# Quantitative Analysis and Decision Methods Formulas

**Topics:**Normal distribution, Variance, Standard deviation, Statistics, Sample size, Arithmetic mean /

**Pages:**4 (853 words) /

**Published:**Nov 22nd, 2011

MISCELLANEOUS, COMMONLY USED FORMULAS

Finite population correction factor:

Multiply SE of sample mean by fpc to make the correction

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Independent samples of same population with same standard deviation (variances are equal).

Confidence interval: df for t-multiple is (df1 + df2), or (n1 – 1) + (n2 - 1)

Pooled estimate of common standard deviation:

SE of difference between two sample means

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Confidence interval for differences in sample means when variance is not equal.

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df for t-multiple is given by complex formula not shown in book when variance is not equal. Use StatTools.

Confidence interval for difference between two proportions.

SE for difference between two proportions.

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Chapters 2 and 3 Describing the Distribution of a Single Variable and Finding Relationships among variables

Mean Formula

Excel Function: = AVERAGE

Coefficient of Variation: Standard Deviation / Mean

Standard Deviation: square root of variance

Sample Variance

Population Variance

Excel Function: Variance = VAR Standard Deviation = STDEV

Mean Absolute Deviation

Covariance

Correlation

Excel Function: =CORREL

Chapter 4: Probability and Probability Distributions

Conditional probability: P(A|B) = P(A and B) / P(B)

Multiplication rule:

P(A and B) = P(A|B) P(B)

If two events are INDEPENDENT:

P(A and B) = P(A) P(B)

Variance of a Probability Distribution:

Standard Deviation of a Probability Distribution:

Conditional Mean:

* when the mean of a variable depend on an external event

Covariance between X and Y:

Correlation between X and Y:

Joint Probability Formula:

P(X = x and Y = y) = P(X = x|Y = y) P(Y = y)

Alternative formula: P(X = x