOVA). It is worth mentioning that in the case of 2 categories you can run a t test or an ANOVA and the result will be the same.
Analysis :
SUMMARY Groups Count Sum Average Variance island 6 16 2.666667 1. mainland 6 28 4.666667 0. peninsula 6 17 2.833333 0.
ANOVA rce of Varia SS df MS F P-value F crit Between G 14.77778 2 7.388889 7.150538 0.006593 3. Within Gro 15.5 15 1.
Total 30.27778 17
Number of mammal species island mainland peninsula 2 5 3 3 4 2 3 6 4 5 5 3 1 4 3 2 4 2
Table 1. Fake data for ANOVA
Does blood pressure increase with age? Does shrub cover decrease with increasing canopy cover? Is there a relationship between phosphorus concentration and algal cell density in ponds? All of these questions can be addressed using regression.
Nature of the data All of the datasets described above are continuous ; that is to say, they vary over some range without breaks. They are not categorical (like male and female), that are not discrete (like number of people in a single car; you would not typically think about 3.5 people in a car). As the range of a discrete variable increases (number of plants per hectare for example), the larger number means that what in fact is a discrete variable can be treated as continuous.
Graphing We typically graph such datasets using a scatter plot (Figure 1). If we have a basis for considering for example that running speed impacts heart rate, then we would use running speed on the horizontal ( x ) axis, and heart rate on the vertical ( y ). In this case running speed is the independent variable. The dependent , or response variable is heart rate because we expect it to depend on, or respond to running speed. Figure 1. Fictional data representing the effects of running speed on heart rate.
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0 2 4 6 8 10 12 14 16 Running Speed (mph)
Heart rate (bpm)
Analysis: We might look at the pattern on the right and perceive a pattern, or not! As is the case with all statistics, the point is to remove subjectivity and have firm criteria for claiming a relationship. The analysis one would use for this sort of question is regression. There are many forms of regression for relationships of different shapes, but for our purposes we are considering only linear regression. In other words we are asking only if, and how well a straight line can describe the relationship between variables. In excel under the Data tab, select data analysis, regression to bring up this window: The response variable goes in the Input Y Range and the independent variable goes in the Input X range. You can click on the tiny red arrow in each case and highlight the appropriate portion of the data (including labels). The output range simply is a place for the statistical output to go.
Output: Output from the preceding data set:
The number under Significance F is the p value. In this case the p value is greater than 0.05 and we can conclude that there is no relationship between running speed and heart rate.
SUMMARY OUTPUT
Regression Statistics Multiple R 0. R Square 0. Adjusted R -0. Standard E 33. Observatio 15
ANOVA df SS MS F ignificance F Regression 1 425.0892857 425.0893 0.384931 0. Residual 13 14356.24405 1104. Total 14 14781.
Coefficients Standard Error t Stat P-value Lower 95%Upper 95%ower 95.0%Upper 95.0% Intercept 130.5238095 18.05655676 7.22861 6.66E-06 91.51499 169.5326 91.51499 169. Running S -1.232142857 1.985956467 -0.62043 0.545699 -5.52254 3.058255 -5.52254 3.
All graphs, maps, photographs, and sketches are considered “Figures” and appear in a numbered sequence in the order cited in your paper. Any set of numbers and/or letters is considered a table and tables have their own numbered sequence (IE, even after three figures, your first table is still Table 1 ).
A good graph minimizes clutter and unnecessary ‘ink’. Use the MS Excel “Scatter Plot” option to make graphs displaying continuous data on the vertical and horizontal axis. The species area data for the upcoming lab report are a good example; area on the X axis; number of species on the Y axis. Remove all of the following items added by Microsoft excel: “Series 1”; background color; frames on right and top; grid lines; 3D effects.
Figure 1. Illustrating the point that more sampling leads to more species observed. Connor & Simberloff (1978) analyzed data from collecting trips to the Galapagos Islands and found that number of collecting trips better explained number of species recorded than did island area, elevation, or isolation. Data extracted from Table 3 in Connor & Simberloff (1978).
The figure legend is always placed underneath and contains roughly a paragraph of information describing the figure content in sufficient detail that the figure stands alone. The
legend inserted by MS excel is useful only if two or more data sets are displayed on one graph using symbols. This figure contains data that span the nearly entire range presented. If we were presenting data from only the largest five islands we would adjust the horizontal axis to run from 20 to 40, and the vertical axis from 150 to 450. Note that the axis lines have been thickened and fonts enlarged beyond the default. Important : Graphs should not start at zero, zero if the data range fall between 75 and 85 (for example).
We use bar graphs when presenting the averages of continuous variables (on the We use bar graphs when presenting the averages of continuous variables (on the Y axis) from one or more categories on the horizontal axis.
The bar height equals the average of the response variables for treatments 1, and treatments 2. The error bars above and below the average in this case equal standard error; calculate these values as: (standard deviation)/(square root of the number of samples). The scale is appropriate to the data; if the averages were 150 and 200, I might start the axis at 100 rather than zero. Important: You should replace the numbers on the horizontal axis with names of sites or treatments (see example under adding error bars handout).
How to add the error bars to your bar graph : Lay your data out as illustrated below. In this case the fake data represent the average number of insect species found several samples taken from each of three locations in a stream.
Note:
for the standard errors that are lined up under the averages. Hit “ Enter ”!
