STATISTICS â UNDERSTANDING HYPOTHESIS TESTS

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Step 4 (and Step 8)Statistics – Understanding Hypothesis Tests:Proportions2014 The estimate is based on the parameter of interest we are investigating:ParameterEstimate1. Single mean µ: estimate x2. Single proportion p: estimate pˆ3. Difference between two means µ 1 – µ 2:(independent samples)estimatex 1 x 24. Difference between two proportions p 1 – p 2 : estimate pˆˆ1 p2Step 5 (and Step 8) The standard error is based on the estimate, the number of samples andsample size(s):Estimatese(estimate)1. estimate xse(x)sn2. estimate pˆse(ˆ)p pˆ(1npˆ)3. estimate x 1 x2se(x1 x2)sn© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 12 of 44The University of Auckland211sn4. estimate pˆˆ1 p Situation (a) Proportions from two2independent samplesse(ˆp1Situation (b)se(ˆpSituation (c)se(ˆp12222 pˆ) 1pˆ ˆ1(1 p1)n1pˆˆ2(1 pnOne sample of size n, severalresponse categories pˆ) 2pˆ1 pˆ2 (ˆ pn12 pˆ)One sample of size n, manyyes / no itemsmin imum(ˆp1 pˆ2,qˆ1 qˆ2) (ˆ p1 pˆ2)nwhere qˆˆ1 1 p1and qˆˆ2 1 p2222) pˆ)22
Statistics – Understanding Hypothesis Tests:Proportions2014The degrees of freedom are based on the problem type:EstimateDegrees of Freedomi.e. forproportions,1. estimate x df n 1assume thedegrees of2. estimate pˆdf = ∞freedom is infinity,hence replace t3. estimate x 1 x2df = minimum(n 1 – 1, n 2 – 1) distribution with zdistribution (i.e.4. estimate pˆˆ1 p2df = ∞the standardNormal). The t-test statistic Is the number of standard errors our estimate is from the hypothesisedvalue. We calculate it using:Step 6 The P-value:t0estimate hypothesised valuestd error Is the probability that sampling variation would produce an estimate thatis further away from the hypothesised value than the estimate weobtained from our data, assuming that the null hypothesis is true. It is a measure of evidence against H 0 .see backpage forFormulaeSheet We calculate the P-value using the t-test statistic and the appropriateStudent’s t distribution.Alternative hypothesis P-value = area of shaded regionT ~ Student(df )H 1 : parameter hypothesised value(2-sided)H 1 : parameter > hypothesised value(1-sided)2-tailed test1-tailed testH 1 : parameter < hypothesised value(1-sided)1-tailed test© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 13 of 44The University of Auckland
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STATISTICS â UNDERSTANDING HYPOTHESIS TESTS

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STATISTICS â UNDERSTANDING HYPOTHESIS TESTS