Statistic Notes

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NOTE Z: SETTING UP THE EXCEL SHEET FOR CALCULATING P VALUES Enter data into the cells. The following are some recommended layouts if functions are used. If the Tool-Pac routines are used, you only need to be able to identify the ranges of the existing data. ONE SAMPLE TESTS MEAN Name μ (1) Mean (2) St. Dev (3) n df t (6) Probability (7) (4) (5) FOR A HYPOTHESIS ON ONE POPULATION MEAN (KNOWN), NORMALLY DISTRIBUTED, ONE TAIL TEST POPULATION σ KNOWN (1) From Claim (2) Function AVERAGE of data (3)
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   NOTE Z: SETTING UP THE EXCEL SHEET FOR CALCULATING P VALUES Enter data into the cells. The following are some recommended layouts if functions areused. If the Tool-Pac routines are used, you only need to be able to identify the ranges of the existing data.   ONE SAMPLE TESTS MEAN Name μ  Mean St. Dev n df t Probability(1) (2) (3) (4)(5) (6) (7) FOR A HYPOTHESIS ON ONE POPULATION MEAN (KNOWN),NORMALLY DISTRIBUTED, ONE TAIL TEST  POPULATION  σ KNOWN  (1) From Claim(2) Function AVERAGE of data(3) From Claim(4) Function COUNT on data(5) Cell(4) - 1(7) Function NORMDIST( (2), (1), (3), TRUE )z = ( ⎯    X −   μ ) / ( σ /  √ n) σ NOT KNOWN, LARGE SAMPLE (1) From Claim(2) Function AVERAGE on data(3) From STDEV on data(4) Function COUNT on data(5) Cell(4) - 1(7) Function NORMDIST( (2), (1), (3), TRUE )z = ( ⎯    X −   μ ) / ( s /  √ n) σ NOT KNOWN, SMALL SAMPLE (1) From Claim(2) Function AVERAGE on Data(3) From STDEV on data(4) Function COUNT on data  (5) = (4) – 1(6) = ( ( (1) – (2) ) ) / ( (4) / SQR (3) )(7) Function TDIST( (6), (5), 1 or 2 from Claim )t = ( ⎯    X −   μ ) / ( s /  √ n) FOR A HYPOTHESIS ON ONE POPULATION MEAN OR MEDIAN(KNOWN), NORMALLY DISTRIBUTED, TWO TAIL TEST  POPULATION  σ KNOWN  Name μ  Sigma Probability(1) (2) (3)(1) From Claim(2) From Claim(3) Function ZTEST( range of data, (1), (2) )  POPULATION  σ UNKNOWN, LARGE SAMPLE Name μ  Probability(1) (2)(1) From Claim(2) Function ZTEST( range of data, (1) ..leave blank.. ) MEDIAN Name PopulationMedian# of +signs# of –signsn Smallerof a or bzValueProbability(1) (2) (4) (3) (5) (6) (7)  FOR A HYPOTHESIS ON ONE POPULATION MEDIAN VALUE, NONPARAMETRIC, LARGE SAMPLES (N > 25) (1) Function MEDIAN on data(2) Manually count the number of data values greater than or equal to (1)(3) Function COUNT on data(4) = (3) – (2)(5) Smaller of (2) or (4)(6) = ( (5) + 0.5 – (3) / 2) / ( SQR(3) / 2 )(7) Function NORMSDIST( (6) )z = [ x + 0.5 – n / 2 ] / [ √ n / 2 ]  FOR A HYPOTHESIS ON PROPORTION Name p q n np nq Numberof successesp-hatz Probability(1) (2) (3) (4) (5) (6) (7) (8)(9)  FOR A HYPOTHESIS ON ONE POPULATION PROPORTION, LARGESAMPLES WHERE NP>5 AND NQ>5 (1) From Claim(2) = 1 – (1)(3) From Claim(4) = (1) * (3)(5) = (2) * (3)(6) From Claim(7) = (6) / (3)(8) = ( (7) – (1) ) / SQR( (1) * (2) / (3) )(9) Function NORMSDIST( (8) )z = (p-hat − p) /  √ (p × q / n) FOR A HYPOTHESIS ON VARIANCE NamePopulation σ 2  Variancen df Chi Probability(1) (2) (3) (4) (5) (6)  FOR A HYPOTHESIS ON ONE POPULATION VARIANCE (1) From Claim(2) From VAR on data(3) Function COUNT on data(4) = (3) - 1(5) = (4) * (2) / (1)(6) Function CHIDIST( (5), (4) ) χ 2 = ( n − 1 ) × s 2 /  σ 2   FOR A HYPOTHESIS ON CORRRELATION COEFFICIENT Name CorrelationCoefficient rn df t Probability(1) (2) (3) (4) (5)(1) Function CORREL(Range of x data, Range of y data) or from Claim  (2) Function COUNT(Range of x) or from Claim(3) = (2) - 2(4) = (1) / SQR( (1 – (1) * (1) ) / (3) )(5) Function TDIST( (4), (3), 1 or 2 from Claim )t = r /  √ ( (1 – r 2 ) / (n – 2) ) TWO SAMPLE TESTS FOR A HYPOTHESIS ON TWO POPULATIONS  MEANS, TWO INDEPENDENT SAMPLES (1) Range of data set 1(2) Range of data set 2(3) Tails, either 1 or 21 is for a one tailed test2 is for a two tailed test(4) Characteristics of the two data sets1 is for paired data values, having equal numbers of values (no missingvalues)2 is for the equal variance (homoscedastic) characteristic3 is for the unequal variance (heteroscedastic) characteristic(5) Probability = TTEST( (1), (2), (3), (4) )(6)  DIFFERENCES, PAIRED DEPENDENT SAMPLES t = ( ⎯    d −   μ d ) / ( s d /  √ n)Equal Variancet = {( ⎯    X 1   −⎯    X 2 ) − ( μ 1   −   μ 2 )} / s m  s m = s p   ×   √ ( 1/ n 1   + 1/ n 2 )s p = √ (pooled variance)(pooled variance) = { (df  × s 2 ) 1   + (df  × s 2 ) 2 } / df  Total  Unequal Variancet = {( ⎯    X 1   −⎯    X 2 ) − ( μ 1   −   μ 2 )} / s m  s m = √ { (s 2 / n) 1   + (s 2 / n) 2 }  PROPORTIONS, RANDOM INDEPENDENT LARGE SAMPLES (n 1 p>5, n 1 q>5, n 2 p>5 and n 2 q>5)
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