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Here we give an answer to the question "How good an estimate of errorv(h) is provided by errors(h) ' for the case in which h is a discrete-valued hypothesis More specifically, suppose we wish to estimate the true error for some discretevalued hypothesis h, based on its observed sample error over a sample S, where

the sample S contains n examples drawn independent of one another, and independent of h, according to the probability distribution V nz30 hypothesis h commits r errors over these n examples (ie, errors(h) = rln)

American Philosophical Society 104 South Fifth Street Philadelphia, PA 19106-3387 Tel: (213) 440-3434 Fax: (215) 440-3436 Internet: wwwamphilsocorg American Institute of Physics 1 Physics Ellipse College Park, MD 20740-3843 Tel: (301) 209-3100 Fax: (301) 209-0840 E-mail: aipinfo@aiporg American Political Science Association 1527 New Hampshire Avenue NW Washington, DC 20036 Tel: (202) 483-2512 Fax: (202) 483-2657

Listing 3 4. Modifying the sayHello: method in HelloController.m #import "HelloController.h" @implementation HelloController -(IBAction)sayHello:(id)sender { //[destinationTextField setStringValue:@"Hello, World!"]; [destinationTextField setStringValue:[sourceTextField stringValue]]; } @end

Under these conditions, statistical theory allows us to make the following assertions:

1 Given no other information, the most probable value of errorD(h)is errors(h) 2 With approximately 95% probability, the true error errorv(h) lies in the

The original line is also included but commented out so that you can compare them directly. This code is saying Set the stringValue property in the destination text field to the text that you get from asking the source text field for its stringValue property. Those are the only code changes you need. Save the .h and .m files and open Interface Builder (double-click MainMenu.xib). Add a Text Field from the Library, rightclick on the HelloController to bring up the HUD, and connect the new sourceTextField outlet to the new Text Field (see Figure 3 18).

errors(h)(l - errors ( h ) )

To illustrate, suppose the data sample S contains n = 40 examples and that hypothesis h commits r = 12 errors over this data In this case, the sample error errors(h) = 12/40 = 30 Given no other information, the best estimate of the true error errorD(h) is the observed sample error 30 However, we do not expect this to be a perfect estimate of the true error If we were to collect a second sample S' containing 40 new randomly drawn examples, we might expect the sample error errors,(h) to vary slightly from the sample error errors(h) We expect a difference due to the random differences in the makeup of S and S' In fact, if we repeated this experiment over and over, each time drawing a new sample S, containing 40 new examples, we would find that for approximately 95% of these experiments, the calculated interval would contain the true error For this reason, we call this interval the 95% confidence interval estimate for errorv(h) In the current example, where r = 12 and n = 40, the 95% confidence interval is, according to the above expression, 030 f (196 - 07) = 030 f 14

If you don t see a sourceTextField outlet in the HUD, you didn t save your HelloController.h file! You may be slightly confused by what you just did. You have a Text Field that supplies data to the Controller, and yet the connection you just made was the other way around from the Controller to the Text Field. Why didn t the connection go from Text Field to Controller as it did when you wired up the button The answer is that the button needed to communicate an action (the user clicking on it) to the Controller, whereas the Text Field is just passively providing its data when the Controller asks for it. The Controller really is in charge of the communications. Save the NIB, quit Interface Builder, and return to Xcode. Build and Run, and this time you should be able to add a message using the Text Field, click the button, and see the message appear in the label (see Figure 3 19).

ConfidencelevelN%: Constant ZN:

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