Infer Ential Statistics
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INFERENIAL STATISTICS www.drjayeshpatidar.blogspot.com
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Inference Statistics
Transcript of Infer Ential Statistics
INFERENIAL
STATISTICS
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INFERENIAL STATISTICS investigate questions, models and
hypotheses. In many cases, the
conclusions from inferential statistics
extend beyond the immediate data
alone.
Statistics that use sample data to
make decision or inferences about a
population
Populations are the group of
interest –but data analyzed on
samples. www.drjayeshpatidar.blogspot.in
INFERENIAL STATISTICS
Based on the laws of probability
The larger the difference between
the groups ,the lower the probability
is that the difference occurred by
chance
Based on the assumption that
samples are randomly selected
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INFERENIAL STATISTICS
to make judgments of the probability that an
observed difference between groups is a
dependable one or one that might have happened
by chance in this study.
Thus, inferential statistics to make inferences from
our data to more general conditions
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Purposes
Estimating population parameter from sample
data
Testing hypotheses
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Estimating population parameter
o Sampling error – when the sample
does not accurately reflect the
population
o Sampling distribution
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Pulse measurements on a population of 20 subjects
Av. pulse rates of a
grp.of cardiac
patients
66,71,70,67,80,63,
65,79,59,70,67,66,
70,74,92,80,71,55,
83,72
Mean pulse rate=71
Random sample#1
Random sample#2
Random sample#3
Mean pulse rate of
population=71
*Above average for
population
66,59,70,55,66
80,92,83,79,80
71,71,70,64,67
Mean pulse rate of
Random
sample#3=71
Mean=61 Mean=83*
Mean=71
Mean pulse rate of
Randomsample#1Consi
derably Below average
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Sampling distribution
A theoretical frequency distribution ,based
on an infinite no of samples
Based on mathematical formulas and logic
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Sampling distribution of mean
In normal distribution 68%values lie between+or –
1SDand approx 95%lies between +or –2SD
ie 95%of the values in a normal distribution lie
between +or –1.96SD from the mean.
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Confidence intervals
It is a range of values that with a specified degree
of probability ,is thought to contain the population
value.
They contain a lower and an upper limit.The
researcher asserts with some degree of confidence
that the population parameter lies within those
boundaries.
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A confidence interval (CI) is an interval estimate of a
population parameterInstead of estimating the
parameter by a single value, an interval likely to
include the parameter is given.
Thus, confidence intervals are used to indicate the
reliability of an estimate.
How likely the interval is to contain the parameter is
determined by the confidence level or confidence
coefficient.
Increasing the desired confidence level will widen
the confidence interval.
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Were this procedure to be repeated on
multiple samples, the calculated
confidence interval (which would differ
for each sample) would encompass the
true population parameter 90% of the
time."
Note that this need not be repeated
sampling from the same population, just
repeated sampling
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The confidence interval represents
values for the population parameter for
which the difference between the
parameter and the observed estimate is
not statistically significant at the 10%
level―
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If the true value of the parameter lies
outside the 90% confidence interval once it
has been calculated, then an event has
occurred which had a probability of 10% (or
less) of happening by chance
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Testing hypothesis The null hypothesis is subjected to statistical
analysis
Steps State the research hypothesis State the null hypothesis to be tested Choose the appropriate statistical test for the data Decide on the level of significance Decide the test –one tailed or two tailed test to be used. Calculate the test statistics using the research data Compare the value to the critical value to that test Reject or fail to reject null hypothesis Determine support or lack of support for the research hypothesis.
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Level of significance
Probability of rejecting a null hypothesis when it
is true ,and it should not be rejected(alpha)
Most common level of significance.. .05
The rresearcher Is willing to risk being wrong
5%of the time or 5 times out of 100,when
rejecting the null hypothesis
More accurate .01or even at .001
Risk 1%
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Degree of freedom
Concerns the no of values that are
free to vary. df and a no.
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Null hypothesis ---false ---reject—
correct decision
Null hypothesis--- true –accept –
correct decision
Null hypotheses--- true--- rejected---
--type I error
Null hypothesis-- false –accepted---
Type II errror
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Type II error –controlled –using a
large sample
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Type I Error No error
No error Type II Error
True false
Null
rejec
ted
Null
not
rejected
Actual situation in population
Null hypothesis
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Choosing statistical test:
1. Are you comparing groups or test scores?Are you correlating variables
2. What is th helevel of measurement of the variables (nominal,ordinal,interval/ratio)
3. How larg eare the groups?
4. How many sets or groups are being considered
5. Are the scores or observations dependent or independent?
6. How many observations are available o the each group
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Statistical tests used
1. T tests
2. analysis of variance
3. chi-square
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Thank you
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