## WAPP: Web-based Analysis Program for Physics

### How Much Uncertainty ("y error")?

WAPP aims to determine the parameters of a function (e.g., a and b for the linear function y=a+bx) which "best" represents your x-y data pairs. "Best" is defined in terms of how much the calculated y values deviate from the y values you determined experimentally compared to the expected error caused by less-than-perfect measuring instruments ("y error"). (Technically WAPP is based on ordinary least squares with deviation assumed in the y coordinate.) There are several ways you can report this expected "error" in your y-values:
Enter separate y errors for each data point
Enter a single constant y error valid for all data points
Enter a single percentage y error valid for all data points
Assume Poisson statistics so the y error is the square root of the y value

The program will use the y errors you enter only to calculate the reduced chi-squared (which should be "near" 1). The program reports errors in the parameters of the fitted function by stretching or shrinking the y errors you entered until the fitted function goes through most of the error bars (i.e., until the reduced chi-squared is 1). Thus if you have no idea what y error to enter, little harm results by just using the default value of a constant y error of 1. Nevertheless, an important part of any lab is reporting and justifying an estimate of y error. You should demonstrate an ability to recognize and numerically evaluate the less-than-perfect nature of all measuring instruments used. On the other hand, do not be alarmed if your reduced chi-squared is not near 1: this happens frequently in introductory labs. You should be alarmed if you cannot justify your estimate of y error (even if your reduced chi-square is exactly 1).

### How Many Items?

You are about to enter pairs of data so that a function can be fit to the data. How many data pairs do you have? (There is no harm in over estimation: blanks will be ignored. Max=99, Min=3)

Number of data points: