Statistics Used

Database

Excel spreadsheets exist for High Park and Cranberry Marsh for all years from 1994 and for Iroquois Shoreline from 2007. All spreadsheet data has been entered into an Access database.

Birds per Hour

The number of birds seen is divided by the number of hours spent observing so that the resulting counts are expressed in “birds per hour”. For example, if there were 1,000 birds seen over a period of 250 hours of observing time then the value for the number of birds seen would be calculated as 1,000/250 = 4 birds per hour.

The birds-per-hour measure is used for all graphs that compare counts from different years under differing weather conditions.

Observing Day

The average number of observing hours per day over the life of the survey is 5.54. Consequently we have chosen 6 hours as the standard ’observing day’. Raw values from a year expressed in terms of hours are divided by 6 to give a value expressed in terms of days which can then be combined and compare with similar data from other years.

Birds per Day
During Peak

The peak date interval for the particular bird is calculated as the average dates for the entire study during which 90% of the birds are seen. (These are the date ranges given in the Migration at a Glance table.) An “observing day” is defined as 6 hours. The number of hours during the time period is divided by 6 to give the number of observing days during the period. The count of birds during the date range is divided by the number of observing days to give “birds per day during peak”. For example, suppose 90% of Turkey Vultures pass over High Park between September 26 and October 23 on average over the lifetime of the project. Suppose that in a given year 2,252 birds pass over and there are 276 hours of observing time during the peak date range. There are 276 / 6 = 46 days during that time. The value for the number of birds seen per day is calculated as 2,252 / 46 = 49 birds per day during peak.

Birds per Day During Peak is used for all Migration Size graphs.

Chi Square Test

The Chi Square test is used to help in deciding whether a trend line on a Migration Size graph is significant.

The test uses the null hypothesis that the “observed numbers for this bird are not changing over time”. The average number of this bird counted across the years is used as the expected value for each year. Observed values for each year are subtracted from this expected value and the difference squared. The resulting values are added up across all years. The result is observed Chi Square.

Expected Chi Square is a table look up using degrees of freedom equal to one less than the number of years of observing and a confidence interval of 0.01 (which gives us a one-tailed, 99% degree of confidence test). If expected Chi Square is less than observed, we reject the null hypothesis and conclude that the observed numbers are significantly changing over the years. The appearance of the graph tells whether the change is up or down.