 |
The
Statistics Calculator
Statistical
Analysis Tests At Your Fingertips
|
Counts menu
The Counts menu selection has
four tests that can be performed for
simple frequency data. The chi-square
test is used to analyze a contingency
table consisting of rows and columns to
determine if the observed cell
frequencies differ significantly from the
expected frequencies. Fisher's exact test
is similar to the chi-square test except
it is used only for tables with exactly
two rows and two columns. The binomial
test is used to calculate the probability
of two mutually exclusive outcomes. The
poisson distribution events test is used
to describe the number of events that
will occur in a specific period of time.
The Counts menu has four
selections:
Chi-square test
The chi-square is one of the most
popular statistics because it is easy to
calculate and interpret. There are two
kinds of chi-square tests. The first is
called a one-way analysis, and the second
is called a two-way analysis. The purpose
of both is to determine whether the
observed frequencies (counts) markedly
differ from the frequencies that we would
expect by chance.
The observed cell frequencies are
organized in rows and columns like a
spreadsheet. This table of observed cell
frequencies is called a contingency
table, and the chi-square test if part of
a contingency table analysis.
The chi-square statistic is the sum of
the contributions from each of the
individual cells. Every cell in a table
contributes something to the overall
chi-square statistic. If a given cell
differs markedly from the expected
frequency, then the contribution of that
cell to the overall chi-square is large.
If a cell is close to the expected
frequency for that cell, then the
contribution of that cell to the overall
chi-square is low. A large chi-square
statistic indicates that somewhere in the
table, the observed frequencies differ
markedly from the expected frequencies.
It does not tell which cell (or cells)
are causing the high chi-square...only
that they are there. When a chi-square is
high, you must visually examine the table
to determine which cell(s) are
responsible.
When there are exactly two
rows and two columns, the chi-square
statistic becomes inaccurate, and Yate's
correction for continuity is usually
applied. Statistics Calculator will automatically use
Yate's correction for two-by-two tables when the
expected frequency of any cell is less than 5 or the
total N is less than 50.
If there is only one column or one row
(a one-way chi-square test), the degrees
of freedom is the number of cells minus
one. For a two way chi-square, the
degrees of freedom is the number or rows
minus one times the number of columns
minus one.
Using the chi-square statistic and its
associated degrees of freedom, the
software reports the probability that the
differences between the observed and
expected frequencies occurred by chance.
Generally, a probability of .05 or less
is considered to be a significant
difference.
A standard spreadsheet interface is
used to enter the counts for each cell.
After you've finished entering the data,
the program will print the chi-square,
degrees of freedom and probability of
chance.
Use caution when interpreting the
chi-square statistic if any of the
expected cell frequencies are less than
five. Also, use caution when the total
for all cells is less than 50.
Example
A drug
manufacturing company conducted a survey
of customers. The research question is:
Is there a significant relationship
between packaging preference (size of the
bottle purchased) and economic status?
There were four packaging sizes: small,
medium, large, and jumbo. Economic status
was: lower, middle, and upper. The
following data was collected.
| |
Lower |
Middle |
Upper |
| Small |
24 |
22 |
18 |
| Medium |
23 |
28 |
19 |
| Large |
18 |
27 |
29 |
| Jumbo |
16 |
21 |
33 |
------------------------------------------------
Chi-square
statistic = 9.743
Degrees of freedom = 6
Probability of chance = .1359
Fisher's exact test
The chi-square statistic becomes
inaccurate when used to analyze
contingency tables that contain exactly
two rows and two columns, and that
contain less than 50 cases. Fisher's
exact probability is not plagued by
inaccuracies due to small N's. Therefore,
it should be used for two-by-two
contingency tables that contain fewer
than 50 cases.
Example
Here are the
results of a public opinion poll
broken down by gender. What is the exact
probability that the difference between
the observed and expected frequencies
occurred by chance?
| |
Male |
Female |
| Favor |
10 |
14 |
| Opposed |
15 |
9 |
-------------------------------------------
Fisher's exact
probability = .0828
Binomial test
The binomial distribution is used for
calculating the probability of
dichotomous outcomes in which the two
choices are mutually exclusive. The
program requires that you enter the
number of trials, probability of the
desired outcome on each trial, and the
number of times the desired outcome was
observed.
Example
If we were to
flip a coin one hundred times, and it
came up heads seventy times, what is the
probability of this happening?
Number of
trials: 100
Probability of success on each trial
(0-1): .5
Number of successes: 70
---------------------------------------------------------
Probability of
70 or more successes < .0001
Poisson distribution events test
The poisson distribution, like the
binomial distribution, is used to
determine the probability of an observed
frequency. It is used to describe the
number of events that will occur in a
specific period of time or in a specific
area or volume. You need to enter the
observed and expected frequencies.
Example
Previous
research on a particular assembly line
has shown that they have an average daily
defect rate of 39 products. Thus, the
expected number of defective products
expected on any day is 39. The day after
implementing a new quality control
program, they found only 25 defects. What
is the probability of seeing 25 or fewer
defects on any day?
Observed
frequency: 25
Expected frequency: 39
---------------------------------------------------
Probability of
25 or fewer events = .0226
How to Order Statistics Calculator
|
