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