Statistics

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Statistics

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Facts and figures; set of methods and rules fororganizing, summarizing, and interpreting information

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Population

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The set of all individuals of interest in aparticular study; absolutely every measure that could fit into that measure

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Explanatory Variable

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if one variable is used to understand or predict values of anothervariable.

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Response Variable

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the variable that is predicted because of the explanatory variable.

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Simple Random Sample

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When choosing a simple random sample of n units, all groups of size n inthe population have the same chance of becoming the sample, each unit of thepopulation has an equal chance of being selected, regardless of the other unitschosen for the sample.

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Parameter

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Value that we obtain from the larger populationthat represents the population; a parameter can never be derived from a sample

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Descriptive Statistics

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Methods for organizing, summarizing, andsimplifying data

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Inferential Statistics

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Takes information from a sample and makesinferences about the entire population

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Level of Measurements

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• Nominal – qualitative categories; i.e., gender,eye color
• Ordinal – set of categories that are organizedin an ordinal sequence; rank observations in terms of size of magnitude; e.g.,1st, 2nd, 3rd
• Interval – ordered categories where all of thecategories are intervals of exactly the same size; most of psychologicalmeasurements; e.g., thermometer
• Ratio – interval scale with an absolute, ortrue, zero point; ratios of numbers do reflect ratios of magnitude; e.g..,height, age
  

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Real Limits

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Each score has two real limits, one at the topof its interval and one at the bottom of its interval, halfway up and down fromthe next interval; e.g., the real limits of 100.29 are 100.285 &100.295

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Histogram

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Frequency Polygram

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Deviation Score

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locationof the score from the mean

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Variance

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averagesum of squares; the mean squared deviation

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Semi-Quartile Range

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the middle 50% of the distribution

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Standard Deviation

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positivesquare root of the variance

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Single Sample Designs

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Data from a single sample are used to test ahypothesis about a single population

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Independent Measure Designs

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A separate sample is obtained to represent eachindividual population or treatment condition.

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Related-Sample Design

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In repeated measures, there is only one sample,with each individual subject being measured in all of the different treatmentconditions; in a matched subjects design, every individual in one sample ismatched with a subject in each of the other samples

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Type I and II Error

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Type I error: Alpha error; error of rejection a truehypothesis

Type II error: Beta error; failing to reject a false hypothesis

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Linear Regression

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Purpose is to find the equation for thebest-fitting straight line for predicting Y scores from X scores; regressionprocess determines the linear equation with the least squared error between theactual Y values and the predicted Y values on the line

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Chi Square Test for Goodness of Fit

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Used in situations where the measurementprocedure results in classifying individuals into distinct categories; testuses frequency data from a single sample to test a hypothesis about the populationdistribution; null hypothesis specifies the proportion or percentage of thepopulation for each category in the scale of measurement

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Standard Error of Estimate

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Provides a measure of the standard distance (orerror) between the actual Y values and the predicted Y values

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Properties of Z-Score

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• shape of z-scores is identical to originaldistribution
• mean = 0, regardless of original distribution
• variance of distribution = 1; standard deviation= 1, regardless of original distribution
• The Z-Score tells how many standarddeviations the value is from the mean, and is independent of the unit ofmeasurement.amp

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Central Limit Theorem

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First, it describes the distribution of samplemeans for any population, no matter what shape, or mean, or standard deviation.Second, the distribution of sample means “approaches” a normal distributionvery rapidly. With an n = 30, the distribution is almost perfectly normal.