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STATISTIK DASARISI:DASAR PENYUSUNAN HIPOTESISKONSEP DASAR P VALUEUJI T
Basic Statisticsintuitively considered
Populations and Samples-an example-Population - all I.U. undergraduatesSample - 100 M342 students its not a random sample, but lets ignore that for now.
Parameters and StatisticsParameter - a characteristic of a populationthe average I.U. undergraduate is 20.8 years oldStatistic - a characteristic of a sample
the standard deviation of the sample was 0.86approximately 68% of the sample is between 19.87 and 21.59for real data, percentage imputations from standard deviations are usually not too accurate
Sampling DistributionsIf we were to administer the Alcohol Consumption Survey in 50 classes, we could calculate 50 means for number of drinks.The distribution of these 50 means is normally distributed.standard deviations are meaningfulthe standard deviation of the mean is called the standard error of the mean
For our class survey - 68% of the sample means will be between (6.09 - 0.36) and (6.09 + .36).(to get the Std. Error of the Mean with SPSS, you need to make the selection in Options)
Every statistic has a sampling distribution.If we calculated a standard deviation for each sample, that distribution would have its own mean and standard error. A standard deviation is a measure of variation, or heterogeneity. Can you think of how a merchandising manager for Sears might use a standard error of a standard deviation?
HypothesesHypotheses make statements about parameters.Suppose a Legislator says, In Bloomington, they have seven or more drinks when they go out.This forms our null hypothesesHo: m > 7.0To refute the Legislator, which we want to do, we try to find evidence for the alternative hypothesisHa: m < 7.0
Hypotheses, cont.Hypotheses cannot prove a population is a particular way.Hypotheses can tell us the probability that our population is not a particular way.Thus, our null hypotheses are usually stated in terms of what we would not like to be true.
Test StatisticsTest Statistics, calculated from a formula, assess the evidence against a null hypothesischoice of a particular test statistic depends upon the type of hypothesis being testedto test a mean, SPSS uses a t statistic
p - valuesa p - value is a probability that answers the conditional question: If the null hypothesis were true, what is the probability of observing the result?the smaller the p value, the greater the significance, the stronger the evidence against Hothe smaller the p value, the smaller the probability that the result occurred by chancethe magnitude of the test statistic is used to reject or not reject the null hypothesisusually, small p values are associated with large (positive or negative) test statistics.
NOT pWhat isnt p?p is not the probability that the null hypothesis is truea statistically significant p-value does not mean the results are of any practical valueWhy should I use a #@$% p-value?it will prevent you from making false conclusions for example:Saying things are different when they are notSaying things are not different when they are
Common Presentation MistakesConcluding that two means are different when they arent.Greeks drink more than independentsConcluding that two means are similar when they arent.Men and women go out the same amountBefore making a conclusion, ask if its testable!
SPSS and p - valuesIn SPSS, p - values are called significance levels and abbreviated Sig.SPSS usually assumes the hypothesis you are testing is one of equality, for example,Ho: m = 7.0a very low, or very high sample mean would lower the p - valueequality tests are often referred to as two-tail tests
p-values cont.In our case, the probability of observing a sample mean as extreme as 6.09 if the population mean were 7.0 is 0.014 .
One-tail testsOur null hypothesis for the legislators challenge is one tailed - Ho: m > 7.0the p - value for a one-tail test, in this case, is half that of a two tailed testthe probability of obtaining our results if the legislator is correct is only .007for I.U.s PR department, this sounds a bit better
The Importance of Common SenseThe sample mean is 6.09, the standard error of the mean is 0.36Intuitively, what do you think the one-tailed p - value would be if Ho: m > 7.0 p = .007Ho: m > 6.5 ?Ho: m > 6.0?Ho: m > 5.5?
0.0070.1300.5950.945
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Population Mean = 6.0
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7.850.071160965307.850.001104078107.850.000002578507.850.00000000090
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7.870.06246861807.870.000898513407.870.000001945407.870.00000000060
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7.930.041498005507.930.000475558507.930.000000820307.930.00000000020
7.940.038660735307.940.000426578707.940.000000708507.940.00000000020
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&A
Page &P
Sheet1
&A
Page &P
Population Mean = 6.5
&A
Page &P
Population Mean = 7.0
&A
Page &P
Population Mean = 6.0
&A
Page &P
Population Mean = 5.5
Chart3
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Population Mean = 5.5
Sheet1
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1.01001.01001.01001.0100
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1.07001.07001.07001.0700
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1.11001.11001.11001.1100
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1.25001.25001.25001.2500
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1.27001.27001.27001.2700
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1.3001.3001.3001.300
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1.35001.35001.35001.3500
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1.38001.38001.38001.3800
1.39001.39001.39001.3900
1.4001.4001.4001.400
1.41001.41001.41001.4100
1.42001.42001.42001.4200
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1.48001.48001.48001.4800
1.49001.49001.49001.4900
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1.51001.51001.51001.5100
1.52001.52001.52001.5200
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1.56001.56001.56001.5600
1.57001.57001.57001.5700
1.58001.58001.58001.5800
1.59001.59001.59001.5900
1.6001.6001.6001.600
1.61001.61001.61001.6100
1.62001.62001.62001.6200
1.63001.63001.63001.6300
1.64001.64001.64001.6400
1.65001.65001.65001.6500
1.66001.66001.66001.6600
1.67001.67001.67001.6700
1.68001.68001.68001.6800
1.69001.69001.69001.6900
1.7001.7001.7001.700
1.71001.71001.71001.7100
1.72001.72001.72001.7200
1.73001.73001.73001.7300
1.74001.74001.74001.7400
1.75001.75001.75001.7500
1.76001.76001.76001.7600
1.77001.77001.77001.7700
1.78001.78001.78001.7800
1.79001.79001.79001.7900
1.8001.8001.8001.800
1.81001.81001.81001.8100
1.82001.82001.82001.8200
1.83001.83001.83001.8300
1.84001.84001.84001.8400
1.85001.85001.85001.8500
1.86001.86001.86001.8600
1.87001.87001.87001.8700
1.88001.88001.88001.8800
1.89001.89001.89001.8900
1.9001.9001.9001.900
1.91001.91001.91001.9100
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1.93001.93001.93001.9300
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1.99001.99001.99001.9900
200200200200
2.01002.01002.01002.0100
2.02002.02002.02002.0200
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2.04002.04002.04002.0400
2.05002.05002.05002.0500
2.06002.06002.06002.0600
2.07002.07002.07002.0700
2.08002.08002.08002.0800
2.09002.09002.09002.0900
2.1002.1002.1002.100
2.11002.11002.11002.1100
2.12002.12002.12002.1200
2.13002.13002.13002.1300
2.14002.14002.14002.1400
2.15002.15002.15002.1500
2.16002.16002.16002.1600
2.17002.17002.17002.1700
2.18002.18002.18002.1800
2.19002.19002.19002.1900
2.2002.2002.2002.200
2.21002.21002.21002.2100
2.22002.22002.22002.2200
2.23002.23002.23002.2300
2.24002.24002.24002.2400
2.25002.25002.25002.2500
2.26002.26002.26002.2600
2.27002.27002.27002.2700
2.28002.28002.28002.2800
2.29002.29002.29002.2900
2.3002.3002.3002.300
2.31002.31002.31002.3100
2.32002.32002.32002.3200
2.33002.33002.33002.3300
2.34002.34002.34002.3400
2.35002.35002.35002.3500
2.36002.36002.36002.3600
2.37002.37002.37002.3700
2.38002.38002.38002.3800
2.39002.39002.39002.3900
2.4002.4002.4002.400
2.41002.41002.41002.4100
2.42002.42002.42002.4200
2.43002.43002.43002.4300
2.44002.44002.44002.4400
2.45002.45002.45002.4500
2.46002.46002.46002.4600
2.47002.47002.47002.4700
2.48002.48002.48002.4800
2.49002.49002.49002.4900
2.5002.5002.5002.500
2.51002.51002.51002.5100
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2.53002.53002.53002.5300
2.54002.54002.54002.5400
2.55002.55002.55002.5500
2.56002.56002.56002.5600
2.57002.57002.57002.5700
2.58002.58002.58002.5800
2.59002.59002.59002.5900
2.6002.6002.6002.600
2.61002.61002.61002.6100
2.62002.62002.62002.6200
2.63002.63002.63002.6300
2.64002.64002.64002.6400
2.65002.65002.65002.6500
2.66002.66002.66002.6600
2.67002.67002.67002.6700
2.68002.68002.68002.6800
2.69002.69002.69002.6900
2.7002.7002.7002.700
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2.73002.73002.73002.7300
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2.78002.78002.78002.7800
2.79002.79002.79002.7900
2.8002.8002.8002.800
2.81002.81002.81002.8100
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2.83002.83002.83002.8300
2.84002.84002.84002.8400
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2.86002.86002.86002.8600
2.87002.87002.87002.8700
2.88002.88002.88002.8800
2.89002.89002.89002.8900
2.9002.9002.9002.900
2.91002.91002.91002.9100
2.92002.92002.92002.9200
2.93002.93002.93002.9300
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2.99002.99002.99002.9900
30030030030.00000000010
3.01003.01003.01003.010.00000000010
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