Terms Population the totality of all possible values (measurements or counts) of a particular characteristic for specified group of objects Sample part of a population selected according to some rule or plan Parameter a descriptive property of a population Statistic any numerical value describing a characteristic of a sample Sampling the process of choosing a representative portion of a population (reading assignment: SAMPLING METHODS) Statistical Method procedure used in the collection, presentation and analysis of dataSTATISTICS - presentation and interpretation of chance outcomes that occur in a planned or scientific investigation - deals with other NUMERICAL DATA representing COUNTS or MEASUREMENTS or CATEGORICAL DATA that can be classified according to some criterion - looks at TRENDS in the data, patternsUses of Statistics 1. Measures probability, predicting odds 2. For maintenance of quality use a statistic as basis or benchmark 3. For verifying claims 4. Predicting outcomes (interpolation) 5. Verifying correlations2 Major Categories of Statistical Methods 1. DESCRIPTIVE STATISTICS collecting and describing a set of data; no inferences or conclusions about a larger set of data 2. INFERENTIAL STATISTICS analyzing a subset of data leading to predictions or inferences about the entire set of data using a sample to gauge the behaviour of the population NOTE: A statistical inference is subject to uncertainty
Introduction to Not tions £ If v e X is the v iable of inte est, and that n meas ements are taken, then the notation X1, X2, X3, ¥¤¡ ¢¡ ¢¡ ¢ ¢¦ , Xn will be used to re resent n observations. § Sigma , Indicates summation of Su ¨¨ ation Notation If variable X is the variable of interest, and that n measurements are taken, the sum of n observations can be written as THEOREMS: 1.2. 3.
MODE Value that occurs most fre uently in the data set Locates the point where scores occur with the greatest density Less popular compared to mean and median measures Properties It may not exist, or if it does, it may not be unique Not affected by extreme values Applicable for both qualitative and quantitative dataMeasures of Variability and DispersionRANGE Measure of distance along the number line over where data exists Exclusive and inclusive range ± Exclusive range = largest score - smallest score ± Inclusive range = upper limit - lower limit Properties Rough and general measure of dispersion Largest and smallest extreme values determine the range Does not describe distribution of values within the upper and lower extremes Does not depend on number of dataABSOLUTE DEVIATIONAverage of absolute deviations of scores from the mean (Mean Deviation) or the median (Median AbsoluteDeviation) Properties Measures variability of values in the data set Indicates how compact the group is on a certain measureVARIANCE Average of the square of deviations measured from the mean Population variance ( 2) and sample variance (s2)
Properties Addition/subtraction of a constant c to each score will not change the variance of the scores Multiplying each score by a constant c changes the variance, resulting in a new variance multiplied by c2STANDARD DEVIATION Square root of the average of the square of deviations measured from the mean square root of the variance Population standard deviation ( ) and sample standard deviation (s) Why n-1? Degrees of freedom ± Measure of how much precision an estimate of variation has ± General rule is that the degrees of freedom decrease as moreparameters have to be estimated Xbar estimates Using an estimated mean to find the standard deviation causes the loss of ONE degree of freedom Properties Most used measure of variability Affected by every value of every observation Less affected by fluctuations and extreme values Addition/subtraction of a constant c to each score will not change the standard of the scores Multiplying each score by a constant c changes the standard deviation, resulting in a new standard deviation multiplied by cCHOOSING A MEASURE Range ± Data are too little or scattered to justify more precise and laborious measures ± Need to know only the total spread of scores Absolute Deviation ± Find and weigh deviations from the mean/median ± Extreme values unduly skews the standarddeviation Standard Deviation ± Need a measure with the best stability ± Effect of extreme values have been deemed acceptable ± Compare and correlate with other data sets