Introduction to Statistics

PSYC 60 Review  Independent Variable : The variable that is manipulated  Dependent Variable : The variable that changes based on the independent variable (what we are measuring)  Measurement Scales : NOIR (Nominal, Ordinal, Interval, Ratio) o Nominal : Names, no ordering (colors) o Ordinal : There’s an order but no numeric relationship (Small < Medium < Large) o Interval : Ordinal, but now there’s numeric steps between them (zero is not meaningful) (degrees Celsius) o Ratio : Ordinal, but there’s an absolute zero that implies absence of it (height, weight, Kelvin)  When to Use Real Limits o Important for Continuous Variables o When calculating percentiles o When calculating range of scores  Range = URL of high – LRL of low (e.g. high 10, low 5, range = 10.5-4.5)  Skewed Distributions o Normal Curve (symmetrical) (Mode = Mean = Median) o Positive Skew (tail is on right side) (Mode < Median < Mean) o Negative Skew (tail is on left side) (Mean < Median < Mode) o Mode is always the highest point (can be more than one)  Use when nominal or ordinal, or if you just want most occurring value o Median is in the middle (in skewed, closer to the end with more scores)  Use if there are extreme values (that would mess up the mean) or if the distribution has undetermined values (like Did Not Finish in a race) o Mean is in the middle (in a skewed distribution, closer to the end with less scores, tail)  Percentiles and Interpolation o If given a percentile and want to find X-score, you take the URL of the X-score  If on a table, 88% correlates to an x-score of 8, then the X-score it relates to is actually 8.5 o If given an x-value of like 9.5, go to the x-value of 9 on the table to find the correlating percentile  Mean M = ∑ X n → ∑ X = M ∗ n  Weighted (Overall) Mean ¿ ∑ X 1 + ∑ X 2 n 1 + n 2  Sum of Squares (SS), Variance, and Standard Deviation (σ) o Sum of Squares : Use computational when X is not a whole number, or when there are a large number of scores  Computational vs. Definitional is sometimes just a matter of preference – both give the same answer  Definitional Formula : SS = ∑ ( X − μ ) 2  Computational Formula : SS = ∑ X 2 − ( ∑ X ) 2 n o Remember that Variance and Standard Deviation calculations are slightly different when working with a population vs. a sample  How to know which to use? Read the question – does it state which? Check the symbols:  Greek symbols (μ,σ) mean population  Normal letters (M,s) mean sample o Variance :  Population : Variance = SS N = σ 2  Sample : Variance = SS n − 1 = s 2  Z-Scores – Location of Scores in a Distribution o Sign (+,-) means above or below o Value means how many standard deviations away o When you transform using z-scores, mean is ALWAYS 0 and standard deviation is ALWAYS 1 o z = x − μ σ = deviation score standard deviation → X = μ + zσ o When you draw a graph of scores, put the scores axis (x) with the mean being in the middle, then draw a separate a separate axis under it of z-scores (σ) where each tick mark away is one standard deviation away  When We Standardize : o Shape stays the same. Individual scores do not change position. o Mean is always 0 o Standard deviation is always 1! o It’s pretty much just re-labeling the x-axis

PSYC | 60 | Introduction to Statistics | study guides | PSYC 60 Review  Independent V

PSYC_60_Notes_S112_Lowe_Niema.docx-Stats Terms  TYPES OF STATISTICS

1. Write hypotheses using symbols and words a. H 0 : µ ≤ 60 (population mean we were given) i. Scores after the program yield results with a mean less than or equal to the normal score of 60 b. H 1 : µ > 60 (population mean we were given) i. Scores after the program yield results with a mean greater than the normal score of 60 2. Set alpha level and accompanying z-score a. α = 0.05 , z = 1.65 3. Use M and n to find σ M and accompanying z-score of M a. σ M = σ √ n b. Graph and stuff c. Make decision 4. Formally write the result if needed a. Scientific: “The Mean of the treated animals was significantly lower than the mean of the untreated population” or some shit 5. Find area of graph in critical region (Power) a. DRAW ALL THE SHIT!!!!!!! i. Sketch the graph, define critical region, label original graph as H 0 and treatment graph as H 1 1. Use σ M as your unit for the x-axis ii. Use means and z scores and shit

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