Download Appendix-B2 - Real Statistical

MEAN(R1)
IQR(R1)
MAD(R1)
RNG(R1)
STDERR(R1)
RANK_AVG(x, R1, order)
FREQTABLE(R1)
same as AVERAGE(R1)
interquartile range of data in range R1
median absolute deviation of the data in range R1
range of data in range R1, i.e. MAX(R1) – MIN(R1)
standard error of the data in range R1, i.e. STDEV(R1)/SQRT(COUNT(R1))
rank of x in range R1 taking ties into account; order is optional (default = 0),
where a zero value indicates increasing order and a non-zero value indicates
decreasing order; equivalent to Excel 2010’s RANK.AVG(x, R1, order).
array function which returns an n x 3 array which contains the frequency table
for the data in range R1, where n = the number of unique values in R1 (i.e. the
number of data elements in R1 without duplicates)
CONFIDENCE_T(alpha,
s, size)
T_CONF(R1, alpha)
T_LOWER(R1, alpha)
T_UPPER(R1, alpha)
DF_POOLED(R1, R2)
STDERR_POOLED(R1, R2)
STDEV_POOLED(R1, R2)
VAR_POOLED(R1, R2)
T_DIST(x, df, cum)
the value k such that x − k, x + k is the confidence interval for the
population mean based on the stated alpha value, standard deviation s and
sample size, assuming a t distribution
the value k such that 𝑥 − 𝑘, 𝑥 + 𝑘 is the confidence interval for the
population mean based on the stated alpha value and sample data in range R1
assuming a 𝑡 distribution
the value 𝑥 − 𝑘 such that 𝑥 − 𝑘, 𝑥 + 𝑘 is the confidence interval for the
population mean based on the stated alpha value and sample data in range R1
assuming a 𝑡 distribution
the value 𝑥 + 𝑘 such that 𝑥 − 𝑘, 𝑥 + 𝑘 is the confidence interval for the
population mean based on the stated alpha value and sample data in range R1
assuming a t distribution
degrees of freedom for the two sample t test for samples in ranges R1 and R2,
especially when the two samples have unequal variances
pooled standard error for two sample t test for samples in ranges R1 and R2
pooled standard deviation for the two sample t test for samples in ranges R1
and R2 when the two samples have equal variances
pooled variance for the two sample t test for samples in ranges R1 and R2
when the two samples have equal variances
value of the cumulative distribution function of the 𝑡 distribution with df
degrees of freedom at x when cum = TRUE, and value of the pdf of the 𝑡
distribution with df degrees of freedom at x when cum = FALSE
NORM_CONF(R1, alpha)
NORM_LOWER(R1,
alpha)
NORM_UPPER(R1, alpha)
SHAPIRO(R1)
SWTEST(R1)
the value k such that x − k, x + k is the confidence interval for the
population mean based on the stated alpha value and sample data in range R1
assuming a normal distribution
the value 𝑥 − 𝑘 such that 𝑥 − 𝑘, 𝑥 + 𝑘 is the confidence interval for the
population mean based on the stated alpha value and sample data in range R1
assuming a normal distribution
the value 𝑥 + 𝑘 such that 𝑥 − 𝑘, 𝑥 + 𝑘 is the confidence interval for the
population mean based on the stated alpha value and sample data in range R1
assuming a normal distribution
the Shapiro-Wilk test statistic W for the data in the range R1
the p-value of the Shapiro-Wilk test on the data in range R1
CHI_STAT2(R1, R2)
CHI_MAX2(R1, R2)
CHI_STAT(R1)
CHI_MAX(R1)
CHI_TEST(R1)
CHI_MAX_TEST(R1)
CHISQ_DIST(x, df, cum)
FISHERTEST(R1, t)
Pearson’s chi-square statistic for observation values in range R1 and
expectation values in range R2
maximum likelihood chi-square statistic for observation values in range R1 and
expectation values in range R2
Pearson’s chi-square statistic for observation values in range R1
maximum likelihood chi-square statistic for observation values in range R1
p-value for Pearson’s chi-square statistic for observation values in range R1
p-value for maximum likelihood chi-square statistic for observation values in
range R1
value of the cumulative distribution function of the chi-square distribution
with df degrees of freedom at x when cum = TRUE, and value of the pdf of the
chi-square distribution with df degrees of freedom at x when cum = FALSE
probability calculated by the Fisher exact test for the 2 x 2 contingency table
in range R1 where t = the number of tails: 1 (one-tail) or 2 (two tail)
COVARP(R1, R2)
COVARS(R1, R2
CORREL_ADJ(R1, R2)
MCORREL(R, R1, R2)
COV(R1)
COVP(R1)
population covariance of the populations defined by ranges R1 and R2;
equivalent to COVAR(R1, R2)
sample covariance of the samples defined by ranges R1 and R2; equivalent to
COVAR(R1, R2) * n/(n-1) where n = COUNT(R1) = COUNT(R2)
adjusted correlation coefficient for the data sets defined by ranges R1 and R2
multiple correlation of dependent variable z with x and y where the samples
for z, x and y are the ranges R, R1 and R2 respectively
array function which returns the sample covariance matrix for the array
defined by range R1
array function which returns the population covariance matrix for the array
defined by range R1
DESIGN(R1)
HAT(R1)
CORE(R1)
LEVERAGE(R1)
RegCov(R1, R2)
RegCoeff(R1, R2)
RegCoeffSE(R1, R2)
RegY(R1, R2)
RegE(R1, R2)
RegStudE(R1, R2)
the design matrix for the data in R1
the hat matrix for the data in R1
the core of the hat matrix for the data in R1
the leverage vector = diagonal of hat matrix for the data in R1
the covariance matrix for the regression coefficients of the regression line
a vector with the regression coefficients for the regression line
a vector with the standard errors of the coefficients for the regression line
a vector of predicted values for Y based on the regression line = TREND(R2,R1)
a vector of residuals based on the regression line
a vector of studentized residuals based on the regression line
RegAIC(R1, R2)
RegAICc(R1, R2)
p-value of the test of the significance of X data in R3 (reduce model) vs. X data
in R1 (full model)
the Akaike’s Information Criterion (AIC) for the regression model
corrected AICc for the regression model
TOLERANCE(R1, j)
Tolerance of the 𝑗th variable for the data in range R1; i.e. 1 − 𝑅𝑗2
VIF(R1, j)
VIF of the 𝑗th variable for the data in range R1; i.e. 1 − 𝑅𝑗2
RSquareTest(R1, R3, R2)
LEVENE(R1)
DunnSidak(α, k)
FSTAR(R1)
DFSTAR(R1)
BFTEST(R1)
p-value of for
Levene’s test for the data in range R1 (organized by columns)
/
1 𝑘
1– 1– 𝛼
Brown-Forsythe’s test statistic F* on the data in range R1
df* for Brown-Forsythe’s test on the data in range R1
p-value of the Brown-Forsythe’s test statistic on the data in range R1
SignTest(R1, m)
p-value for the sign test where R1 contains the sample data and m = the hypothesized median
WILCOXON(R1, R2)
WILCOXON1(R1, n)
minimum of W and W’ for the samples contained in ranges R1 and R2
minimum of W and W’ for the samples contained in the first n columns of range R1 and the
remaining columns of range R1. If the second argument is omitted it defaults to 1
WTEST(R1, R2)
p-value of the Wilcoxon rank-sum test for the samples contained in ranges R1 and R2
WTEST1(R1, n)
p-value of the Wilcoxon rank-sum test for the samples contained in the first n columns of range
R1 and the remaining columns of range R1. If the second argument is omitted it defaults to 1
MANN(R1, R2)
MANN1(R1, n)
MTEST(R1, R2)
MTEST1(R1, n)
RankSign(R1)
RTEST(R1)
RSignPair(R1)
RTESTPair(R1)
KRUSKAL(R1)
KTEST(R1)
FRIEDMAN(R1)
FrTEST(R1)
U for the samples contained in ranges R1 and R2
U for the samples contained in the first n columns of range R1 and the remaining columns of
range R1. If the second argument is omitted it defaults to 1
p-value of the Mann-Whitney U test for the samples contained in ranges R1 and R2
p-value of the Mann-Whitney U test for the samples contained in the first n columns of range R1
and the remaining columns of range R1. If the second argument is omitted it defaults to 1
T for a single sample contained in range R1
p-value for Rank-Sign test using the normal distribution approximation for the sample contained
in range R1
T for a pair of samples contained in range R1, where R1 consists of two columns, one for each
paired sample
p-value for Rank-Sign test using the normal distribution approximation for the pair of samples
contained in range R1, where R1 consists of two columns, one for each paired sample
value of the Kruskal-Wallis’s test statistic on the data in range R1
p-value of the Kruskal-Wallis’s test on the data in range R1
value of the Friedman’s test statistic on the data in range R1
p-value of the Friedman’s test on the data in range R1
MULTINOMDIST(R1, R2)
value of multinomial distribution where R1 contain the number of successes
and R2 contain the corresponding probabilities of success
DET(R1)
DIAG(R1)
IDENTITY(R1)
ISCELL(R1)
ISSQUARE(R1)
LENGTH(R1)
NORM(R1)
TRACE(R1)
same as MDETERM(R1)
array function that returns a column vector with the values on the diagonal of
the matrix in range R1 (esp. useful when R1 is a square matrix)
array function that returns an identity matrix of the size of the highlighted
range
returns TRUE if R1 is a single cell and FALSE otherwise
returns TRUE if R1 is a square range and FALSE otherwise
length of matrix in range R1 = the square root of the sum of the squares of all
the elements in R1 (esp. useful for column or row vectors)
array function that returns the normalized version of the matrix in range R1
trace of matrix in range R1
ELIM(R1)
LINEQU(R1)
array function which outputs the results of Gaussian Elimination on the
augmented matrix found in the array R1. The shape of the output is the same
as the shape of R1
array function which returns a column vector with solution to linear equations
defined by R1; returns an error if no solution or the solution is not unique
INTERPOLATE(r, r1, r2,
v1,v2)
MLookup(R1, r, c)
ILookup(R1, r, c)
the value between v1 and v2 that are proportional to the distance that r is
between r1 and r2, where v1 corresponds to r1 and v2 corresponds to r2
the value in the table defined by range R1 in the row headed by r and the
column headed by c.
the value in the table defined by range R1 corresponding to row r and column
c. If r or c can refer to some value that must be interpolated between row or
column headings, provided those headings are numbers. If the first row (or
column) heading is preceded by “>” it refers to values smaller than the next
row (or column heading). If the last row (or column) heading is preceded by
“>” it refers to values bigger than the previous row (or column heading).
TauCRIT(n, α, t)
RhoCRIT(n, α, t)
RSignCRIT(n, α, t)
KSCRIT(n, α, t)
WCRIT(n1, n2, α, t)
MCRIT(n1, n2, α, t)
QCRIT(k, df, α, t)
RLowerCRIT(n1, n2)
RUpperCRIT(n1, n2)
SWLookup(n, W)
critical value in the Kendall’s Tau table
critical value in the Spearman’s Rho table
critical value in the Rank Sign table
critical value in the Kolmogorov-Smirnov table
critical value in the Wilcoxon Rank-Sum table
critical value in the Mann-Whitney table
critical value in the Studentized Range Q table
the lower value in the Runs Test table
the upper value in the Runs Test table
The p-value for n and W in the Shapiro-Wilk table 2
QSORT(R1, b)
NODUPES(R1)
REVERSE(R1)
RESHAPE(R1)
SHUFFLE(R1)
RANDOMIZE(R1)
array function which fills highlighted array with data from R1 in sorted order
(by columns); b is an optional parameter (default = TRUE); if b is TRUE then
sort is in ascending order and if b is FALSE (or 0) sort is in descending order.
array function which fills highlighted array with data from R1 eliminating any
duplicates (by columns); assumes that range R1 is in sorted order (by column).
array function which fills highlighted array with data from R1 in reverse order
(by columns)
array function which fills highlighted array with data from R1 (by columns)
array function which fills highlighted array with a permutation of the data
from R1 (selection without replacement)
array function which fills highlighted array with a random selection of data
from R1 (selection replacement)
SSRes(R1, R2) = 𝑆𝑆𝑅𝑒𝑠
SSReg(R1, R2) = 𝑆𝑆𝑅𝑒𝑔
SSRegTot(R2) = 𝑆𝑆𝑇
MultipleR(R1, R2) = 𝑅
REGF(R1, R2) = 𝐹
dfRes(R1) = 𝑑𝑓𝑅𝑒𝑠
dfReg(R1) = 𝑑𝑓𝑅𝑒𝑔
dfRegTot(R1) = 𝑑𝑓𝑇
RSquare(R1, R2) = 𝑅 2
RegTEST(R1, R2) = p-value
MSRes(R1, R2) = 𝑀𝑆𝑅𝑒𝑠
MSReg(R1, R2) = 𝑀𝑆𝑅𝑒𝑔
MSRegTot(R1, R2) = 𝑀𝑆𝑇
AdjRSquare(R1, R2) = Adjusted 𝑅 2
RegSE(R1, R2) = standard error = 𝑀𝑆𝑅𝑒𝑠
SSW(R1) = 𝑆𝑆𝑊
SSBet(R1) = 𝑆𝑆𝐵
SSTot(R1) = 𝑆𝑆𝑇
ANOVA1(R1) = 𝑀𝑆𝐴 /𝑀𝑆𝑊
dfW(R1) = 𝑑𝑓𝑊
dfBet(R1) = 𝑑𝑓𝐵
dfTot(R1) = 𝑑𝑓𝑇
ATEST(R1) = p-value for A factor
MSW(R1) = 𝑀𝑆𝑊
MSBet(R1) = 𝑀𝑆𝐵
MSTot(R1) = 𝑀𝑆𝑇
SSWF(R1, r) = 𝑆𝑆𝑊
SSRow(R1, r) = 𝑆𝑆𝐴
SSCol(R1, r) = 𝑆𝑆𝐵
SSInt(R1, r) = 𝑆𝑆𝐴𝐵
SSTot(R1, r) = 𝑆𝑆𝑇
dfWF(R1, r) = 𝑑𝑓𝑊
dfRow(R1, r) = 𝑑𝑓𝐴
dfCol(R1, r) = 𝑑𝑓𝐵
dfInt(R1, r) = 𝑑𝑓𝐴𝐵
dfTot(R1, r) = 𝑑𝑓𝑇
MSWF(R1, r) = 𝑀𝑆𝑊
MSRow(R1, r) = 𝑀𝑆𝐴
MSCol(R1, r) = 𝑀𝑆𝐵
MSInt(R1, r) = 𝑀𝑆𝐴𝐵
MSTot(R1, r) = 𝑀𝑆𝑇
ANOVARow(R1, r) = 𝑀𝑆𝐴 /𝑀𝑆𝑊
ANOVACol(R1, r) = 𝑀𝑆𝐵 /𝑀𝑆𝑊
ANOVAInt(R1, r) = 𝑀𝑆𝐴𝐵 /𝑀𝑆𝑊
ATESTRow(R1, r) = p-value for A factor
ATESTCol(R1, r) = p-value for B factor
ATESTInt(R1, r) = p-value for AB factor
Cell
F4
F5
F6
F7
F8
Content
=MIN(A4:A13)
=QUARTILE(A4:A13,1)-F4
=MEDIAN(A4:A13)-QUARTILE(A4:A13,1)
=QUARTILE(A4:A13,3)-MEDIAN(A4:A13)
=MAX(A4:A13)-QUARTILE(A4:A13,3)