Statistical Functions Part One

INTERCEPT function points of intersection intersections mw added two entries INTERCEPT Calculates the point at which a line will intersect the y-values by using known x-values and y-values. Syntax INTERCEPT(DataY; DataX) DataY is the dependent set of observations or data. DataX 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.

COUNT function numbers;counting mw added one entry 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 function number of entries mw added one entry 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.UFI: fix to #i35888# 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.

B function probabilities of samples with binomial distribution mw added one entry B Returns the probability of a sample with binomial distribution. Syntax B(Trials; SP; T1; T2) Trials is the number of independent trials. SP is the probability of success on each trial. T1 defines the lower limit for the number of trials. T2 (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%.

RSQ function determination coefficients regression analysis mw added regression analysis 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(DataY; DataX) DataY is an array or range of data points. DataX is an array or range of data points. Example =RSQ(A1:A20;B1:B20) calculates the determination coefficient for both data sets in columns A and B.

BETAINV function cumulative probability density function;inverse of mw added one entry 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. Example =BETAINV(0.5;5;10) returns the value 0.33.

BETADIST function cumulative probability density function;calculating mw added one entry BETADIST Returns the beta function. Syntax BETADIST(Number; Alpha; Beta; Start; End; Cumulative) 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. Cumulative (optional) can be 0 or False to calculate the probability density function. It can be any other value or True or omitted to calculate the cumulative distribution function. Example =BETADIST(0.75;3;4) returns the value 0.96

BINOMDIST function 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).

CHISQINV function CHISQINV Returns the inverse of CHISQDIST. Syntax Probability is the probability value for which the inverse of the chi-square distribution is to be calculated. Degrees Of Freedom is the degrees of freedom for the chi-square function.

CHIINV function CHIINV Returns the inverse of the one-tailed probability of the chi-squared distribution. Syntax CHIINV(Number; DegreesFreedom) Number is the value of the error probability. DegreesFreedom 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 function 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(DataB; DataE) DataB is the array of the observations. DataE 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.

CHIDIST function 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; DegreesFreedom) Number is the chi-square value of the random sample used to determine the error probability. DegreesFreedom 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%.

CHISQDIST function chi-square distribution CHISQDIST Returns the value of the probability density function or the cumulative distribution function for the chi-square distribution. Syntax CHISQDIST(Number; Degrees Of Freedom; Cumulative) Number is the number for which the function is to be calculated. Degrees Of Freedom is the degrees of freedom for the chi-square function. Cumulative (optional): 0 or False calculates the probability density function. Other values or True or omitted calculates the cumulative distribution function.

EXPONDIST function exponential distributions EXPONDIST Returns the exponential distribution. Syntax EXPONDIST(Number; Lambda; C) Number is the value of the function. Lambda is the parameter value.UFI removed a double bookmark 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.