EDMS 451 Final Review (Concepts and Formulas to know) PDF

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A crash course in all of the concepts and formulas in EDMS 451....

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EDMS 451 Final Review Normal line equation: Y= a+bX (it becomes Y’= a+bX when predicting a Y value for regression or line of best fit) SY ) , SX ´ Y − Y´ X− X , ZY = Z X= SY SX Y Intercept :b=r (

´ Slope :a=Y´ −b X

Y −Y ' Z score for actual Y: Z = S Y .X

Standard error of estimate:

√

S Y . X =S Y (

n−1 2 )( 1−r ) n−2

Error of estimate: e= Y-Y’ ' ' Confidence interval for the actual Y value: (Y −z crit S Y . X , Y +z crit SY . X ) Regression Assumptions  Linearity of the Relation between X and Y  Independence of observations  Normality of errors around the regression line  Homoscedasticity(evenness of the spread) of errors around regression line Slope: Change in Y/Change in X (Note: it is also related to correlation) When the X and Y relation gets weaker, the Y predictions regress from their actual values. 2

Chi-square ( x )  Relies more on nominal and ordinal data  Observes the frequencies/counts of events while comparing the observed results with the expected ones  Only 1-tailed tests are used, but the degrees of freedom are necessary  Df= K-1, K represents the number of categories  Relies more on the modes of the data, while z and t tests, correlations, covariance, and regressions H 0 : P A =a certain ratio∧ percentage H 1 : P A ≠ a certain ratio∧ percentage When testing independence: df= (# of rows-1)* (# of columns-1) Expected frequency= Probability of an event occurring* the number of subjects 2 ( f obs −f exp ) 2 x obs =∑ f expi 2 Retain the null: x 2obs ≤ x crit 2 2 Reject the null: x obs>x crit i

i

Stuff to know from past exams Nominal: Each number represents a category Ordinal: the numerical order of scores represent order with respect to being measured Interval: Sets of numbers are grouped together to represent equal amounts

Ratio: The number zero represents a complete absence of the attribute being measured Power- the probability of rejecting the null hypothesis when it is actually false and the probability of a statistical test detecting a real population mean difference. Independent group design: people in one group are completely independent/unrelated to those in the other group  random samples of males and females  randomly assigned treatment versus control groups Dependent group design: individuals in each group have a one‐to‐one connection with someone i n the other group (also called paired, correlated, or matched groups)  married couples, split into husband and wife groups  same people measured twice (e.g., pre‐post or under two different conditions) Type I error: The null hypothesis is rejected when it is actually true Type II error: The null hypothesis is accepted when it is actually false. Power: the probability of rejecting a null hypothesis that is false In general, if you have a larger effect size you need fewer subjects to detect it. In general, if you want more power you need more subjects. Dependent group design threats  Testing- the effect of taking a test (or being exposed to an instrument) upon the scores of a later testing  Instrumentation- changes in measurement procedures during a study so scores differ due to a procedural difference than any real difference on the measured trait  Experimental Mortality- nonrandom loss of subjects during a study  Statistical Regression- the statistical effect whereby a group of subjects selected on the basis of extreme scores will tend to have less extreme scores on average if tested again on the same or another imperfectly measured variable  Maturation- biological or psychological processes that naturally occur within subjects during the course of a study (learning or fatigue)  History- occurrences during the course of a study extraneous to the independent (treatment) variable Independent group design threats  Internal validity: a study is internally valid to the extent that the differences on the dependent variable can be attributed to the differences of the independent variable to the extent that other explanations can be ruled out/ignored  Selection: group differences on some relevant variable before experimental treatment Central limit theorem: As the sampling size increases, the sampling distribution becomes increasingly normal (The shape of the curve is affected) Null hypothesis: a formal statement of the value of the population parameter of interest when it is not different from that of the reference population or the direction hypothesized H 0 : μ=n

Alternative hypothesis: a formal statement of the value of the population parameter of interest when it is different from that of the reference and possibly in a hypothesized direction of manner H 1: μ ≠ n The average value of a parameter of interest is not n. It could be higher or lower. The alpha level represents the area of the sampling distribution where the null hypothesis is rejected if the sample mean falls under that area. (The two-tailed tests separate the areas which make up the total alpha level while a one-tailed test only blocks off one side of the distribution). The t-test is used when we do not know the population variance or the population standard deviation. Population Parameters

∑X

μ=

∑ ( X−μ)2

√

σ=

∑X X´ = n

mean

N

σ2 =

Sample Statistics

N

∑ ( X−μ) 2 N

variance

standard deviation

∑ ( X − X´ ) s= 2

n−1

s=

√

∑ ( X − X´ )

2

n−1

2...