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## Explore anything with the first computational knowledge engine.

The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are statistically significantly different from each other. Specifically, it tests the null hypothesis:

Times default to a 24 hour clock. Use "a" or "p" to indicate "am" or "pm" if you use a 12 hour clock (e.g. "8:30 p" is interpreted as 8:30 PM). To enter the current time, press "control"and ":" (shift-semicolon) at the same time.

## Solve integrals with Wolfram|Alpha.

It is clear that a given joint distribution determines the marginal distributions uniquely. However, the converse is not true; a given marginal distribution can come from many different joint distributions. The function that links the marginal densities and the joint density is called the copula. In practice, one picks the marginal distributions first and then selects an appropriate copula to achieve the right amount of dependency among the individual random variables.

One of the main goals of statistical hypothesis testing is to estimate the P value, which is the probability of obtaining the observed results, or something more extreme, if the null hypothesis were true. If the observed results are unlikely under the null hypothesis, your reject the null hypothesis. Alternatives to this "frequentist" approach to statistics include Bayesian statistics and estimation of effect sizes and confidence intervals.

## Knowledge-based programming for everyone.

The team used flight path information from the Greenland 2007 field deployment. This data was imported into MATLAB® so that they could be converted from text files into actual MATLAB® script files. With these MEX files, the team was able to create a script within MATLAB® that could plot the flight path data into a graph with the axes of the graph being labeled latitude for the x-axis and longitude for the y-axis.

Use any or online interactive tools available on the WWW to perform statistical experiments (with the same purpose, as you used to do experiments in physics labs to learn physics) to understand statistical concepts such as are entertaining and educating.

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## Miller, R. G. Boca Raton, FL: Chapman & Hall, 1997.

The appearance of other computer software, , , and are the most important events in the process of teaching and learning concepts in model-based statistical decision making courses. These tools allow you to construct numerical examples to understand the concepts, and to find their significance for yourself.

## "ANOVA." From --AWolfram Web Resource.

My teaching style deprecates the 'plug the numbers into the software and let the magic box work it out' approach. Personal computers, spreadsheets, e.g., , professional statistical packages (e.g., such as SPSS), and other information technologies are now ubiquitous in statistical data analysis. Without using these tools, one cannot perform any realistic statistical data analysis on large data sets.

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The relative costs of false positives and false negatives, and thus the best P value to use, will be different for different experiments. If you are screening a bunch of potential sex-ratio-changing treatments and get a false positive, it wouldn't be a big deal; you'd just run a few more tests on that treatment until you were convinced the initial result was a false positive. The cost of a false negative, however, would be that you would miss out on a tremendously valuable discovery. You might therefore set your significance value to 0.10 or more for your initial tests. On the other hand, once your sex-ratio-changing treatment is undergoing final trials before being sold to farmers, a false positive could be very expensive; you'd want to be very confident that it really worked. Otherwise, if you sell the chicken farmers a sex-ratio treatment that turns out to not really work (it was a false positive), they'll sue the pants off of you. Therefore, you might want to set your significance level to 0.01, or even lower, for your final tests.

## Explore anything with the first computational knowledge engine.

The significance level (also known as the "critical value" or "alpha") you should use depends on the costs of different kinds of errors. With a significance level of 0.05, you have a 5% chance of rejecting the null hypothesis, even if it is true. If you try 100 different treatments on your chickens, and none of them really change the sex ratio, 5% of your experiments will give you data that are significantly different from a 1:1 sex ratio, just by chance. In other words, 5% of your experiments will give you a false positive. If you use a higher significance level than the conventional 0.05, such as 0.10, you will increase your chance of a false positive to 0.10 (therefore increasing your chance of an embarrassingly wrong conclusion), but you will also decrease your chance of a false negative (increasing your chance of detecting a subtle effect). If you use a lower significance level than the conventional 0.05, such as 0.01, you decrease your chance of an embarrassing false positive, but you also make it less likely that you'll detect a real deviation from the null hypothesis if there is one.

## The data is summarized in the table.

Forecasting with regression requires the Excel add-in called "," and linear programming requires the Excel add-in called"." How you check to see if these are activated on yourcomputer, and how to activate them if they are not active, varies withExcel version. Here are instructions for the most common versions. IfExcel will not let you activate Data Analysis and Solver, you must usea different computer.

Start Excel, then click Tools and look for Data Analysis and forSolver. If both are there, press Esc (escape) and continue withthe respective assignment. Otherwise click Tools, Add-Ins, andcheck the boxes for Analysis ToolPak and for Solver, then clickOK. Click Tools again, and both tools should be there.

Start Excel 2007 and click the Data tab at the top. Look to seeif Data Analysis and Solver show in the Analysis section at the farright. If both are there, continue with the respectiveassignment. Otherwise,
-click the “Office Button” at top left
-click the Excel Options button near the bottom of the resulting window
-click the Add-ins button on the left of the next screen
-near the bottom at Manage Excel Add-ins, click Go
-check the boxes for Analysis ToolPak and Solver Add-in if they are notalready checked, then click OK
-click the Data tab as above and verify that the add-ins show.

Start Excel 2010 and click the Data tab at the top. Look to seeif Data Analysis and Solver show in the Analysis section at the farright. If both are there, continue with the respectiveassignment. Otherwise,
-click the File tab at top left
-click the Options button near the bottom of the left side
-click the Add-ins button near the bottom left of the next screen
-near the bottom at Manage Excel Add-ins, click Go
-check the boxes for Analysis ToolPak and Solver Add-in if they are notalready checked, then click OK
-click the Data tab as above and verify that the add-ins show.

## The ratio SSM/SST = ² is known as the .

Forecasting with regression requires the Excel add-in called "," and linear programming requires the Excel add-in called"." How you check to see if these are activated on yourcomputer, and how to activate them if they are not active, varies withExcel version. Here are instructions for the most common versions. IfExcel will not let you activate Data Analysis and Solver, you must usea different computer.

Start Excel, then click Tools and look for Data Analysis and forSolver. If both are there, press Esc (escape) and continue withthe respective assignment. Otherwise click Tools, Add-Ins, andcheck the boxes for Analysis ToolPak and for Solver, then clickOK. Click Tools again, and both tools should be there.

Start Excel 2007 and click the Data tab at the top. Look to seeif Data Analysis and Solver show in the Analysis section at the farright. If both are there, continue with the respectiveassignment. Otherwise,
-click the “Office Button” at top left
-click the Excel Options button near the bottom of the resulting window
-click the Add-ins button on the left of the next screen
-near the bottom at Manage Excel Add-ins, click Go
-check the boxes for Analysis ToolPak and Solver Add-in if they are notalready checked, then click OK
-click the Data tab as above and verify that the add-ins show.

Start Excel 2010 and click the Data tab at the top. Look to seeif Data Analysis and Solver show in the Analysis section at the farright. If both are there, continue with the respectiveassignment. Otherwise,
-click the File tab at top left
-click the Options button near the bottom of the left side
-click the Add-ins button near the bottom left of the next screen
-near the bottom at Manage Excel Add-ins, click Go
-check the boxes for Analysis ToolPak and Solver Add-in if they are notalready checked, then click OK
-click the Data tab as above and verify that the add-ins show.

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