#
Statistics 1 course notes
**Topics:**
Variance,
Statistics,
Regression analysis,
Statistical hypothesis testing,
Normal distribution,
Errors and residuals in statistics /
**Pages:** 6 (1376 words) /
**Published:** Nov 7th, 2013

**Topics:**Variance, Statistics, Regression analysis, Statistical hypothesis testing, Normal distribution, Errors and residuals in statistics /

**Pages:**6 (1376 words) /

**Published:**Nov 7th, 2013

Variable types (SS Stevens, 1946) Nominal - assign item to category; are discrete / categorical Ordinal - rank order items; are categorical, but often treated as continuous Interval - rank order items and distance between cases is equal; are continuous Ratio - same as interval, includes a true zero; are continuous

Z score: Z = (X - M) / SD

Mean z-score is always 0. Negative is below average; positive is above.

Mean = average

Median = midpoint score in population (half fall below, half fall above). Middle number in a sorted list. If population is an even number, divide between neighbors on the midpoint.

Mode = most frequent score

Deviation = (X - M)

Sum of Squares (SS) = ∑ (X - M)^2

Variance = ∑ (X - M)^2 / N (mean squares)

Standard Deviation = sqrt of variance

Pearson product-moment correlation coefficient (r): degree to which X and Y vary together, relative to the degree to which they vary independently

Sum of cross products SPxy: Measure of the degree to which X and Y vary together.

SPxy = ∑ [(X - Mx) * (Y - My)] r = SPxy / sqrt (SSx * SSy). SSx, SSy are measures of the degree to which X and Y vary independently.

Z score formula: r = ∑ (Zx * Zy) / N

Covariance = SP / N

Assumptions for r:

1) normal distribution of X and Y - check histograms

2) linear relationship between X and Y - check scatterplots

3) homoscedasticity - vertical distance between scatterplot dots and regression line; indicates level of prediction error (aka “residual”)

Measurement

Reliability - correlation between X1 and X2 is an estimate of reliability (and is a limit for how X can correlate to anything else)