## Statistics on the TI-83 and TI-83 Plus

For use in Georgetown University statistics classes: Math-006 and Math-040. Updated 8/4/04.

• Basic familiarity with the TI-83 or TI-83 Plus is assumed.
• These instructions should allow you to do basic statistical procedures at the level of Math-006 on the TI-83.
• The instructions are not necessarily complete. There may be more things one can do on these calculators, and you may be able to do some tasks differently.
• These instructions have been tried out on the TI-83 and the TI-83 Plus.  They should also work on the new TI-84 Plus.  Some may also work on other Texas Instruments calculators, such as the  TI-86, TI-89, and TI-85.
• Special thanks for Rachel for showing me (H.E.) some of the graphing tricks and for general insight and good cheer.

#### Confidence Intervals for Means and Proportions

Inference for Regression

Other TI-83 Manuals

#### Statistics and the TI-83 Keyboard

The TI-83 keyboard is shown below.  The four menu key for doing statistics are the STAT PLOT key, the STAT key, the VARS key, and the DISTR key. Various submenus appear when you press these keys.

#### Entering Data

• Statistical data are stored in the TI-83 as lists. Up to six lists can be stored.Tables are stored as matrices.
• To enter data, press STAT and got to EDIT. Don't press LIST.
• In the first empty column (usually column L1), enter the observations for variable 1.
• If you have a second variable, move the cursor to column L2, and enter the second variable’s observations in that column.
• Continue as necessary with columns L3, L4, etc. Once your data are entered, you can share them with other calculators.
• To enter a table, press MATRX (2nd x-1) and chose EDIT. Choose the matrix you want to edit (A through J). Choose the size of the table (= matrix). Then enter the values.
• You can also upload statistical lists from a computer if you have TI Graphlink software and the appropriate cables.  This allows you to enter e.g. data from the CD that accompanies Moore and McCabe's book or from the Internet.
• You can also share data with other TI-83 calculators, using the appropriate cable.

#### Statistical Graphing

• You can make scatterplots, box plots, and histograms on the TI 83.
• Before you make a plot, set the window size for your plot so that your plot will fit in the screen.  Box plots are done horizontally, so you have to adjust xMin and xMax before you make such a plot.
• Press 2nd STAT PLOT and press enter.  Switch plot 1 to "on".  Select the type of the plot.  For example, to make a scatter plot of the data in list 6 against the data in list 4, move the cursor to the scatter plot symbol and presse enter.  Select L4  as Xlist and L6 as Ylist.  This is done by pressing "2nd 6" = L6  and "2nd 4" = L4. Finally choose the symbol for your plot and press GRAPH.

#### Descriptive Statistics

Press STATand activate CALC.

• One variable statistics: If you are interested in only one variable, press 1:1-Var Stats.
• Select the variable for which you wish to do the computation.  For example, to compute the descriptive statistics for the vaiable in L5, press "2nd 5" = L5 .
• The screen should now read 1-Var Stats L1.
• Press ENTER. Mean and standard deviation for your variable will appear on the screen.
• To do the five-number summary, first make a boxplot (see above). You can find the median and the quartiles by pressing VARS.  Go to 5:Statistics and then to PTS. Scroll down to find 7:Q1, 8:Med and 9:Q3.  Choose one and hit Enter twice to see the values. You can also find the minimum and maximum in VARS > 5:Statistics  > XY. Scroll down to find 8:maxX and 9:minX.
• Two variable statistics: To obtain the descriptive statistics for two variables, start the same way as for one variable.
• Press STAT, then move cursor to CALC. Press 2: 2-Var Stats.
• Select the variables for which you wish to do the computation.  For example, to compute two-variable statistics for the vaiables in L4 and L5, press "2nd 4" = L4, then ",", then "2nd 5" = L5.
• The screen should now read 2-Var Stats L4, L5.
• Press ENTER. The screen fills with all values for the two variables that you would also get from one variable statistics, plus the sum of the products of the entries in the two lists.  Scroll down to see everything.
• To use 2-Var Stats, the columns have to be the same length.

#### Correlation and Regression

• To compute the linear regression of a variable in L5 on another variable in L4,
• press STAT > CALC and choose 4:LinReg(ax+b),
• hit enter and type "2nd 4" = L4, then ",", then "2nd 5" = L5,
• hit enter.
• The screen shows the coefficients of the regression equation and the values for  r  and  r2.
• You can find all this information by pressing VARS.  Go to 5:Statistics and then to EQ. Choose 1:RegEQ to see the regression equation,  2:a to see the slope,  3:b to see the intercept, 7:r to see the correlation coefficient, and 8:r2.
• Other regression methods (quadratic, cubic, exponential etc.) are also available.  Consult the TI 83 manual for details.
• The TI 83 also allows you to do a "robust" version of regression that is more resistant than least squares regression, just like the median is more resistant than the mean. To do this,
• press STAT > CALC and choose 3:Med-Med,
• hit enter and type "2nd 4" = L4, then ",", then "2nd 5" = L5,
• hit enter.
• Inference to linear regression is discussed below.

#### Normal Probability Calculations

• Finding the area under the curve between two points for a distribution that is N(µ,s):
• Press "2nd DISTR" key (in yellow, above VARS key).
• Choose 2:normalcdf.  Normalcdf(  will appear in the display.
• Enter the number for the left point, then the number for the right point, then the value of µ, then the value of s, all separated by commas.  You don't have to close the parenthesis.
• Press ENTER.  The display will show the value of the area under the curve between the two points.  Note that you do not need to convert the values of the two points from the normal distribution into z values of the standard normal distribution.
• Note:  If your distribution is N(0,1), you can leave out 0 and 1 after you type in the given points.  For example, normalcdf(-1,1 is sufficient to find the area under the standard normal curve within 1 standard deviation of the mean.
• Finding the area under the curve to the left of a given point:
• The first steps are as above.
• Choose -1,000,000,000 as your left point.  You can do this by pressing "(–) 2nd EE 9".  (EE is in yellow above the comma key.)  Then continue as before.
• Finding the area under the curve to the right of a given point:
• Same as for the previous task.  Choose 1,000,000,000 as your right point, e.g. by pressing "2nd EE 9".
• Displaying a graph of an area under the normal curve:
• Turn off any Y= functions that may be active.  Press the Y= key.  Move the  cursor to any = sign that is highlighted, and press ENTER.)  If the = sign is black on a white background, then the function is deactivated.
• Make sure the graphing window is set correctly.  In particular, choose Ymin = 0 and Ymax not too large.
• Press MODE and choose Func in the fourth row. This will set the graphing mode to function graphs.
• Clear all previous graphs: Press "2nd DRAW", then 1:ClrDraw, then ENTER.  Caution: This will clear all existing graphs from memory.  The display will show DONE.  You now have a clean slate for your graph.
• Press "2nd DISTR" and move the cursor to DRAW.  Choose 1: ShadeNorm(  .  ShadeNorm( will appear in the display.
• At this point, depending on whether you want to see the area under the curve between two points or the area under the curve to the left or right of a given point, the steps are similar to those described above.
• The area under the graph is shaded, and its value appears on the screen.
• Inverse probability calculation: To find the number  x  such that a variable that follows a  N(µ,s) distribution is less than x with a given probability  p:
• Press "2nd DISTR" key (in yellow, above VARS key).
• Choose 3:invNorm.  invNorm(  will appear in the display.
• Enter the value of  p,  then the value of µ, then the value of s, all separated by commas.  You don't have to close the parenthesis.
• Press ENTER.  The display will show the value of x.  Note that you do not need to convert  x  a standard normal distribution to a N(µ,s) distribution.
• Note:  If your distribution is N(0,1), you can leave out 0 and 1 after you type in the value of  p.  For example, invNorm(.75  is sufficient to find the third quartile of a standard normal distribution.

#### Hypothesis Tests for Means and Proportions

• To carry out a hypothesis test for a single population mean, in the case of known standard deviation:
• If the data are given, first into them into a list, say list L1.
• Press "STAT", scroll right to "TESTS", press 1 for Z-Test, and select "Inpt:DATA".
• Enter the value of µ0 (null hypothesis), the standard deviation, the location of the list, and the frequency (1).  Choose the type of alternative (one-sided or two sided). Scroll to "Calculate" and press ENTER.
• You can see the z-score, the p-value, the sample mean, and the sample standard deviation.
• If the sample mean is given, press "STAT", scroll right to "TESTS", press 1 for Z-Test, and select "Inpt:Stats".
• Enter he value of µ0 (null hypothesis), the standard deviation, the sample mean, the sample size, and choose the type of alternative (one-sided or two sided). Scroll down to "Calculate" and press ENTER.
• You can see the z-score and the p-value.
• To carry out a hypothesis test for a single population mean, in the case of unknown standard deviation:
• If the data are given, first into them into a list, say list L1.
• Press "STAT", scroll right to "TESTS", press 2 for T-Test, and select "Inpt:DATA".
• Enter the value of µ0 (null hypothesis), the location of the list, and the frequency (1).  Choose the type of alternative (one-sided or two sided). Scroll to "Calculate" and press ENTER.
• You can see the t-score, the p-value, the sample mean, and the sample standard deviation.
• If the sample mean and the sample standard deviation are given, press "STAT", scroll right to "TESTS", press 2 for T-Test, and select "Inpt:Stats".
• Enter the value of µ0 (null hypothesis), the sample standard deviation Sx, the sample mean, the sample size, and choose the type of alternative (one-sided or two sided). Scroll down to "Calculate" and press ENTER.
• You can see the t-score and the p-value.
• To carry out a hypothesis test for the difference of two population means, for two independent samples:
• If the data are given, first into them into lists, say  L1 and L2.
• Press "STAT", scroll right to "TESTS", press 4 for 2-SampTTest, and select "Inpt:DATA".
• Enter the location of the lists, and the frequencies (1).  Choose the type of alternative (one-sided or two sided).
• Select whether you want pooled standard deviations or not (recommendation: NO). Scroll to "Calculate" and press ENTER.
• You can see the t-score, the p-value, an approximated value for the degrees of freedom, the sample means, and the sample standard deviations.
• If the sample means and the sample standard deviations are given, press "STAT", scroll right to "TESTS", press 4 for 2-SampTTest, and select "Inpt:Stats".
• Enter the sample standard deviation Sx, the sample mean, and the sample size for both samples.
• Choose the type of alternative (one-sided or two sided) and decide  whether you want pooled standard deviations or not.. Scroll down to "Calculate" and press ENTER.
• You can see the t-score, the p-value, and an approximated value for the degrees of freedom.
• To carry out a hypothesis test for a single population proportion:
• Press "STAT", scroll right to "TESTS", and press 5 for 1-PropZTest.
• Enter the value of p0 for the null hypothesis, the number of successes x, and the sample size n.
• Choose whether you want a two-sided or one-sided alternative. Scroll down to "Calculate" and press ENTER.
• To carry out a hypothesis test for the difference of two population proportions:
• Press "STAT", scroll right to "TESTS", and scroll to  2-PropZTest.
• Enter the numbers of successes x1 and x2 and the sample sizes n1 and n2.
• Choose whether you want a two-sided or one-sided alternative. Scroll down to "Calculate" and press ENTER.

#### Confidence Intervals for Means and Proportions

• To compute a confidence interval for a single population mean, in the case of known standard deviation:
• If the data are given, first into them into a list, say list L1.
• Press "STAT", scroll right to "TESTS", press 7 for ZInterval, and select "Inpt:DATA".
• Enter the standard deviation, the location of the list, the confidence level, and the frequency (1).  Scroll down to "Calculate" and press ENTER.
• If the sample mean is given, press "STAT", scroll right to "TESTS", press 7 for ZInterval, and select "Inpt:Stats".
• Enter the standard deviation, the sample mean, the sample size, the confidence level. Scroll down to "Calculate" and press ENTER.
• To compute a confidence interval for a single population mean, in the case of unknown standard deviation:
• If the data are given, first into them into a list, say list L1.
• Press "STAT", scroll right to "TESTS", press 8 for TInterval, and select "Inpt:DATA".
• Enter the location of the list, the confidence level, and the frequency (1).  Scroll down to "Calculate" and press ENTER.
• If the sample mean and sample standard deviation are given, press "STAT", scroll right to "TESTS", press 8 for TInterval, and select "Inpt:Stats".
• Enter the sample mean and sample standard deviation, the sample size, and the confidence level. Scroll down to "Calculate" and press ENTER.
• To compute a confidence interval for the difference of two population means, in the case of unknown standard deviation and two independent samples:
• The data should either be entered in two lists, or sample means, sample standard deviations, and sample sizes for the two samples should be given.
• Press "STAT", scroll right to "TESTS", and press 0 for 2-SampTInt.
• Select "Inpt:DATA" or "Inpt:Stats" as needed.  Scroll down to "Calculate" and press ENTER.
• To compute a confidence interval for a population proportion:
• Note that the TI-83 does not use Wilson estimates. You will therefore have to enter adjusted values.
• Press "STAT", scroll right to "TESTS", and press 1 for 1-PropZInt.
• Enter the number of successes x, the sample size n, and the confidence level. Scroll down to "Calculate" and press ENTER.
• To compute a confidence interval for the difference of two population proportions:
• Note that the TI-83 does not use Wilson estimates. You will therefore have to enter adjusted values.
• Press "STAT", scroll right to "TESTS", and scroll down to 2-PropZInt (press alpha-B)
• Enter the number of successes x1 and x2, the sample sizes n1 and n2, and the confidence level. Scroll down to "Calculate" and press ENTER.

#### c2 - Tests

• To do a c2 test for independence or homogeneity of proportions for a 2-way table:
• Enter the table as a matrix (e.g. as A, see above).
• Press "STAT", scroll right to "TESTS", and scroll down to c2- Test (press alpha-C).
• The calculator expects the table of observed counts in A and will write the the table of expected counts to B. To change this, move the cursor to the left of the matrix name, hit the MATRX key, choose the matrix you want to use, and press ENTER.
• Scroll down to "Calculate" and press ENTER. Read off the values of the c2-statistic, the p-value, and the number of degrees of freedom.
• Read off the table of expected counts by going to MATRX and choosing the appropriate matrix.

#### Inference for Linear Regression

• To do a model utility test (a test of the null hypothesis that the slope of the regression line is non-zero):
• The explanatory variable (X) should be in one list (e.g. L5) and the response variable (Y) in another list (e.g. L6).
• Press "STAT", scroll right to "TESTS", and scroll down to LinRegTTest (press alpha-E).
• Choose the XList (explanatory) and YList (response). To change from the defaults L1 and L2, move the cursor to the left of the list name, hit the LIST key, choose the list you want to use, and press ENTER.
• Choose the null hypothesis (usually this is b not equal 0).
• Scroll down to "Calculate" and press ENTER. Read off the values of the t-statistic, the p-value, the estimated values of slope and intercept, the correlation coefficient r and the coefficient of determination r2, and the estimated standard deviation of the errors s.
• The residuals are stored as a list with the name RESID.

#### Other TI-83 manuals on the web

• Walter Schreiner's manual at CBU (pdf)
• A manual at UT-Pan American
• A statistics handbook for the TI-83 may be bought from Texas Instruments for \$19.95.