HP 28S User Manual

STAT

~+

TOT

COU

UTPC

HP-28S

statistics

~

MEAN CORR

UTPF

commands

n x m matrix called

matrix is

The not the numbers), data statistics matrix . data

Data

defined

current

already

statistics matrix

exist,

command

and

point

entered

points

that

Point

1

2 X

to

when

~

+. A

is

stored

The n dimension

have

N~

SDEV

COY

UTPN

deal

the

current statistics matrix.

be

a matrix

~DAT

you

begin

data

point

as

one

sets

the m dimension

been

entered

Coordinate

1 2 .

X

11

21

CU

VAR

LR

UTPT

with

statistical

stored

in

the

is created automatically, if it

entry

of

statistical is a vector row

in

of

the

statistics matrix.

(number

X

12

X

22

as

illustrated

of rows) is

Number

STO~

MAX~

PRDEV

COMB

data

The

variable

m

coordinate

of

below:.

..

.. .

...

RCU

MIN~

PERM

collected in

current

data

statistics

~DAT.

points values (real

The

columns)

the

number

m

X

X2m

1m

does

with

of

an

first

the

of

n

Certain of numbers, the list tion

statistics

the

statistics matrix. User variable

the

columns

are

the

slope

of

the

linear

X

commands

first two

with

the

and

regression

n1

intercept

combine

of

which

command

X

n2

data

~PAR

identify

COL~.

computed

.. .

from two specified

contains a list

the

two

columns. You

The

from

last two

the

numbers

most

LR.

Dictionary

Xnm

columns

of

four

real

select

in

the

recent execu-

245

un

STAT

Because ndry the

The

(covariance)

ple

If

the

lation

1.

2.

3.

4.

These data

~DAT

commands

specific statistics

commands

calculate

of

the

population. These

data

represent

statistics as follows.

Execute data.

Execute Execute SDEV,

population. Execute ~-

data.

~+

commands

to

or

delete

and

~PAR

are

ordinary

to recall, view,

commands

SDEV (standard deviation),

sample

the

entire

MEAN

~+

~-

to

add

VAR,

DROP

allow

data

from

return a data

you to select a statistics matrix,

or

alter their contents, in

that

statistics using

commands

population,

the

mean

or

COY.

to

remove

the

matrix.

variables, you

deal

with

VAR

data

that

are described in detail below.

you

can

point

representing

data

point

to

The

result is

the

mean

data

CL~

can

addition

the

variables.

(variance),

represent a sam-

calculate

the

data.

the

statistics for

point

STO~

and

use

ordi-

and

the

popu-

mean

from

RCL~

to

COY

the

add

~+

~

+

adds

~DAT.

246

[X1

[[x11

one

or

Dictionary

Level 1

x

X2

•..

X12

more

Sigma Plus

xm]

...

x1m]

data

I

..

.. ..

points to

the

current

Command

statistics matrix

...

STAT

For a statistics matrix

~+

in several ways:

Entering one

gument

Entering one

argument

Entering several

n

rows

of

In

each

case,

rent

statistics matrix creates it as does

exist, number doesn't

~-

data

for

~

+ is a real

data

for

~

+ is a vector

m real

the

an

n x m matrix

an

error occurs if it

of

coordinate

match

the

data

coordinate

number

with

m columns, you

point with a single coordinate value.

number

point with multiple coordinate values.

points.

of

.

m real

The

can

coordinate

argument

enter

for

values.

~

the

argument

+ is a matrix

values.

stored

values

values are in

~DAT.

stored

does

in

of

columns

Sigma Minus

not

each

..

added

If

~DAT

in

the

contain

data

in

as

new does

variable

a real matrix,

point

entered

~DAT.

Level 1

x

rows

to

not

exist,

~DAT.

If

with

Command

The

the

cur-

~+

~DAT

or

if

~+

for

ar-

of

the

~

-

returns corresponding by

~+

into

matrix is

The to

the

deleted

vector

returned

statistics matrix

a vector

to

the

of

the

coordinate

statistics matrix

.

by ~ -

m real

by

~

numbers,

values

~DAT.

can

be

+ .

in

The

edited

or

one

number

the

last

data

last

row

or replaced,

Dictionary

of

if m =

point

the

then

1,

entered

statistics

restored

247

..• STAT

N~

returns stored of

CL~

STO~

the

in

matrix.

clears

the

number

~DAT.

The

the

statistics matrix

of

number

Level 1

obj

Sigma N

It

data

points

of

points

Clear Sigma

It

by

purging

Store Sigma

It

Level 1

n

entered

is

equal

the

in

the

statistics matrix

to

the

number

~DAT

Command

of

Command

variable.

Command

rows

STO~

~DAT.

RCL~

takes

returns rectory. (when

248

~DAT

Dictionary

To

an

object from

the

recall

doesn't

Recall Sigma

contents

the

of

statistics matrix

exist

in

the

stack

Level 1

It

variable

current

and

stores it

obj

~DAT

from

from a

directory), execute

in

the

parent

variable

Command

current

di-

directory

::

D AT .

...

STAT

TOT

These column

commands

TOT

computes

in

the

statistics matrix

real

numbers,

MEAN

of

the

MEAN

compute

current

the

sum

or

as a single real

SDEV

elementary

statistics matrix.

Total Command

• x

of

each

of

the m columns

~DAT.

The

sums number

Mean

• x

VAR

statistics for

Level 1

are

returned

if m =

Level 1

MAX2:

the

data

of

coordinate

as a vector

1.

MIN2:

in

each

values

of

m

Command

MEAN values of computed

where of

in

m real

xi is

data

computes

points.

the

statistics matrix

numbers,

from

the

or

the

ith

coordinate

mean

of

each

~DAT,

as a single real

formula

mean

value

of

the m columns

and

returns

number

in a column,

if m = 1.

the

mean

and

n is

Dictionary

of

coordinate as a vector

The

mean

the

number

is

249

...

STAT

SDEV Standard Deviation Command

Level 1

.. x

SDEV columns standard a single real from

where data

computes

of

deviations

the

formula

xi

is

the

in this

coordinate

number

column,

VAR

computes the m columns turned

m =

1.

as

a vector

The

variance is

the

are

ith

coordinate

the

sample

of

the

of

sample

values

returned

if m =

and

n is

variance

current

m real

computed

11

standard

in

1.

The

value

the

deviation

the

current

as a

vector

standard

in a column,

number

of

each

statistics matrix.

of

m real

deviations

of

data

x is

numbers,

are

the

points.

of

the

computed

mean

Variance Command

Level 1

.. x

of

the

statistics matrix.

numbers,

from

1/

1

L (Xi -

1 i = l

coordinate

or

as

a single real

the

formula

X)

2

values

The

variance is re-

in

each

number

m

The

or

of

as

the

of

if

where data

250

Xi is

in this

Dictionary

the

ith

coordinate

column, and

n is

value

the

in a column,

number

of

x is

data

the

points

mean

.

of

the

•.. STAT

MAX~

MAX~ finds

of

the

current

of

m real

MIN~

of

the

m real

numbers,

finds

current

numbers,

the

maximum

statistics matrix.

or

as a single real

the

minimum

statistics matrix .

or

as a single real

Maximum Sigma

Level 1

• x

coordinate

The

Minimum Sigma Command

coordinate

The

value

in

maxima are

number

Level

• x

value in

minima

number

are

if m = 1.

each

returned

if m =

1

each

returned

Command

of

the m columns

as a vector

1.

of

the m columns

as a vector of

COL~

CORR

Level

2

COY

Sigma Columns Command

Level 1

LR

PREDV

•

Dictionary

251

...

STAT

COL~

stores

~PAR.

matrix pairs pendent

SCL~

For CORR

takes two

them

The

numbers

~DAT,

of

columns.

variable for

.

n2

designates

and

column

as

the

first two objects in

identify

and

are

nl

designates

LR,

the

COY, the

numbers,

column

used

by

or

the

dependent

order

nl

the

numbers

statistics

the

column

horizontal

variable or

of

the

and

n2' from

list

contained

in

commands

corresponding

coordinate

the

two

column

the

current

that

vertical

numbers

stack

in

the

work

to

for

DRW~

coordinate

and

variable

statistics

with

the

inde-

or

is

unimportant.

If

any

of

the

two-column

not

yet exist, it is automatically created

and

n2

=

2.

commands

is executed

with

default values

when

~PAR

nl

does

= 1

CORR Correlation Command

Level 1

It

correlation

CORR the elements the

returns

current

of

formula

the

correlation of two

statistics matrix.

~PAR

(default 1

The

and

columns

2).

The

of

coordinate

are specified

correlation

by

the

is

computed

values in

first two

from

.

where

xiII is

ordinate

nl'

xn

' is

2

data

points.

252

"

L

(XiII

I -

XIII)

(Xi"2

- X

)

i = 1

the

ith

in

the

coordinate

column

of

the

I 2

value

the

mean

Dictionary

n2'

data

value in

xn

is

the

I

in

column

1I2

column

mean

n2'

and

nl'

of

xin is

the

n is

data

the

ith co-

in

column

number

of

...

STAT

COY

returns columns the

first two

computed

where nate

xn;:

pomts.

LR

value

is

the

xil11

of

the

from

is

in

mean

the

sample

current

elements

the

formula

the

ith

coordinate

the

column

of

the

Covariance Command

Level 1

..

covariance

covariance of

statistics matrix.

in

~PAR

(default 1

value

n2' x

data

Linear Regression Command

nl

in

column

is

the

coordinate

The

columns

and

in

column

the

mean

of

n2'

and

Level

2 Level 1

..

intercept slope

are specified

2).

The

nl'

xil12 is ith coordi-

the

data

n is

the

number

values

in

covariance is

in

column

of

two

by

nl'

data

LR

computes independent rent

statistics matrix.

data

are

specified

The

intercept

and 1 of

the ficients as the

variable

the

linear

regression

data

column,

The

by

the

first two elements

and

slope

of

stack, respectively.

the

third (intercept)

~PAR.

of a dependent

where

the

columns

of

independent

regression line are

LR

also stores

and

fourth

data

column

of

data

exist in

and

in

~PAR

(default 1

returned

these

regression coef-

(slope) items in

Dictionary

on

the

cur-

dependent

and

to levels 2

the

list

253

an

2).

in

·uSTAT

PREDV Predicted Value Command

Level 1 Level 1

x

PREDV using LR

computes a predicted

the

linear

regression coefficients

and

stored

in

the

variable

predicted value =

The

regression coefficients intercept

third

and

fourth cute PREDV of

zero is

zero.

used

UTPC

The

HP-28S provides four upper-tail probability

you

can

use to

The

upper-tail probability where

F(x)

items, respectively, in

without

for

UTPF

that X is

is

the

having

both

coefficients, so

UTPN

determine

probability function

greater

distribution

the

•

value from a real

~PAR:

(x x slope)

and

previously executed

statistical significance

of a random

than a number

function

predicted

most

value

number

recently

+ intercept.

slope

are

stored

the

variable

that

PREDV will always

UTPT

of

x,

X.

and

COMB

commands,

is

argument

computed

by

LR

~PAR.

LR, a default

If

you exe-

PERM

which

of

test statistics.

variable X is

equal

to 1 - F(x),

x,

with

as

the

value

return

the

The

inverses fidence intervals. function is a value from 0 as a percent, example, which 100% -

254

of

the

90th

the

probability

90%

= 10%.

Dictionary

distribution

The

argument

inverse function values are called percentiles . For

percentile

that

functions

through

of a distribution

the

random

are useful for constructing con-

of

an

1;

when

inverse

variable X is greater

upper-tail

the

argument

is

the

is expressed

number

probability

x for

than

x is

You

can ability normal

use

the

Solver to

functions. Suppose

distribution

. Let

P

M

x =

obtain

mean

the

you

wish

=

percentile/IOO

of

the

v = variance

random

·

inverses

to

distribution

variable

of

the

upper-tail

determine a percentile

..

STAT

of

prob-

the

UTPN distribution.

for X, create

and pr

Try a

Now

yi

(described below)

store it as

ess

SOLVR

normal

compute

elds

the

result X = 1.6449.

To

solve

1 - P =

the

program

.:,::

1 P -

the

current

to

produce

distribution

the

95th

returns

the

equation

utpn

t'1

',}

equation

Solver

with M = 0, V =

o 1

percentile:

.

95

upper-tail

(M,

~<

U T P t·j -

by

pressing I

menu

•

V,

:

X),

1:

probability

;,:.

,

SOLV I STEQ

for

normal

.

Then

Dictionary

255

·

..

STAT

UTPC

UTPC variable dom

returns

is

of

the

greater

UTPF

Level

3

n1

UTPF

returns

dom

variable is greater denominator be

positive integers .

UTPN

Upper Chi-Square Distribution Command

Level 2 Level 1 Level 1

n

the

probability

than

distribution. n

Upper Snedecor's f Distribution Command

Level

2

the

probability

degrees of

x

x,

where

Level 1

x •

than

freedom

Upper Norma. Distribution

utpc(n,

must

utpf

x,

where

•

n is

be

I

(nl'

of

the F distribution

utpc(n,

x)

that

a chi-square

the

number

a positive integer.

Level 1

utpf(n1, n2,

n2' x)

that

nl

and

n2

are

x)

of

degrees

x)

a Snedecor's F

the

numerator

.

nl

and

random

of

free-

ran-

and

n2

must

Command

Level

3 Level 2

m v

UTPN variable respectively, number.

256

returns

is

Dictionary

the

greater

of

the

Level 1

probability

than

x,

where m and

normal

I

x •

utpn

(m,

distribution. v

Level 1

utpn(m,

v,

x)

that a normal

v are

the

must

v,

x)

mean

be a

random

and

variance,

non-negative

•••

STAT

UTPT

Upper Student's t Distribution

Level 2 Level 1 Level 1

n x

•

UTPT returns the probability utpt(n, variable dom of the distribution.

COMB

is

greater than

Level 2 Level 1

n m

x,

where n is the

n must be a positive integer.

Combinations

•

x)

that

Level

utpt(n,

x)

a Student's t

number

1

of degrees of free-

Command

random

Command

COMB returns the number of combinations of n items taken m at a time:

m!

(n -m)!

n!

than

10

12

.

The arguments

n

C

m =

,

nand m must

be less

PERM

Level 2 Level 1

n m

PERM returns the time:

The arguments

nand

Permutations Command

number

of permutations of n items taken m

,

P

m =

n

m must be less

•

---------

(n

Level

11!

-

than

m}!

1

at

a

12

.

10

Dictionary

257