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Types of errors.ppt

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Types of errors.ppt

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									Zubair Latif
-   Measurements even being valid,
     if lack in precision and accuracy, irrespective
    of the magnitude or quantity of deviation
    from the intended measurement, are called
    errors.
    - One sided repeated errors or
      systematic errors are called   bias.
- Selection or allocation biases,
- Measurement bias,
- Instrument bias,
- Inter & intra investigator or
- Observer’s bias,
- Misclassification bias etc.
   are some of the frequently encountered
                                  bias
   Sometimes primary goal is to describe data.
    Then we are interested in estimation. We
    estimate parameters such as
     Means
     Variances
     Correlations

   When primary goal is to draw a conclusion
    about a state of nature or the result of an
    experiment, we are interested in statistical
    testing
1- NULL and Alternative Hypothesis

   H0: μ = μ0 OR μ ≤ μ0 OR μ ≥ μ0

OR      μ1 = μ2 OR μ1 ≤ μ2 OR μ1 ≥ μ2

   HA: μ ≠ μ0 OR μ > μ0 OR μ < μ0

        μ1 ≠ μ2 OR μ1 > μ2 OR μ1 < μ2
2- Level of Significance

Criterion used for rejecting the null hypothesis.
Or true null hypothesis can be incorrectly
  rejected, the chance of committing this error is
  level of significance

Alpha (α) is used as symbol with some pre
  assigned value as 5%, 1%, 10%, etc.
                                                  Equal           Unpaired t-test
                                                  Variance
                                                  Unequal         Welch (modified
                                  Independent
                                                  Variance        t-) test
                      t-test
       Quantitative   (perhaps)
                                  Paired         Variance
                                                                  Paired t-test
data                                             doesn’t
                                                 matter
       Ordinal or
       Nominal
                      X2 Test                   Pearson X2 Test
                                  Independent

                                  Paired        McNemar’s X2 Test
4- Calculation
Calculate the value of test-statistics by
   using sample data (using formula).

5- Critical Region
Divide the entire set of values of test-
   statistics into two mutually exclusive
   regions in which one will lead to
   rejection of Null Hypothesis according to
   your level of significance.
    Level of Significance, a
   and the Rejection Region
H0: m  μ0                           a       Critical
                                             Value(s)
H1: m < μ0
             Rejection Regions   0
                                         a
H0: m  μ0
H1: m > μ0
                                 0
                                         a/2
H0: m = μ0
H1: m  μ0
                                 0
6- Decide about rejection or acceptance of Null
   Hypothesis


P-value: The P value of the null hypothesis is a
  probability, with a value ranging from zero to
  one, the probability of obtaining a test statistic
  at least as extreme as the one that was actually
  observed, assuming that the null hypothesis is
P-value = Prob. of making Type I error.
P-Value = pr(reject H0 / H0 is true)
Generally, one rejects the null hypothesis if the
   p-value is smaller than or equal to the
   significance level often represented by the
   Greek letter α (alpha).
P-Value = pr (test statistic falls in CR/parameter
   is consistent with H0)
 P-Value = pr(t ≥(?)tobs)
 H0 : ρ=0 at α=0.05
r=0.25, n=20
P-value = 0.30
r ≥ 0.44 to get
P ≤ 0.05
•   Type I Error
     Reject True Null Hypothesis (“False Positive”)

     Probability of Type I Error Is a

       Called Level of Significance

       Set by researcher



•   Type II Error
     Do Not Reject False Null Hypothesis (“False
      Negative”)
     Probability of Type II Error Is b (Beta)
           Result Possibilities
                             H0: Innocent


           Jury Trial                       Hypothesis       Test

              Actual Situation                    Actual Situation

Verdict      Innocent     Guilty   Decision      H 0 True   H 0 False

                                    Do Not
                                                              Type II
Innocent      Correct     Error     Reject         1- a
                                                             Error (    b )
                                       H0
                                                  Type I
                                    Reject                    Power
Guilty         Error     Correct                  Error
                                       H0                     (1 - b )
                                                    (a )
      a & b Have an
    Inverse Relationship
             Reduce probability of one error and the
             other one goes up.




             b

a

								
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