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# Types of errors.ppt

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Types of errors.ppt

• pg 1
```									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
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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