In using the Ecostat software, keep each of the Ecostat windows open and tile them on your computer so you can see multiple windows at once.

The Excel file contains the data for lab. Each column is a different data set. In the EXCEL spreadsheet, the data are grouped; that is, you are given the numbers of 0s, 1s, 2s, …  You need to create a text file with the first line being the total number, say n, of observations in the data set.  Then each of the next n lines represents a single observation.  So, if you have 20 zeroes, there will be 20 lines, each with a zero on this.  By using copy and paste in EXCEL, you can create this data file relatively quickly and save it as a text file in a location you know where it is.  

We are going to take one of these data sets and see what distributions best fit this data.  To do this open the Ecostat software. Click Discrete Distributions tab (hint drag the new window so it doesn't sit on top of the old window) then click data. A window will pop open for you to navigate to the data file you saved in the step above. You may need to change the file type from .dat to .txt.  Open your data file.  Your data is now read into Ecostat.  In the window that is showing your data (it should look a bit like a spreadsheet) you will see the names of different distributions across the top of the screen.  Remember we are trying to see what distribution best fits the data we are examining.  So chose one of the distributions to test (for example, geometric). When you click on the distribution Ecostat provides the mean, variance, and parameter estimates for that distribution (different parameters depending on the distribution chosen).  

Now let's check to see if our variance is equal to the mean. To do this click on the variance-mean tab (a new window will pop up) and input your sample size (the number of rows of data), the mean, and the variance. Click the variance to mean tab, and the output will provide a test statistic testing whether the mean is equal to the variance.  

Based on the results of this test we go to the Discrete distributions mass function tab and click on the distribution tab for the distribution that is most appropriate (based on the variance-mean test).  For example, if the geometric is the distribution you want to examine, you will click the geometric tab and then input the Mu value that was provided back on the screen where the mean, variance, and parameter estimates were calculated.  This screen (which looks like a spreadsheet and has a graph) is showing the expected probability for each expected observation and plotting these probabilities.  These are your expected cell probabilities for your data set and the distribution you are examining.  Copy and paste these probabilities to Excel and then multiply these probabilities times the number of data observations to get the expected observations (probability times the data).  For cells where there are less than five observations you will need to sum these probabilities and the data and then multiply them.  Now as shown in class, calculate the chi-square goodness of fit test between the observed and expected cell values. Now repeat the process for another data set.