With the Texas Instruments TI-83 or TI-84, you can calculate the most commonly-used descriptive statistics for one variable (mean, standard deviation, sum of values, sum of the values-squared, 5-number description) and for regression/correlation between two variables (regression coefficient and intercept, correlation coefficient). There are also options for other (non-linear) forms of regression. The TI-83 will also perform a number of hypothesis test calculations (1 & 2 sample tests on means & proportions, chi-square for independence, 1-way ANOVA) and confidence interval calculations [see your manual for information].

You can also use the calculator to make plots (histogram, boxplot, scatterplot) of data you have entered.

Data are entered and stored in a table
(which allows checking that you have entered correctly & keeps
the numbers for recalculation)

**For all statistical functions: **Press STAT to see the first
statistics menu, then EDIT for data entry (or to clear data) CALC
(for calculation), or TESTS for statistical tests.

**For plots:** Press 2nd, then Y= [for STAT PLOT]

The TI-83 has six **lists** which can be used for
entering data [others can be defined - see your manual for fancier work]. There
are three situations in which you enter data - one variable (actual data), one
variable (with frequencies - grouped or ungrouped), two variable. **Always
clear old data** from any list in which you will enter data, or your results
will be messed up:

**To clear a list:**
Press STAT, (EDIT is highlighted), 1[Edit], use the up cursor
to highlight the label (L1,L2 or whatever) of the column, press
CLEAR and then ENTER. [you are then ready to enter data]

## A. One Variable:

Press STAT, (EDIT is highlighted), 1[Edit]

Values for one variable go in one column - use the cursor keys to move to the first entry in the column you choose, enter the number (you see it at the bottom of the screen), press down-arrow, enter the next, etc.

To change a value already typed in: Use the up & down arrows to highlight it, enter the new number & press the down-arrow or ENTER to put the new number in.You need to remember which column contains your data [especially if you have entered several columns of data]

## B. One Variable, with frequencies

[Also can be used for calculations with a discrete variable whose distribution is given by a table]

Press STAT, (EDIT is highlighted), 1[Edit]

Values go in one column, frequencies in another- enter the number (you see it at the bottom of the screen), press down-arrow, enter the next, etc. It is easiest to enter the values (x's) first and then the frequencies. Frequencies must be whole numbers (not decimals or fractions).

To change a value already typed in: Use the up & down arrows to highlight it, enter the new number & press the down-arrow or ENTER to put the new number in.

If you are entering data from a grouped data table (or histogram) use theclass midpointfor value, class frequency as frequency.

You need to remember which column holds values and which column holds frequencies.## C. Two variable

[For paired data of either sort - matched pairs experiments/observations or predictor/respone (x/y) data]

Press STAT, (EDIT is highlighted), 1[Edit]

Values go in pairs : x values (values of the predictor) in one column, y-values (values of the response) in another (it's easiest to enter all x-values down the column, then y-values down their column, next to corresponding x-values) [For paired-data: values from one group in one column, values from the second group - in maching order - in another]

You will need to remember which column holds x-values and which holds y-values.

## A. One-variable

Press STAT, highlight CALC, press 1[1-Var Stats] (command 1-var stats appears on screen), then the column number [column numbers are obtained with 2d - number (2nd, 1 gives L1, 2d, 2 gives L2, etc), then ENTER

You see a screen with mean( x-bar), sum of x's sum of x-squares ( not "sum of squares" SS(x)) sample standard deviation (Sx) population standard deviation [not much use] and sample size (n) - scrolling down will show minimum, maximum, 1st & 3d quartiles and median [5-number description]

## B. One-variable with frequencies

Press STAT, highlight CALC, press 1[1-Var Stats] (command 1-var stats appears on screen), 2nd-number[number of the values column] , [a comma - key is above the numbers], 2nd-2[L2], then ENTER

You see a screen with mean( x-bar), sum of x's, sum of x-squares ( not "sum of squares" SS(x) ), sample standard deviation (Sx) population standard deviation [not much use] and sample size (n) - scrolling down will show minimum, maximum, 1st & 3d quartiles and median [5-number description]

## C. Two-variable

Regression/correlationPress STAT, highlight CALC, press 4[LinReg(ax+b)] (command appears on the home screen) 2nd-number (of column for x's), a comma [key is above the numbers], 2nd-number (of column for y's), then ENTER -

You see screen giving a (coefficient), b (intercept) and r (correlation coefficient) (also shows form of equation: y = ax + b, so you can see which number is which)

Note:to save the regression equation for graphing, you add to the regression command - after the y-variable column, add: , [a comma], VARS, select Y-VARS (top of screen), select 1:Function )(from the list) and select Y1 or Y2 . . . (whichever function you want for the equation of the line). If you had x in L3, y in L4 and want Y1 to be the line, the screen should show LinReg L3,L4,Y1 . Then you press ENTER

NOTE:To have the calculator displayr and r^2, you need to make a one-time adjustment in the settings, as follows: press 2nd-0 [Catalog], scroll down the list (with the down-arrow cursor) until the pointer is on "DiagnosticOn" and press Enter (This copies "DiagnosticOn" to the home screen). Press Enter again. This process turns on the "diagnostics" for regression - specifically r and r^2.## Combined statistics

Press STAT, highlight CALC, press 2[2-Var Stats] 2nd-number (of the x-column), [a comma - key is above the numbers], 2nd-number (of the y-column)

You to see a screen giving mean of data in x-list (x-bar), sum of x-list data ( sum of x's) sum of x-squared ( not "sum of squares" SS(x)) sample standard deviation for x-list (Sx), then same data for y-list (called y on screen) and the sum of the xy's .

The TI-83 will produce six different types of plots, and up to three different plots can be defined [each can be turned on or off once it is defined]

To define a plotPlots are defined using the "Statplots" options.

Press 2nd - Y= [STAT PLOTS] and you see a list. The information shown with this list shows: whether the plot is turned On or Off [is displayed on the graphing screen or not], the type of plot [shown with a symbol] the column [or columns] used for data and the graphing symbol (box, plus sign or point).

Select a number (1 to 3) for the plot you want to define [options 4 & 5 turn all plots on or off at once].

For the plot you are defining, you select several options either by highlighting the choice or by typing your choice.

To turn the plot On/Off - highliight your choice & press ENTER. Cursor down to select type.

To select type: use right/left cursor to highlight type, press ENTER to make highlight your choice, then press ENTER

The choices of types: Scatterplot,Scatterplot with points connected in order (from the list-will not be inorder of x's or y'sunless you sorted lists), histogram, modified boxplot (potential outliers shown as dots), basic boxplot (whiskers go to largest & smallest values), normal quantile plot

Type in the choice of lists [using 2nd-number of the data list]. The choices you must make depend on the type of plot:

For scatterplot and connect-line scatterplot - must select x-list and y-list

For histogram & two boxplot types: select data list for "Xlist" [then press ENTER]. If frequencies are used (as in I.B above), enter the name of the frequncy list for "Freq:" - otherwise you should enter 1 [then press "ENTER"]

For normal quantile plot:: enter the list containing the data as "Data List", select which axis of the graph will match the data (other will be z-values).

Select graphing symbol as "Mark" by highlighting & pressing "ENTER" (default is a box - it works fine)To show the plot, with the plot turned on, press ZOOM and select 9:ZoomStat to get a window sized to show your plot.. [If some of the functions were turned on in the "Y=" list, they will also graph, which can be distracting].

Note:

If you have two or more plots turned on, they will all graph at once. If you have two boxplots turned on, they will appear one above the other. (side-by side boxplots - but horizontal)

You can control the window size and the spacing on a histogram with the "window" key - the "xscale" option is the class width.

The trace function can be used with statplots - giving coordinates of points (scatterplots), min & max (class limits) and frequency (n) for each bar in a histogram [notation a bit odd - be careful], min Q1, median, etc. for boxplot.

If you define a scatterplot and calculate the regression line with the same data (using the form that saves the line to Y1) the line will appear on the plot.

The statplots can be turned on and off (but not redefined) from the Y= window - highlight & press ENTER (just as for the functions)

Errors or questions? Please let me know: cpeltier@saintmarys.edu

Last update 8/7/2000