STAT Keystrokes for TI-83 and TI-84

You need (just once) to turn on access to certain menus in your TI calculator from the catalog on your calculator. Catalog is above the number 0. Select the catalog and scroll down to DiagnosticOn and hit enter twice. You should see Done on your screen. You have done it.

To clear data out of one or more lists go to the Stat menu and select ClrList and hit enter. Then go to the list menu and select the list you want to clear. Then hit enter twice.

To sort the entries in a list go to the Stat menu and select SortA. Then go to the list menu and select the list you want to sort. Then hit enter twice.

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Enter the data:

Press [STAT] [ENTER] to enter the statistics list editor
• Enter the numbers into L1 (or any of the lists) by pressing each number and [ENTER]

Boxplot using the TI-83 or TI-84:``````
Graph the data:

• Press [2nd] [STAT PLOT] [ 1 ]
• Press [ENTER] to turn on the stat plot.
• Select the box plot (the 4th graph type available in the menu) using the right arrow key and press [ENTER]
• Be sure that Xlist is L1
• Allow Freq to default to 1
• Press [GRAPH] to see the Box Plot

Note: Press [ZOOM], select 9:ZoomStat, and press [ENTER] to adjust the window settings.``````

If you want the 1-variable statistics for a list (such as mean, standard deviation, quartiles and the 5-number summary) go to STAT and then CALC and select 1-Var Stats and then put in the list name of your list. You can do this for two lists (of the same length) at once: use 2-Var Stats.

To produce a list of n "random integers" in the range between a and b hit the math button (right below the alpha button) and go to the PRB menu and select randInt. Then finish typing in randInt(a,b,n) and hit enter.

How to plot a scatterplot and (if you want) its regression line on the same graph:

First go to " Stat Calc 4" and enter the two lists to do the regression calculation LinReg(ax+b).
When you do this you will see the slope and y-axis intercept of the line and also the r value (the correlation coefficient) for these two variables displayed.
Then go to StatPlot and turn on the scatterplot (the first plot type) for these two lists. If you just want the scatterplot, quit out of StatPlot and hit "ZOOM 9".
To graph the regression line too, go to the regular graph "Y=" button and hit "Clear".
You want to put the formula for the regression line in Y_1. You can just type in the line formula here. (Alternatively, hit "VARS 5" and go to "EQ" and hit "ENTER".) Now hit "ZOOM 9".
If you want a prediction off the regression line go to the calc menu "2nd TRACE" and hit "ENTER" and then use up-or-down arrow to go to the line and enter the X value you want. Zoom9 will give you a decent window, but you may want or need to resize this window to see things (like the axes or a specific X value) better.

How to plot a histogram on the TI-83

Go to StatPlot and select the histogram icon (last type on the top row) and enter the list name below that. To change the number or placement of bins from default values go to WINDOW (on the top line next to Y=) enter the interval you want divided up in Xmin and Xmax and enter the bin width in Xscl. Then hit graph.

To calculate the probability that a random variable X which is normally distributed with mean M and standard deviation S will hit an interval between a and b:
On a TI-83 go to 2nd DISTR and select normalcdf(a,b,M,S) and enter. The TI-84 is similar.

To calculate the value V so that a random variable X which is normally distributed with mean M and standard deviation S will hit an interval to the left of V with probability p:
On a TI-83 go to 2nd DISTR and select invNorm(p,M,S) and enter. The TI-84 is similar.

The number invNorm(p,0,1) is often called a z-score associated with probability p. It is the place, on the standard normal, so that you will hit there or to the left with probability p the next time you take a sample.

If you have the place and want the probability use normalcdf. If you have the probability and want the place use invNorm.

If X is a data point from a normal distribution with mean M and standard deviation S the z-score of X is the fraction (X-M)/S. It is the number of standard deviations that X is away from the mean.

How to decide if data you collect is approximately normally distributed:

plot the data in a normal quantile plot, which compares the fraction of the data in intervals to the fraction that should be in the interval if it were normal. This graph should be close to a straight line if the data is distributed normally, like a "bell curve". If it is not nearly straight then the data is NOT normally distributed.
First enter the data into a list, say L1. It does not have to be in any particular order.
Clear out any graph in the "Y=" list.
Go to StatPlot and select the very last (sixth) type of plot.
Select your data list and X as the data axis.
Now Zoom 9 and look at the normal quantile plot.

If you wish application of the tests given below to be accepted by statisticians you must verify that the conditions statisticians have established as "standard practice" are in place in your situation. If you require something different you should chat with a statistician to see what can be done. STATISTICIANS ARE NOT UNIFORM IN THEIR OPINIONS on these matters. I collect, below, conditions extracted (mostly) from a standard text.

In all cases the sample must be selected using proper randomization procedures.

You generally want the population size to be at least 20 times the sample size n.

For 2-sample procedures it is best if the two samples are nearly equal size.

Personally, I would want sample sizes a lot bigger than the minimums specified below before I would give much weight to the calculations, though these ARE generally accepted minimums. And the overarching requirement, that the samples be taken by a legitimate random procedure from your intended population, is not just some pro forma ideal: it is essential!

Numerical Variables

If a variable is normally distributed with known standard deviation the sample means are also normally distributed and the Z-distribution Confidence Interval and Hypothesis Testing methods below are acceptable for any sample size.

Unfortunately, usually you will not know if the variable is normally distributed, nor will you know its standard deviation. However we do know that if the sample size is "large enough" the sampling distribution will be close to normal and in this case the T-distribution methods are used. These use the sample standard deviation in place of the unknown population standard deviation, which causes the confidence intervals to be wider than those calculated from a normal distribution.

If your sample looks to be normally distributed the T-procedures are acceptable (according to standard statistical practice) for all sample sizes. If the sample is less normal but not strongly skewed and with no strong outliers we require n to be at least 15. If strong outliers or strong skewness is present in your sample we require n to be at least 40 for an acceptable calculation.

For 2-sample T-procedures the two sample sizes n1 and n2 must both be at least 5. If both samples appear to be normally distributed the T-procedures are acceptable for n1+n2 less than 15. If either sample is less normal but not strongly skewed and with no strong outliers we require n1+n2 to be at least 15. If strong outliers or strong skewness is present in either sample we require n1+n2 to be at least 40 for an acceptable calculation. These 2-sample T-procedures may be inappropriate entirely if the samples seem to be from populations which are greatly skewed, or skewed in opposite directions. And you should consult a statistician if one sample standard deviation is more than twice the other.

Numerical when you DO know the population standard deviation...

To calculate the P-value for the Sample Mean when you DO know the population standard deviation on the TI-83 go to STAT-Tests-Z-Test and input the null hypothesis and the test type (2-sided or 1-sided.) You must indicate the data list itself or enter the list statistics---sample mean, population standard deviation and sample size---directly.

To calculate the Confidence Interval for the Population Mean when you DO know the population standard deviation on the TI-83 go to STAT-Tests-ZInterval and input the confidence level required and indicate the data list itself or enter the list statistics---sample mean, population standard deviation and sample size---directly.

Numerical when you DO NOT know the population standard deviation...

To calculate the P-value for a Sample Mean when you DON'T know the population standard deviation on the TI-83 go to STAT-Tests-T-Test and input the null hypothesis and the test type (2-sided or 1-sided.) You must indicate the data list itself or enter the list statistics---sample mean, sample standard deviation and sample size---directly. Check the normality of your sample!

To calculate the Confidence Interval for the Population Mean when you DON'T know the population standard deviation on the TI-83 go to STAT-Tests-TInterval and input the confidence level required and indicate the data list itself or enter the list statistics---sample mean, sample standard deviation and sample size---directly. Check the normality of your sample!

Numerical, compare two means, when you DO NOT know the population standard deviations...

To calculate the P-value for a Comparison of Two Sample Means when you DON'T know the population standard deviations on the TI-83 go to STAT-Tests-2-SampTTest and input the comparison type (2-sided or 1-sided.) You must indicate the data lists themselves or enter the list statistics---sample means, sample standard deviations and sample sizes---directly. Check the normality of both of your samples!

To calculate the Confidence Interval for the difference of two Population Means when you DON'T know the population standard deviations on the TI-83 go to STAT-Tests-2-SampTInt and input the confidence level required and indicate the data lists or enter the list statistics---sample means, sample standard deviations and sample sizes---directly. Never select "pooled." Don't use this test unless both samples are of size 5 or larger. Check the normality of both of your samples!

Categorical Variables

If you are doing Hypothesis Testing for population proportion you want the number of successes and failures corresponding to the null hypothesis proportion to BOTH be 10 or larger. These numbers are given by np and n(1-p) where p is the null hypothesis proportion.

If you are creating Confidence Intervals for a population proportion you can use the "Large Sample" criterion which is that the number of successes and failures IN YOUR SAMPLE should both be 15 or larger. The Large Sample condition for confidence intervals for the difference of two proportions is that successes and failures for both your sample proportions should all be at least 10.

However I recommend that, instead, you always use the +4 calculation method (add two fictitious successes and four fictitious samples) to your data.

For population proportion Confidence Intervals using the +4 method you want the total number of observations taken to be at least 10 and don't use confidence levels below 90%. (Be cautious: as a practical matter, these population proportion confidence intervals are close to useless unless sample sizes are quite a bit bigger than the minimums!)

Categorical, Sample Proportions

To calculate the P-value for a Sample Proportion on the TI-83 go to 1-PropZTest and input the null hypothesis proportion value (the P sub 0 you are assembling evidence AGAINST), the test type (2-sided or 1-sided and the number of successes and the sample size. You NEVER use the "Plus Four" method here. You want the number of successes and failures corresponding to the null hypothesis proportion to BOTH be 10 or larger. These numbers are given by np and n(1-p) where p is the null hypothesis proportion.

To calculate a Confidence Interval for a Population Proportion on the TI-83 go to 1-PropZInt and input the number of successes and the sample size and the confidence level required. I recommend that you always use the "Plus Four" method here. n should be at least 10 and don't use confidence levels less than 90%.

Categorical, Compare Two Sample Proportions

To calculate the P-value for a Comparison of Two Sample Proportions on the TI-83 go to 2-PropZTest and input the comparison type. You must indicate successes and sample sizes of each proportion. You NEVER use the "Plus Four" method here. Use this test when the number of successes and failures in both samples are all be at least 5.

To calculate a Confidence Interval for a Difference of Two Population Proportions on the TI-83 go to 2-PropZInt and input the number of successes and the sample sizes and the confidence level required. I recommend that you always use the "Plus Four" method here and in this case it means add 1 fictitious success and 2 fictitious samples to each of the two samples. n1 and n2 should each be at least 5 and don't use confidence levels less than 90%.