Statistics Programs

A number of programs are provided for performing statistical tests such as t-tests and linear regressions. These programs will be used to analyze the data obtained in the experiments.
One sample t-test (1SAMPT)
A one sample t-test is performed when you wish to test whether the mean of a single distribution of numbers (one "sample") differs significantly from some specified value.
To run the program, type 1SAMPT and [Enter]. Enter the data values, one at a time, followed by [enter]. After entering the last data value, enter an X. Each entry is assigned a line number as it is typed in. If you made a mistake you will have an opportunity to correct any line after you finish entering the data. After you have edited the data, a number of statistics will be presented. The important ones are: Mean, the mean of the values entered; and Degrees of freedom, this equals the number of data values minus 1, and is used when looking in a table of t-distribution probabilities. Next you are asked to enter a value to test the distribution against. The t-statistic is then computed and displayed, along with the p-value for the test. (For many purposes, you can ignore the sign of the t-statistic.)
The p-value represents the probability of obtaining, by chance, a t-statistic as extreme as the t that you obtained if the population distribution really was equal to the test value that you specified. (Or, in simpler terms, the p-value is the probability that the difference between your sample and the specified value is due to chance.) Thus, if the p-value is very small (less than "alpha" which is usually .05), then you can conclude that your distribution of numbers is significantly different from the value you specified.
Between subjects t-test (BETWST)
To perform a between subjects (randomized) t-test, use the program BETWST. This test is performed when you have two groups of numbers and wish to test whether the two distributions are likely to have come from the same underlying distribution.
To run the program, type BETWST and hit [enter]. First enter data from group 1, one at a time, and enter an X when finished. Then enter the data for Group 2, followed by X. You will have an opportunity to correct any data- entry errors. The t-statistic, degrees of freedom, and p-value are then computed and presented. The p-value is interpreted just like it is for any other statistical test. In this case, the p-value represents the probability that you could get a t-statistic as extreme as the one that you obtained if the two groups of data values were actually sampled from the same underlying distribution. (Or, in other words, the p-value is the probability that the difference you observed between the two groups was due to chance.) Thus, if the p-value is small, it is unlikely that the two samples of observations came from the same underlying distribution in the population.
Paired t-test (PAIREDT)
A paired t-test (or "within subjects" t-test) is used when you have two groups of numbers that you wish to compare (much like a between subjects, randomized t-test). However, to use a paired t-test, the data must have the additional property that each data value in group 1 has a corresponding data value in group 2 and those two observations share something in common that is not shared by any of the other data values. In other words, each data value in one of the two groups of numbers must be able to be logically paired with a value in the other group. For example, if the two groups of numbers that you are comparing represent responses under two different conditions, and if each subject was studied under each condition, then you would be able to perform a paired t-test. This is because a subjects data value in one condition can be logically paired with their data value in the other condition. These two numbers would have in common the fact that they came from the same subject.
To run the program, switch to the correct directory and type PAIREDT [enter]. Then enter each pair of observations, separating the members of each pair with a comma. Hit [enter] after each pair of observations. You'll have a chance to correct any errors after you have entered all of the data. When you have entered all of the data, type X,X [enter] and the program will compute and display the t-statistic, the degrees of freedom, and the p-value for the test.
Linear Regression and Correlation (REGRESS)
The program REGRESS performs linear regression on the input data. To run the program, type REGRESS and hit [enter]. Enter data in (x, y) pairs, separated by a comma (for example: 34.5,765.0 [enter]). Enter X,X after entering the last x,y pair. The slope, intercept, and correlation coefficient are computed and displayed.
Analysis of Variance (RANOVA)
T-tests can be used to compute inferential statistics when the factor being tested has only two levels (i.e., when there are only two groups of data to compare). If an experiment involves a factor with more than two treatment levels, or if the experiment includes more than one factor, then an Analysis of Variance (ANOVA) must be used. The program RANOVA will perform ANOVAs with up to 8 within subject factors (independent variables) and up to 8 between subject factors. Each factor can have many different levels.
To run the program, type RANOVA . You will first be asked "How many subjects in each group?". If the design of the experiment is completely within subjects (i.e., each subject serves in every condition), then the correct value to enter is simply the number of subjects. If there is a between subject factor, then the correct response is the number of subjects in each level of the between subject factor (if there is only one between subject factor). Note that RANOVA can only analyze designs that have an equal number of subjects in each level of the between subject factors. (If there is more than one between subject factor, then the "number of subjects per group" is the number of subjects in each combination of between subjects factor levels.) Next, you will be asked for the number of between-subject and within-subject factors, the number of LEVELS of each factor, and labels for each of the FACTORS and FACTOR LEVELS. Try to use labels that are somewhat descriptive. For example, a FACTOR might be "set size", and that factor might have six levels that could be labeled: "ss1", "ss2", "ss3", etc. You will then be asked to enter the data for one subject at a time. The labels that you supplied will be used as prompts for the appropriate data value to enter. When you have entered all of one subjects data, you will be given a chance to change any of the entries, in the event that you made a typing error.
After you have entered all of the data, tables with marginal means (means for each level of each factor, and for each combination of factor levels), and then the F-table will whiz by you. You can stop these numbers from scrolling by holding down the CTRL key and then pressing S. Then, hitting any key will unfreeze the screen. But, you don't need to worry about the scrolling because everything that is written to the monitor is also put into a file called ANOVA.OUT. You can view the contents of that file by entering the command TYPE ANOVA.OUT . You can print the contents of that file by issuing the command PRINT ANOVA.OUT .

RANOVA has some limitations: Most importantly, it can only analyze experiments that include at least one within subject factor. In other words, it will not work on a completely between-subject design. Next, although RANOVA will work properly (and produce correct values) if you have several between subject factors, the output may be somewhat messy and difficult to interpret. It is sometimes necessary to reboot some computers (CTRL-ALT-DEL) before running RANOVA if a graphics-based experiment has just been run. You will know if you need to do this because RANOVA will present a blank screen and will fail to prompt you for data input.

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