STATISTICS Week 2

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STATISTICSWeek 2
I.T.Ü. Faculty of Naval Architecture and Ocean
EngineeringShipyard Organization GEM412E
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What is statistics?

• A variety of analytical procedures to aid the
  statistician in making decision in the presence
  of uncertainty.

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STATISTICS

• DESCRIPTIVE Procedures used to summarize the
  information in a set of measurements and to
  describe the characteristics of the set.
• INFERENTIAL Procedures used to make inferences
  about population characteristics from information
  contained in a sample.

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RAW DATA
Delay time of a passenger ferry (minutes)
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Frequency Table
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HISTOGRAM
Frequency
Delay in minutes
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Relative Frequency
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Frequency in Groups
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FREQUENCY HISTOGRAM IN GROUPS
Frequency
Delay in Minutes
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MEASURES OF LOCATION

• MEAN
• MEDIAN
• MODE

The median is the number in the middle of a set
of numbers that is, half the numbers have values
that are greater than the median, and half have
values that are less.
The most frequently occurring, or repetitive,
value in an array or range of data
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Mean, Median, Mode

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Mode 8
Median 9
Mean 11
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Range, Variance, Std.Deviation

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Range 23 - 3 20
Variance 31.17
s 5.58
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MEASURES OF SPREAD

• RANGE
• VARIANCE
• STANDARD DEVIATION

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MEASURES OF SPREAD

• SKEWNESS
• ( or -)
• KURTOSIS
• (lt3 or gt3)

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Correlation

• The Correlation Coefficient, r is the indicator
  of the strength of the linear relationship
  between two variables.

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MS Excel Functions
DATA STATISTICS

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MODE(A1A12) MEDIAN(A1A12) AVERAGE(A1A12) VA
R(A1A12) STDEV(A1A12)
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Statistical Presentations
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Statistical Presentations
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Statistical Distributions

• RANDOM VARIABLE
• DISTRIBUTION

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Distribution

• DISCRETE DISTRIBUTION
• CONTINUOUS DISTRIBUTION

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Discrete Distribution vs Continuous Distribution
Probability
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NORMAL Distribution
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NORMAL Distribution
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HISTOGRAM and Frequency Distribution Curve
Freq.
Diameter (mm)
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BETA DISTRIBUTION
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Statistical Measures - 1
MEAN
MEDIAN
MODE
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Statistical Measures - 2
Range
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Results
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Statistical Inference

• Instead of examining the entire population,
  which may be difficult or impossible to do, we
  may examine only a small part of tis population,
  which is called a sample. (Confidence Interval).
• If the sampling distribution of S is
  approximately normal, we can expect to find S
  lying in the intervals (Confidence Interval).
• Sample data can be used to make assumptions or
  guesses about the populations. Such assumptions
  are statements about the probability
  distributions of the populations.

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Confidence Level
I am 95 confident that the mean value is
between 46.1 and 53.9
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Main Population vs Sample
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CONTROL LIMITS FOR SAMPLE MEAN
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A TYPICAL CONTROL CHART (MEAN VALUES)
Upper Control Limit (out)
0.14
0.11
Upper Control Limit (in)
0.09
X 12.43
x
x
x
x
0.09
0.11
0.14
Lower Control Limit (in)
Lower Control Limit (out)
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Confidence Range
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TESTS OF HYPOTHESES
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Null Hypotheses (H0)

• It is a statement about the probability
  distribution of a random variable.
• It is a statement about the main population not
  the statement about the sample
• If the null hypothesis is false, the research
  hypothesis must be true.

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Alternative Hypothesis (Ha)

• It is the hypothesis that the reseacher wishes to
  support.
• Even though we wish to gain evidence in support
  of the alternative hypothesis, the null
  hypothesis is the one to be tested.

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Decision Table
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Type I and Type II error

• One can reduce Type I error (i.e. rejecting H0
  when H0 is true) only by increasing the
  confidence level.
• But reducing the Type I errors leads to an
  increase in Type II errors (i.e. accepting H0
  when H0 is false )

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Type I error, ?

• It is the producers risk,and the decision is
  made by the top management level.
• The producer does not want items of this quality
  rejected.

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Choosing the Right Significance Level

• In order to reduce both type of error one should
  increase the number of samples...
• ... But this requires both extra time and money.

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Questions ?