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# Str statistics lec notes

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### Str statistics lec notes

1. 1. 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
2. 2. 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.
3. 3. MEASURES  Measures of Central Tendency ± Mean ± Median ± Mode  Measures of Variability and Dis ersion © ± Range ± Average deviation ± Variance ± Standard deviationMeasures of Central TendencyMEAN  The sum of all values of the observations divided by the total number of observations  The sum of all scores divided by the total fre uency Properties  The most stable measure of central tendency  Can be affected by extreme values  Its value may not be an actual value in the data set  If a constant c is added/substracted to all values, the new mean will increase/decrease by the same amount cMEDIAN  Positional middle of an array of data  Divides ranked values into halves with 50% larger than and 50% smaller than the median value. Properties  The median is a positional measure  Can be determined only if arranged in order  Its value may not be an actual value in the data set  It is affected by the position of items in the series but not by the value of each item  Affected less by extreme values
4. 4. 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)
5. 5. 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