Inferential statistics Flashcards
بسم الله الرحمن الرحيم
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population measures and smaple measures
population :
u For mean - sigma for SD - sigma square FOR variance - and pi for proprtion
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sample
X for mean
S2 for vairane
S for SD
Proptrion =p
The process of drawing conclsions from data obtained from the sample to the population form which it was selected?
Statistical inferences
Statistical inference imp in ?
Paramater estimation
Hypothesis testing
how to get SD?
To get the mean then
The value - mean then square the result and divde it on( n-1)
so you got variane get the root
SE=
SD/Root of N of sample
Unkownpopulation parameter =
Sample statistic +- Sampling error
The difference between a sample statitistic used to estimate a population parameter and the actual but unkonwon value of the parameter
It is ?
Sampling RANDOM error
As the sample size increases the stadnaed error ?
decreased!
population proprtion =
sample proportion p +- rendom error
=p +- z X SE proption
=p +- z X root of (P(1-P)/N)
We have 1000 person scanned for DM :
25 diabetics
so :
The proption of sample
The SD of proption
The SE = ?
get 95 % confidence interval
The proprtion of sample= 25/100= 0,25
SD = Root of ( p(1-p))
= root of ( .25 x ,75 )
=0.43
SE Proptortion = SD/Root of N =
=0,043
95 % CONFIDENCE INTERVAL = 0.25+- ( 1,96 X 0,043)=(17,1 - 32.8)
Central limit therorem
If we have a variable as SBP
- that is normally distributed in a population with
- mean u
-standard deivation sigma
-and we have many samples of the same size of N THEN
The means of these samples will be normally distributed with mean= u of population
and Standard devtiation = sigma / root of N
Unknwon population parameter = sample statistics +- sample error
but
Population parameter =
Sample statistics +-( Z*sampling error )
Z= Confidence cofficent which is constant
The best point of estimate for Population parameter is ?
the one you deduce from Random representational sample but without Certtainity
sample 64
Mean of SBP =129
SD = 4
so you can say without certainity the population mean bp= 129
if you want certainity use? Confidence Interval
Z 95% = ?
1,96
Z90% =
1.64
Z99% Confidence coffienet = ?
2,58
sigma =
root of
(Value -mean)square /N
SE=
SD/root of N
If a 64 PERSON sample with SD= 4 calculate the SE?
if the mean BP = 129
then calulcate Confidence interval and intepret the result
SE =4/Root 64
=4/8
=1/2
CI=
129+- 1.96*,5
128.02:129,98
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YOU ARE KNOW SURE 95% that population means lie in the range between ,,,m,,,,
A reange of values between Lower Confidence Linit and Upper Conifence limit that the population parameter lies within this range with a certain degree of Confidence called confidence level usually 95%
Confidence Interval
As the Z value becomes larger
The range of Confidence interval becomes larges
As the range of confidence interval become lesser
The More it beomces percise
What is the result of increasing sample in confidence interval give reason ?
Decreasing the range of confidence interval so becomes more percise
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The SE= sd / root of N
N increased so SE decreased and in consequncse
the Z*SE decrreases so the range decrease
Can be used to inference pipulation parameter
Each static form of sample
SD RR OR mean
ولما جاءت رسلنا إبراهيم بالبشري قالوا سلاما
standard deviation of sampling distribution
Standar erroe
Mean SE
Proportion SE?
MEAN SE=Sd/root N
Proporiton SE= ROOT
(P(1-P)/N)
