Statistical Functions Part One
B
Returns the probability of a sample with binomial distribution.
Syntax
B(trials;SP;T_1;T_2)
Trials is the number of independent trials.
SP is the probability of success on each trial.
T_1 defines the lower limit for the number of trials.
T_2 (optional) defines the upper limit for the number of trials.
Example
What is the probability with ten throws of the dice, that a six will come up exactly twice? The probability of a six (or any other number) is 1/6. The following formula combines these factors:
=B(10; 1/6; 2) returns a probability of 29%.
BETADIST
Returns the cumulative beta probability density function.
Syntax
BETADIST(Number;Alpha;Beta;Start;End)
Number is the value between Start and End at which to evaluate the function.
Alpha is a parameter to the distribution.
Beta is a parameter to the distribution.
Start (optional) is the lower bound for number.
End (optional) is the upper bound for number.
In the OpenOffice.org Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.
Example
=BETADIST(0.75; 3; 4) returns the value 0.96
BETAINV
Returns the inverse of the cumulative beta probability density function.
Syntax
BETAINV(Number;Alpha;Beta;Start;End)
Number is the value between Start and End at which to evaluate the function.
Alpha is a parameter to the distribution.
Beta is a parameter to the distribution.
Start (optional) is the lower bound for number.
End (optional) is the upper bound for number.
In the OpenOffice.org Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.
Example
=BETAINV(0.5; 5; 10) returns the value 0.33.
BINOMDIST
Returns the individual term binomial distribution probability.
Syntax
BINOMDIST(X;trials;SP;C)
X is the number of successes in a set of trials.
Trials is the number of independent trials.
SP is the probability of success on each trial.
C = 0 calculates the probability of a single event and C = 1 calculates the cumulative probability.
Example
=BINOMDIST(A1; 12; 0.5; 0) shows (if the values 0 to 12 are entered in A1) the probabilities for 12 flips of a coin that Heads will come up exactly the number of times entered in A1.
=BINOMDIST(A1; 12; 0.5; 1) shows the cumulative probabilities for the same series. For example, if A1 = 4, the cumulative probability of the series is 0, 1, 2, 3 or 4 times Heads (non-exclusive OR).
CHIDIST
Returns the probability value from the indicated Chi square that a hypothesis is confirmed. CHIDIST compares the Chi square value to be given for a random sample that is calculated from the sum of (observed value-expected value)^2/expected value for all values with the theoretical Chi square distribution and determines from this the probability of error for the hypothesis to be tested.
The probability determined by CHIDIST can also be determined by CHITEST.
Syntax
CHIDIST (Number; degrees_freedom)
Number is the chi-square value of the random sample used to determine the error probability.
Degrees_freedom are the degrees of freedom of the experiment.
Example
=CHIDIST(13.27; 5) equals 0.02.
If the Chi square value of the random sample is 13.27 and if the experiment has 5 degrees of freedom, then the hypothesis is assured with a probability of error of 2%.
CHIINV
Returns the inverse of the one-tailed probability of the chi-squared distribution.
Syntax
CHIINV(number; degrees_freedom)
Number is the value of the error probability.
Degrees_freedom is the degrees of freedom of the experiment.
Example
A die is thrown 1020 times. The numbers on the die 1 through 6 come up 195, 151, 148, 189, 183 and 154 times (observation values). The hypothesis that the die is not fixed is to be tested.
The Chi square distribution of the random sample is determined by the formula given above. Since the expected value for a given number on the die for n throws is n times 1/6, thus 1020/6 = 170, the formula returns a Chi square value of 13.27.
If the (observed) Chi square is greater than or equal to the (theoretical) Chi square CHIINV, the hypothesis will be discarded, since the deviation between theory and experiment is too great. If the observed Chi square is less that CHIINV, the hypothesis is confirmed with the indicated probability of error.
=CHIINV(0.05; 5) returns 11.07.
=CHIINV(0.02; 5) returns 13.39.
If the probability of error is 5%, the die is not true. If the probability of error is 2%, there is no reason to believe it is fixed.
CHITEST
Returns the probability of a deviance from a random distribution of two test series based on the chi-squared test for independence. CHITEST returns the chi-squared distribution of the data.
The probability determined by CHITEST can also be determined with CHIDIST, in which case the Chi square of the random sample must then be passed as a parameter instead of the data row.
Syntax
CHITEST(Data_B; Data_E)
Data_B is the array of the observations.
Data_E is the range of the expected values.
Example
|
Data_B (observed) |
Data_E (expected) |
|
|
1 |
195 |
170 |
|
2 |
151 |
170 |
|
3 |
148 |
170 |
|
4 |
189 |
170 |
|
5 |
183 |
170 |
|
6 |
154 |
170 |
=CHITEST(A1:A6; B1:B6) equals 0.02. This is the probability which suffices the observed data of the theoretical Chi-square distribution.
COUNT
Counts how many numbers are in the list of arguments. Text entries are ignored.
Syntax
COUNT(value1; value2; ... value30)
Value1; value2, ... are 1 to 30 values or ranges representing the values to be counted.
Example
The entries 2, 4, 6 and eight in the value 1 - 4 fields are to be counted.
COUNT(2;4;6;"eight") = 3. The count of numbers is therefore 3.
COUNTA
Counts how many values are in the list of arguments. Text entries are also counted, even when they contain an empty string of length 0. If an argument is an array or reference, empty cells within the array or reference are ignored.
Syntax
COUNTA(value1; value2; ... value30)
value1; value2, ... are 1 to 30 arguments representing the values to be counted.
Example
The entries 2, 4, 6 and eight in the value 1 - 4 fields are to be counted.
COUNTA(2;4;6;"eight") = 4. The count of values is therefore 4.
EXPONDIST
Returns the exponential distribution.
Syntax
EXPONDIST(Number; lambda; C)
Number is the value of the function.
Lambda is the parameter value.
C is a logical value that determines the form of the function. C = 0 calculates the density function, and C = 1 calculates the distribution.
Example
=EXPONDIST(3; 0.5; 1) returns 0.78.
INTERCEPT
Calculates the point at which a line will intersect the y-values by using known x-values and y-values.
Syntax
INTERCEPT(data_Y; data_X)
Data_Y is the dependent set of observations or data.
Data_X is the independent set of observations or data.
Names, arrays or references containing numbers must be used here. Numbers can also be entered directly.
Example
To calculate the intercept, use cells D3:D9 as the y value and C3:C9 as the x value from the example spreadsheet. Input will be as follows:
INTERCEPT(D3:D9;C3:C9) = 2.15.
RSQ
Returns the square of the Pearson correlation coefficient based on the given values. RSQ (also called determination coefficient) is a measure for the accuracy of an adjustment and can be used to produce a regression analysis.
Syntax
RSQ(Data_Y; Data_X)
Data_Y is an array or range of data points.
Data_X is an array or range of data points.
Example
=RSQ(A1:A20; B1:B20) calculates the correlation coefficient for both data sets in columns A and B.
Index
INTERCEPT function
points of intersection
intersections
COUNT function
numbers,counting
COUNTA function
number of entries
B function
probabilities of samples with binomial distribution
RSQ function
determination coefficients
regression analysis
BETAINV function
cumulative probability density function,inverse of
BETADIST function
cumulative probability density function,calculating
BINOMDIST function
CHIINV function
CHITEST function
CHIDIST function
EXPONDIST function
exponential distributions
density function
This help text is published from the OpenOffice-Help files under the Public Documentation License 1.0.
