Stats Final Equation

I = P/100(N)

Percentile

Sum of (X-Population Mean)²/N

Population Variance

Sqrt (Population Variance)

Population Standard Deviation

Sum of (X-Sample mean)²/N-1

Sample Variance calculation

(X - Population Mean) / Population Standard Deviation

Z score

Population Standard Deviation / Population Mean

Coefficient of Variation

Sum of (X*Probability of X)

Mean or Expected Value

Sum of ( (X-Population Mean)² * Probability of X)

Variance (using probability)

n!/x!(n-x)! P^x Q^(n-x)

Binominal Formula (Probability)

n*p

Mean (Binomial formula)

Sqrt (n*p*q)

Standard Deviation (Binomial formula)

(Sample Mean - Population Mean) / Population Standard Deviation/Sqrt(n)

Z formula (when dealing with sample means using central limit theorem)

(p^ - p) / Sqrt (p*q/n)

Z formula (when dealing with sample proportions using central limit theorem)

-where p^ is sample proportion and p is population proportion

(Sample mean - Population Mean) / Sample standard deviation / sqrt(n)

T formula (When dealing with sample means)

p^ ± Z * Sqrt(p^q^/n)

Formula for calculating a confidence interval for population proportion

n - 1

Degrees of freedom for t test (for sample means)

(Sample 1 mean - Sample 2 mean) - (Population 1 mean - Population 2 mean) / Sqrt (Population 1 standard deviation²/n1 + Population 2 standard deviation²/n2)

Z formula for testing population mean of two variables

(Sample 1 mean - Sample 2 mean) - (Population 1 mean - Population 2 mean) / Sqrt (Sample 1 standard deviation*(n1 - 1) + Sample 2 standard deviation*(n2 - 1) / (n1 + n2 -2)) * Sqrt (1/n1 + 1/n2)

T formula for testing population mean of two variables

-assuming population variances are equal

n1 + n2 - 2

Degrees of freedom for T when testing population mean of two variables

-assuming population variances are equal

(Sample 1 mean - Sample 2 mean) - (Population 1 mean - Population 2 mean) / Sqrt (Sample 1 standard deviation / n1 + Sample 2 standard deviation / n2)

T formula for testing population mean of two variables

-when you cannot assume population variances are equal

(Sample 1 standard deviation/n1 + Sample 2 standard deviation/n2)² / ((Sample 1 standard deviation/n1)²/n1 -1 + Sample 2 standard deviation/n2)²/n2 -1)

Degrees of freedom for T when testing population mean of two variables

-when you cannot assume population variances are equal

(Mean sample difference - Mean population difference) / Standard deviation of sample difference / Sqrt(n)

T formula (for dependent samples/matched pairs)

Sqrt ( (Sum of (d²) - (Sum of (d))²/n) / (n-1) )

Standard deviation of sample difference calculation

( (p1^ - p2^) - (p1 - p2) ) / Sqrt ( (p bar q bar) * (1/n1 + 1/n2) )

Z formula (with proportions from two samples using central limit theorem)

-Where p is population proportion

-Where p^ is sample proportion

-Where p bar is calculated in another flashcard

(n1p1^ + n2p2^) / (n1 + n2)

P bar formula (for proportions from two samples using central limit theorem)

Sample 1 variance / Sample 2 variance

F formula (given sample variances)

Sum of ( Column n * (Column mean - Grand mean)²)

SSC formula (ANOVA)

Sum for each column (Sum of (Xij in each column- Column mean)² )

SSE calculation (ANOVA)

SSC/Dfc

MSC calculation (ANOVA)

C - 1

Dfc calculation (ANOVA)

-where C is # columns

SSE/Dfe

MSE calculation (ANOVA)

N - C

Dfe calculation (ANOVA)

-Where N is # entries and C is # columns

MSC/MSE

F calculation (ANOVA)

Q*Sqrt(MSE/n)

HSD calculation (Tukey HSD)

Q*Sqrt( MSE/2*(1/Nr + 1/Ns) )

HSD calculation (Tukey kramer)

C * Sum of ( (Row mean - Grand mean)² )

SSR calculation (ANOVA with blocking variable)

N * Sum of ( (Column mean - Grand mean)² )

SSC calculation (ANOVA with blocking variable)

Sum of (Xij - Column mean - Row mean + grand mean)²

SSE calculation (ANOVA with blocking variable)

SSC / C-1

MSC calculation (ANOVA with blocking variable)
Where C is # of columns

SSR / n - 1

MSR calculation (ANOVA with blocking variable)

Where n is # of rows

SSE / N - n - c + 1

MSE calculation (ANOVA with blocking variable)
Where N is # of total observations

MSC/MSE

F calculation for treatments (ANOVA with blocking)

MSR/MSE

F calculation for blocking variables (ANOVA with blocking)

Sum of ( (observed frequency - expected frequency)² / expected frequency )

X² calculation (chi square goodness of fit test)

K - 1 - C

Degrees of freedom calculation for chi square goodness of fit test

Where K is # of categories, C is # of estimated parameters

Total number of row entries * Total number of column entries / Total entries

How do you calculate the expected frequency of each entry in contingency table

Sum of ( (observed frequency - expected frequency)²/expected frequency)

X² calculation (Chi Square Test of Independence)

(#Rows-1)(#Columns-1)

Degrees of freedom calculation for Chi Square Test of Independence

(Sum of (XY) - (Sum of X * Sum of Y)/n ) / Sqrt ( (Sum of X² - (Sum of X)²/n) *(Sum of Y² - (Sum of Y)²/n )

Coefficient of correlation calculation

( (Sum of X)*Y - (Sum of X)(Sum of Y)/n ) / ( Sum of X² - (Sum of X)²/n )

Regression coefficient calculation

(Sum of Y)/ n - b1 * (Sum of X)/n

Y intercept of regression line calclulation

Sum of (Y²) - b0* (Sum of Y) - b1* (Sum of X) *Y

SSE calculation (for simple regression)

Sqrt (SSE / n-2)

Standard error of estimate calculation

b1² *SSxx / SSyy

Coefficient of determination calculation (r²)

y^ ± t * standard error of estimate * Sqrt (1/n + (X - X bar)²/SSxx)

Confidence interval for y^ calculation

SSR/k / SSE/(n-k-1)

F calculation (for multiple regression)

-where k is # independent variables and n is # observations

Sqrt (SSE / (n-k-1))

Standard error of the estimate calculation (for multiple regression)

1 - SSE / SSyy

R² calculation

1 - ( SSE/(n-k-1) / SSyy/(n-1) )

Adjusted R² calculation