# Mesa Community College

 STATISTICS SYMBOLS & FORMULAS
##### Chapter 4: Distributions
 Symbol Stands For X a score f frequency of a score N sum of the frequencies, or total sample size Cum f cumulative frequency

Equation to convert frequencies into percentages

f is the frequency or the number of times each score occurs; N is the number of observations or the sum of the frequency column in a frequency distribution.

Equation to convert cumulative frequencies to cumulative percentages

Cum f stands for the cumulative frequency, which is the total number of observations up to and including the observations in the interval you're considering.

##### Chapter 6: Central Tendency
 Symbol Stands For Mo mode Md median sample mean Σ "Big" sigma directs you to add up all of the values that follow deviation of a score from the mean μ population mean, read "mu"

The first formula above tells you to add all the Xs or scores and then to divide the result by the total number of scores (N).

In a frequency distribution, N is the sum of frequencies. The second formula above tells you to multiply each score by its frequency before summing and dividing by N.

##### Chapter 7: Dispersion and Variability
 Symbol Stands For AD average deviation R or r range σ2 population variance s2 sample variance σ population standard deviation s sample standard deviation s approx an approximation of s; s-approx = R/4 SS sum of squares or the numerator of variance z standard score or z score

FORMULAS

Formula for calculating the range

R (range) = High score - Low score

Definitional formula for calculating sample variance (an estimate of population variance)

The definitional and computational formulas (below) for variance yield the exact same value. To calculate standard deviation from the definitional formal for variance, just take the square root of the entire formula after completing all other calculations indicated in the formula.

Computational formula for calculating sample variance (an estimate of population variance)

Computational formula for the sample variance, for a frequency distribution

Computational formula for sample standard deviation (an estimate of population standard deviation)

Computational formula for sample standard deviation for a frequency distribution

Formula for finding a z score from a raw score using sample statistics

Formula for finding a raw score from a z score using sample statistics

##### Chapter 8: Probability
 Symbol Stands For p(A) probability of event p(A or B) probability of event A or event B p(A, B) probability of both A and B p(B|A) probability of event B given that event A has occurred

FORMULAS

Equation for the addition rule of probability

p(A or B) = p(A) + p(B)

p(A or B) means the probability of either event A or event B, and it is equal to the probability of event A
[p(A)] plus the probability of event B [p(B)].

Equation for the multiplication rule of probability

p(A, B) = p(A) x p(B)

p(A, B) is the probability of occurrence of both event A and event B, which is equal to the product of their individual probabilities. This equation is used when events A and B are independent.

Equation for determining the probability of a sequence of nonindependent events

p(A, B) = p(A) x p(B|A)

When events A and B are not independent—that is, when the probability of B depends on whether A has occurred—then the multiplication rule must be modified as shown. p(B|A) reads "probability of B given A."

##### Chapter 9: Normal Curve

The formulas for this chapter are two of the formulas covered in the Dispersion & Variability chapter--the formulas for converting any raw score to a z score and for converting any z score back to a raw score.

FORMULAS

Formula for finding a z score from a raw score using sample statistics

Formula for finding a raw score from a z score using sample statistics

##### Chapter 10: Hypothesis Testing

SYMBOLS

 Symbol Stands For standard error of the mean (for population) mean of the sampling distribution of means, which equals µ z score for the sampling distribution of means estimated standard error of the mean (for sample) or t t score, which is really just a z score with estimated error added CI confidence interval df degrees of freedom; df = N-1 for a one-sample t-test t.05 or t.01 t scores from t table; cut off deviant 5% or 1% of the t distribution H0 null hypothesis α alpha level, the level at which we test H0 H1 alternative hypothesis μ0 specific value representing the "untreated" population mean tcomp computed t score--this is the one that you calculate tcrit critical t score from t table--this is the standard for rejection Type I, or alpha error rejecting true H0 Type II, or beta error failing to reject false H0

FORMULAS

Equation for estimated standard error of the mean

The estimated standard error is found by dividing the sample standard deviation by the square root of sample size.

One-sample t-test equation; yields computed t score

This equation is used to test hypotheses about the value of m. It is the formula for the one-sample t test.

Equations for 95% and 99% confidence intervals

t.05 and t.01 are the t scores cutting off the deviant 5% and 1% of the distribution of t, respectively.

The values of t are found in the t table with df = N – 1.

##### Chapter 11: Two Sample T-Tests

SYMBOLS

 Symbol Stands For estimated standard error of the mean differences score in the sampling distribution of the differences mean of the sampling distribution of the differences t score (t-comp) based on the sampling distribution of the differences mean of the differences standard deviation of the differences D difference between a pair of scores

FORMULAS

Computational formula for the estimated standard error of the mean differences for independent samples

This formula is used to compute the estimated standard error of the mean differences. N1 and N2 are the numbers of subjects in the first and second samples, respectively. s12 and s22 are the variances of the two samples.

Short equation for the two-sample t test for independent samples

The t ratio for the two-sample t test for independent samples is the difference in sample means divided by the estimated standard error of the mean differences. When the computational formula for s is substituted in the denominator, the t ratio becomes...

Computational formula for the two-sample t test for independent samples

Computational formula for the t test for dependent (a.k.a., matched, within subjects, repeated measures) samples

 LAST UPDATED: 2013-10-02 12:49 PM

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