Basic Statistics With Excel

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Basic Statistics

with Microsoft Excel

Helen Dixon



Aim and Objectives

Aim of today¶s course

To illustrate how Excel can be used to carryout some basic statistical analyses and tests

Objectives

To show you how to use some of thestatistical worksheet functions available withinExcel

To show you how to use some of the toolsavailable in the Analysis ToolPak

To make you aware of the limitations of Excel



Why use Excel?

Software more accessible

Previous familiarity with software

Easy to format output

Better charting facilities than some

statistical applications

Access to other key Excel facilities

Easy to use results with other applications



Problems with Excel Errors due to rounding, missing data or extreme

values

Not suitable for very large data sets

Output labelled or arranged inappropriately Need to repeat processes for different variables

or options

No record of analyses

Some algorithms are numerically unstable - littleor no information about algorithms employed

Analysis ToolPak results are not dynamic andmay vary with results generated by functions



Statistical Functions Frequency Distributions

Mean, Median and Mode

Percentiles and Quartiles

Deviation and Squared Deviation about

the Mean

Variance and Standard Deviation

Covariance and the Correlation Coefficient



Frequency Use COUNTIF to count how many times

an item appears in a list

=COUNTIF(range, criteria) Use FREQUENCY to calculate how often

values occur within a range

=FREQUENCY(data_array, bins_array)

Can also use Histogram tool in Analysis

Toolpak



Mean, Median, Mode Use AVER AGE or AVER AGE A to

calculate the arithmetic mean

= AVER AGE(number1, number2, etc.)

Use MEDI AN to return the middle number

=MEDI AN(number1, number2, etc)

Use MODE to return the most common

value

=MODE(number1, number2, etc)



Percentiles and Quartiles Use PERCENTILE to return the kth percentile of

a data set

=PERCENTILE(array, percentile)

Percentile argument is a value between 0 and 1

Use QU ARTILE to return the given quartile of a

data set

=QU ARTILE(array, quart)

Quart is 1, 2, 3 or 4

IQR = Q3-Q1

May return different values to statistical package



Variance and Standard Deviation Use V AR, V AR A, V ARP or V ARP A to

calculate the variance for a range

E.g. =V AR(value1, value 2, etc.)

Squared deviations about the mean/N or /n-1

Use STDEV, STDEV A, STDEVP or

STDEVP A to calculate the standard

deviation for a range

=E.g. =STDEV(value1, value2, etc.)

Positive square root of variance



Covariance and

the Correlation Coefficient Use COV AR to calculate the covariance

=COV AR(array1, array2)

Average of products of deviations for eachdata point pair

Depends on units of measurement

Use CORREL to return the correlationcoefficient

=CORREL(array1, array2)

Returns value between -1 and +1

Also available in Analysis ToolPak



Probability Numerical measure of the likelihood that

an event will occur

Some probabilities that can be calculatedusing Excel:

Binomial Probabilities

Poisson Probabilities

Hypergeometric Probabilities

Normal Probabilities

Exponential Probabilities



Binomial Probabilities Use BINOMDIST to compute binomial

distribution probabilities and cumulative

binomial probabilities

=BINOMDIST(number_s, trials, probability_s,

cumulative)

Calculates the probability that a sequence of independent trials with two possible outcomes

will have a given number of successes

Cumulative is either TRUE or F ALSE



Poisson Probabilities Use POISSON to compute Poisson

Probabilities

=POISSON(x, mean, cumulative)

Shows the probability of x occurrences of an

event over a specified interval of time or

space



Hypergeometric Probabilities Use HYPGEOMDIST to compute

hypergeometric probabilities

=HYPGEOMDIST(sample_s,

number_sample, population_s, number_pop) Computes the probability of x successes

(sample_s) in n trials (number_sample) whenthe trials are dependent

Similar to Binomial except trials are notindependent ± probability of success changesfrom trial to trial

Does not compute cumulative probabilities



Normal Probabilities Use NORMSDIST or NORMDIST tocompute the cumulative probability

=NORMSDIST(z)

=NORMDIST(x, mean, standard_dev,cumulative)

Use NORMSINV or NORMINV to computethe z or x value given a cumulativeprobability

=NORMSINV(probability)

=NORMINV(probability, mean, standard_dev)



Exponential Probabilities Use EXPONDIST to compute exponential

probabilities

=EXPONDIST(x, lambda, cumulative) x is the random variable

Lambda is 1/mean

Useful in computing probabilities for the time it

takes to complete a task



Analysis ToolPak

Descriptive Statistics

Correlation

Linear Regression

t-Tests

z-Tests ANOV A

Covariance



Descriptive Statistics Mean, Median, Mode

Standard Error

Standard Deviation

Sample Variance

Kurtosis

Skewness Confidence Level for

Mean

Range

Minimum

Maximum

Sum

Count

kth Largest kth Smallest





t-Tests and z-Tests Used to test hypotheses by comparing

means

If sample means are equal suggests bothsamples came from same population

t-Test ± n <30

Equal or unequal variances or paired test Check result using TTEST function

z-Test ± n>30

Used for means with known variances



ANOV

A: A

nalysis of Variances Compares variances in two or more data sets

If difference is found it can be assumed that the

means of the data sets are different

Single Factor ± use instead of t-Test for more

than 2 samples

Two Factor with Replication ± useful when datacan be classified along 2 different dimensions

Two Factor without Replication ± as above but

only one observation for each pair



PivotTables Use for crosstabulations

Data must be in tabular format: columns

with headings, no blank columns Easy to pivot data

Easy to create PivotCharts

Can summarise and analyse data withoutaffecting data source



Final Tips Excel only suitable for basic analysis using small

data sets

Later versions of Excel more reliable than Excel97

Check Analysis TookPak results with worksheet

functions

Check overall results by hand or with dedicated

statistical package

Documents

Basic Statistics With Excel