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.
Contents
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.