Statistical Decision Making
Brief description and instructions (DRAFT):
Inferential statistics assist us in making a decision about whether something is happening in a data set other than random fluctuation of the values. We have two statistical hypotheses,
Inferential statistics is possible because we can determine with some degree of certainty what values of a statistic will be obtained if the null hypothesis is true. The Central Limit Theorem helps us understand how sample means will vary around the true population mean. If the null hypothesis is true, then if I have two conditions, each condition will be sampling from the same population set of values. Each sample distribution gives us a similar knowledge about what happens to its value, whether the F of ANOVA or the r of Pearson's bivariate correlation, when the null hypothesis is true.
So if your study generates a statistic that is very unlikely when the null hypothesis is true, then you can feel confident in rejecting the null hypothesis and accepting the alternative hypothesis. Each inferential statistical test will give you a p (or sig) value that is the probability that the null hypothesis is true. The researcher should preselect an alpha level (usually 0.05) which serves as the cutoff value. If p < alpha then the researcher will reject H0.
Using the illustration:
The main part of the screen is a graph with, initially one distribution, in red, indicating the probability of getting different statistical values if H0 is true. The yellow line indicate the alpha level which can be set by the slider at the bottom or the buttons below the slider to one of three preselected alpha levels.
On the right ran slide you can see some summary values. Most important is the value in green which is the probability that you will reject a true H0, also called a type one error. You can highlight that option with the button in the table to the right under the phrase (Type I Error).
Below the legend you can do an study and draw a sample. The sample value will be shown as a dashed line on the graph. The probability that a sample value at least that far from the mean of the sample will be given below the sample button as "p = ". This value will be red if it is equal or less than the alpha level.
Now you do not know whether H0 or Ha is true. You can find out which distribution was used to generate the statistical value by pressing the Show True Hypothesis button (of course in reality you do not have this option). There is a 50% chance for each hypothesis to be true and if you press the new experiment button, it will do the same probability determination to select whether H0 or Ha are true.
To further investigate the situation, you can select the Show Ha check box to see the possible statistical values for Ha and also get a slider to alter how different the populations are for Ha and H0, called effect size.
Click here to open the applet. It will open a new window that will fill your screen.