Bio 100- Name:

Lab 2 graphs and graphing- Data analysis For credit in lab today complete this handout and graph the temperature data in Part A page 21 of the lab manual (use the graph paper in the back of the lab manual for the temperature data.

The results of an experiment are always summarized when presented within a formal report. The raw data is not presented. There are several methods for representing data in an organized presentation and the graphs and graphing lab describes some of these methods. This additional exercise will illustrate how to record, analyze, and summarize data for an experiment with results similar to the experiment that will be used for the lab report.

The following is an introduction to and description of the experimental set-up that produced the data in Table 1:

The sediment content of a freshwater stream can be affected by the amount of rainwater run off that enters a stream (Anderson 1996). Fresh water invertebrates require a moderate stream flow rate. The moderate stream flow reduces the amount of sediment in the water within areas of a stream. The reproductive rates of invertebrates have been observed to significantly decline after more than 3 centimeters of rain fall if the stream receives direct soil run-off (Brown 1994). The reproduction rate of freshwater stream invertebrates is reduced within stream sections with higher than average sediment levels (Brown 1995). Freshwater streams will vary in their average sedimentation levels, therefore each stream has to be sampled to determine if any portion of the stream has higher than normal levels. Several stream bank features can have an effect on the amount of sediment run-off into the stream. One indication that the slope of a stream bank could affect the sedimentations levels, is the observations of a significant increase in sedimentation after moderate rainfalls (Anderson 1996). Rainfall can cause soil erosion and hillsides with increased slope angles experience more erosion (Smith and Anderson 1993). Therefore, I hypothesize that the amount of sedimentation within a stream is positively related to the slope angle of the stream bank.

To test this hypothesis five-meter troughs with moderate water flows were exposed to five different bank slope angles. Once treated with a moderate water runoff the amount of sedimentation for each treatment was compared using a chi-square significance test. If the slope angle of the side bank does have an effect on the sedimentation levels of a stream the sedimentation levels should be significantly different from the average sedimentation score of the stream. If the slope angle did not have an effect then there should be no significant difference between the observed sedimentation levels and the average stream sediment level.

The data in Table 1 was collected by the following method.

Six samples water were taken from different sloped bank treatments (0%, 5%, 10%, 15%, & 20%. The solutions were compared to set of standard solutions to score the amount of sediment on a scale from 0- 8; 8 as the highest concentration of sediment.

What was the Hypothesis of this experiment ?

Identify the Independent Variable:

(the variable manipulated in the experiment)

Dependent Variable:

(method of measuring the effect of the independent variable)

Table 1. The class raw data scores of sediment samples collected from different treatments to the slope of a stream bank. n = 6.

Table group(samples)	0% slope score	5% slope score	10% slope score	15% slope score	20% slope score
1	2	1	4	5	3
2	3	3	6	3	5
3	0	2	3	2	3
4	1	4	7	7	9
5	2	0	2	4	8
6	2	2	5	5	5

Statistical Significance

The results section contains a statistical analysis of the experimental data. For the lab project this quarter the appropriate statistical test necessary to compare the treatments is a Chi-Square test.

A significance test is performed to determine if an observed value of a sample differs enough from a hypothesized value of a parameter to draw the inference that the hypothesized value of the parameter is not the true value. A significance test consists of calculating the probability of obtaining a statistic as different or significantly different from the predicted value. If this probability is sufficiently low, then the difference between the parameter and the statistic is said to be "statistically significant."

Just how low is sufficiently low? The choice is somewhat arbitrary but by convention the level of .05 is most commonly used.

To test whether observed sedimentation scores are significantly deviated from the stream average sedimentation score of 2, we have to calculate the chi-square values and the total chi-square value. The first step in calculating the chi-square values is to record the number of samples for each category in Table 2.

Table 2. The chi-square observed values. Total the number of samples that exceed the average stream sedimentation score and the total number of samples that were equal to or less than the mean stream sedimentation score.

Treatment	number of samples with sedimentation scores equal to or less than the mean of 2.	number of samples with sedimentation scores greater than the mean of 2.	row totals
0% slope
5% slope
10% slope
15% slope
20% slope
column totals			sum of column totals = total of table cells

The χ² test

The χ² (or chi² – pronounced kai-squared) test is very useful when dealing with categorical data. Categorical data are usually counts of occurrences in different, mutually exclusive categories. For example, either greater than 2 or equal to and less than 2. Table 2 is simply the number of samples with values greater than 2 and number of samples equal to or less than 2. Thus these are categorical data, and a χ² test is appropriate. This test uses the observed numbers and the numbers expected if the results were random to calculate the probability that the observed results could have occurred by chance. To set it up we need to calculate some simple information.

Using the numbers in the data table (table 2) you need to calculate:

The Expected Ratios. This is the sum of the column the cell is in divided by the sum of all cells in the table. Calculate this for each cell in table 3.

Table 3: Expected ratios (calculated from sample values in table 2)

Treatment	expected ratio of samples with sedimentation scores equal to or less than the mean of 2.	expected ratio of samples with sedimentation scores greater than the mean of 2.
0% slope
5% slope
10% slope
15% slope
20% slope

The Expected Number. This is the sum of the rows in table 2 multiplied by the expected ratio. Calculate this number for each cell in table 2 and record in table 4

Table 4: Expected values for calculating the Chi-square value.

Treatment	expected numbers of samples with sedimentation scores equal to or less than the mean of 2.	expected numbers of samples with sedimentation scores greater than the mean of 2.
0% slope
5% slope
10% slope
15% slope
20% slope

Next, take the observed number from table2 and subtract the expected value (table 4) from it.

Do it for each cell in table 5.

Table 5: (Observed-Expected) ² divided by the Expected value

(O – E )² / E record each value in the corresponding cell.

Treatment	(O – E )2 / E of samples with sedimentation scores equal to or less than the mean of 2.	(O – E )2 / E of samples with sedimentation scores greater than the mean of 2.
0% slope
5% slope
10% slope
15% slope
20% slope
column totals

Take all of the numbers from this last calculation and add them together. This is the χ² statistic.

Calculate the degrees of freedom = (# of rows – 1)* (# of columns – 1).

Sum the column totals for the total Chi-Square value = ___________________

How many degrees of freedom are there for this Chi-Square test? ______________________

What is the Chi-Square critical value? ___________________________________

Is the total chi-square (sum of all chi-square values) greater or lesser than the critical value? _________

Are the observed sedimentation scores due to a random chance pattern? (is the total chi-square value less than the critical value?

Critical values for the Chi Square Distribution

 Significance Level
 df  0.10   0.05  0.025  0.01   0.005
 
 1  2.705   3.841  5.023  6.634  7.879
 2  4.605  5.9915  7.377   9.210  10.59
 3  6.251  7.8147  9.348  11.34  12.83
 4  7.779  9.4877  11.14  13.27  14.86
 5  9.236  11.070  12.83  15.08  16.74
 6  10.64  12.591  14.44  16.81  18.54

Read the graph descriptions in your lab manual starting on page 21 for the graphing lab. Choose the graph that should be used to correctly represent the data in Table 1. Use the space below to graph the data in Table 1 (remember you can not graph the raw data so you will also summarize the data in Table 1 prior to graphing the information). Be sure to label the independent variable (x – axis) and dependent variable (y – axis)