Uji Q Ketepatan Ketelitian

8/10/2019 Uji Q Ketepatan Ketelitian

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1.Uji Q

2.Ketepatan dan Ketelitian


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(1) Measurement data:0.189, 0.169, 0.187, 0.183, 0.186, 0.182, 0.181, 0.184, 0.181, 0.177

Q Test

Do the smallestand largestpoints need to be discarded?

ble

Number of values:

3 4 5 6 7 8 9 10

Q90%: 0.941 0.765 0.642 0.560 0.507 0.468 0.437 0.412

Q95%: 0.970 0.829 0.710 0.625 0.568 0.526 0.493 0.466


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Q Test

In statistics, the Qtestis used for identification and rejection of

outliers.

To apply a Qtest for bad data, arrange the data in order of increasing

values and calculate Qas defined:

Q(calculated)= Qgap/Qrange

Where Qgap =|outlier - value closest to the outlier|Qrange=|highest valuelowest value |

If Qcalculated> Qtable, DISCARD the questionable point.


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(1) For the data:

0.189, 0.169, 0.187, 0.183, 0.186, 0.182, 0.181, 0.184, 0.181, 0.177

Arranged in increasing order:

0.169, 0.177, 0.181, 0.181, 0.182, 0.183, 0.184, 0.186, 0.187, 0.189

Outlier is 0.169. Calculate Q:

With 10 observations at 90% confidence, Qcalculated< Qtable. Thereforekeep 0.169 at 90% confidence.


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The following replicate observations were

obtained during a measurement and theyare arranged in ascending order:

6.69, 6.18, 6.28, 4.85, 6.49

Can we reject observation 4.85 as an outlier

at a 95% confidence level?


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The following masses, in grams, were recorded in an

experiment to determine the average mass of a U.S.

penny:

3.067, 3.049, 3.039, 2.514, 3.048, 3.079, 3.094, 3.109,

3.102

Determine if the value of 2.514 g is an outlier at 95%

confidence level.


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1). Rata-rata (mean) dan standar deviasi (deviation)

2). Ketepatan (accuracy) dan ketelitian (precision)


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Rata-rata (mean)

The mean, X, is the numerical average obtained by dividing the sum

of the individual measurementsby the number of measurements


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Table Berat Uang Koin

What is the mean for the data in Table above?

Answer:

3.080 + 3.094 + 3.107 + 3.056 + 3.112 + 3.174 + 3.198 = 21.821


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Standard Deviation)

The absolute standard deviation, s, describes the spread of

individual measurements about the mean

Relative Standard Deviation X 100%


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What are the standard deviation, the relative standard

deviation, and the percent relative standard deviation for the

data in Table above ?

Table Berat Uang Koin


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Hasil pengukuran berat

koin bisa dituliskan sbb:

Berat koin = 3.1170.051g


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Accurate and Precise

Conceptual illustration

Accuracy and Precision

Accurate, but not Precise

Precise, but not accurate Not accurate, Not Precise


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ACCURACY

Accuracy can be defined as how close a

number is to what it should be.

Accuracy is determined by comparing anumber to a known or accepted value.

Assessing Accuracy


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Assessing Precision

Measurement of precision for a data set is the standard deviation (s)

For data sets that have more than 20 points

For data sets < 20 points

Relative Standard Deviation X 100%


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Example 1:

How old are you?

I am 22 years old (1)

I am 22 years and 8 months old (2)

I am 22 years, 8 months, and 5 days old

(3)

I am 22 years, 8 months, 5 days, and 10

hours old (4)


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Accuracy vs. Precision for

Example 1 Statement (2) is more accurate and more

precise that statement (1).

Statement (3) is more accurate and moreprecise than statement (2).

Statement (4) is more accurate and more

precise than statement (3).


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Example 2:

How long is a string ?

Student A measures the string at 2.63

0.02 m.

Using the same ruler, Student B

measures the string at 1.980.01 m.

Who is most precise?

Who is most accurate?


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Example 2 The actual measurement is 2.65 m.

Student A is fairly accurate and also very

precise.

Student B is very precise, however, he is

not very accurate. The lack of accuracy is

due to using the ruler incorrectly.


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Example 3 The actual measurement is 3.01 g.

Student A is reasonably accurate. He/She

was not very precise because the balancewas not capable of measuring to twodecimal places.

Student B is much more accurate because ofthe precision of his/her measurement andcloseness of her value to the actual value.

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Uji Q Ketepatan Ketelitian