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If X has the B(n, p) distribution and the sample size n is large enough (namely np t10 and n(1 p) t10), then X is approximately N np, np(1 p) . Sample Proportions n pˆ Mean E pˆ P pˆ p Standard Deviation n p p p p (1 ) s.d.( ˆ) ˆ V Sampling Distribution of pˆ If the sample size n is large enough (namely, np t10 and n(1 p) t10) then pˆ is ...
Matched pairs (dependent samples) /2 Confidence Interval < < where with d.f. = 1 Hypothesis Test with . . 1 d d d d dE d E s Et n n d t df n s n α µ µ −+ =− − = = − Two Sample Variances 22 2 2 12 2 22 1 11 2 2 2 2 2 1 2 2 2 12 2 12 Confidence Interval for and 11 Hypothesis Test Statistic: where numerator . . 1 and denominator . . 1 ...
The approach of this Handbook is to present commonly used steps and formulas in statistics, provide an example of how to conduct the calculations by hand, and then an example of software output.
Partitioning Total Sum of Squares. “The ANOVA approach is based on the partitioning of sums of squares and degrees of freedom associated with the response variable Y”. We start with the observed deviations of Y. around the observed mean ̄Y. i Y − ̄Y.
escriptive statistics. As you can probably figure out based on the name, descriptive statis. ics describe the data. There are three essential characteristics of descriptive statistics we need to discuss: scales of measurement, measures of central tendency, and measures of v.
1 sample 2 samples 3 or more samples 1 sample 2 samples σ known Confidence Interval n E z σ = α/2 x −E <µ<x +E Sample Size 2 /2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ = E z n α σ Test Statistic n x z σ −µ = σ unknown Confidence Interval n E t s = α/ 2 p df = n – 1 x −E <µ<x +E Test Statistic s n x t −µ = df = n – 1 Matched Pairs ...
For locating a sample mean’s position within a population: z= −μ σM √M= zσ Q+μ σ = σ √n OR σ = σ 2 n Finding Degrees of Freedom z-Scores Single Sample t-Statistic Paired / Related Sample t-Statistic df=n−1 Independent Samples t-Statistic Paired Samples t-Statistics df= :n1−1 ;+ :n2−1 ; Independent Measures ANOVA:
