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7/29/2019 Statistical Methodology (TQM Report)
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STATISTICAL METHODOLOGY
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StatisticalMethodology
Data
Collection
Organization
&
Presentation
Descriptive
MeasuresStatistical
Inference
PredictiveStatistics
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Descriptive Statistics
• It is the first major component of statistical
methodology. It is also the efficient collection,
organization, and description of data. Results
are useful in identifying quality problems and
as a means of measuring improvement.
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Descriptive Statistics
• Measures of Central Tendency – Mean is the
average score. The mode is the most
frequently occurring score. The median is the
middle most score.
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N
X N
i
i 1
n
X
X
N
i
i 1
MEAN PROPORTION Population:
Sample:
n
q p
N
Q
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MEDIAN
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Descriptive Statistics
• Measures of Dispersion – Range is the
difference between the highest and lowest
score. We usually use two other measures of
dispersion: Variance which is the average
squared distance between each score and the
mean and Standard Deviation which is the
average distance between each score and themean.
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Range LS HS R
Standard Deviation Variance
Population:
Sample:
N
x N
i
i
1
2
n
x x
s
n
i
i
1
2
N
x N
i
i
1
2
2
n
x x
s
n
i
i
1
2
2
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Measures of Central Tendency and
Dispersion by Level of Measurement
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Statistical Analysis with Microsoft
Excel
Microsoft Excel provides data analysis tools,called the Analysis ToolPack. To view a list of available analysis tools, click on Data Analysis
group under the Data Tab in the menu. Asecond useful tool is the Histogram tool.A histogram is a representation of a frequencydistribution by means of rectangles whose
widths represent class intervals and whoseareas are proportional to the correspondingfrequencies.
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Statistical Inference
• It is the process of drawing conclusions aboutunknown characteristics of a population fromwhich the data were taken.
• Sampling Distributions – It is a distribution of all possible statistics calculated from all
possible samples of size n drawn from apopulation. Samples are drawn to infersomething about the population.
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Statistical Inference
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For Simple Random Sampling
• The expected value of the sample mean is the
population mean.
• The standard deviation of the sample mean
(often called standard error of the mean):
Infinite: Finite:
x E
n x
n N
n N x
1
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Central Limit Theorem
• As the variance decreases, the sample size
increases. Normal distribution is
approximately 30 in its sample size.
• If the population is known to be normal, the
distribution of the sample mean is normal for
any sample size.
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Sampling distribution n = 354321
Sampling distribution n = 454321
Means (n=30)432
Means (n=60)
432
Means (n=120)432
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For Sampling Distribution of p:
• The expected value of the sample mean is the
population mean.
• The standard deviation of the sample mean
(often called standard error of the mean):
Infinite: Finite:
p E
n
s p
1
n N
n N s p
1
1
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Statistical Inference
• Confidence of Intervals – It is an estimate of
population parameter that specifies the
likelihood that the interval contains the true
population parameter. Commonly usedconfidence levels are 90, 95 and 99. The higher
the cf, the more assurance we have that the
interval contains the true population parameter.
expressed as a percentage. 1cf
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Statistical Inference
• Hypothesis Testing –
It involves drawinginferences about two contrasting propositions(hypotheses) relating to the value of a populationparameter, one of which is assumed to be true in
the absence of contradictory data.• The null hypothesis is the proposition that
implies no effect or no relationship.
• The alternative hypothesis is the proposition that
implies with effect or has a relationship.• The level of significance is denoted by and
determines the size of the rejection region.
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Steps:
• Formulate the hypotheses to test.
• Select a level of significance.
• Determine a decision rule.
• Collect data and calculate a test statistic.
• Apply the decision rule to the test statistic and
draw a conclusion.
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Decision Making:
• Critical Value Method – one of the methods that
leads to a decision about rejection or non-rejectionof the null hypothesis, wherein critical values arethe tabular values of the test statistic that dividesthe rejection and non-rejection region.
1. If the computed value is within the non-rejection region, the null hypothesis isaccepted.
2. If the computed value lies or falls on therejection region, the null hypothesis is rejected.
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Decision Making:
• P-Value Method – P stands for PROBABILITY, it
is referred to as the observed level.
1. If P-value is less than or equal to alpha ,
then is rejected.
2. If P-value is greater than alpha ,
then is not rejected.
P 0 H
P
0 H