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## Hypothesis Testing with z testsArlo Clark-FoosReview: St in addition to ardizationAllows us t

Ruelas, Richard, Features Profiles Reporter has reference to this Academic Journal, PHwiki organized this Journal Hypothesis Testing with z testsArlo Clark-FoosReview: St in addition to ardizationAllows us to easily see how one score (or sample) compares with all other scores (or a population).CDC Example: JessicaJessica is 15 years old in addition to 66.41 in. tallFor 15 year old girls, = 63.8, = 2.66

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CDC Example: Jessica1. Percentile: How many 15 year old girls are shorter than Jessica50% + 33.65% = 83.65%CDC Example: Jessica2. What percentage of 15 year old girls are taller than Jessica50% – 33.65% OR 100% – 83.65% = 16.35%CDC Example: Jessica3. What percentage of 15 year old girls are as far from the mean as Jessica (tall or short)16.35 % + 16.35% = 32.7%

CDC Example: ManuelManuel is 15 years old in addition to 61.2 in. tallFor 15 year old boys, = 67, = 3.19Consult z table as long as 1.82 46.56%CDC Example: Manuel1. PercentileNegative z, below mean: 50% – 46.56% = 3.44%CDC Example: Manuel2. Percent Above Manuel100% – 3.44% = 96.56 %

CDC Example: Manuel3. Percent as extreme as Manuel3.44% + 3.44% = 6.88%Percentages to z ScoresSAT Example: = 500, = 100You find out you are at 63rd percentileConsult z table as long as 13% THIS z Table lists the percentage under the normal curve, between the mean (center of distribution) in addition to the z statistic.63rd Percentile = 63%50% + 13%z = –

Percentages to z ScoresSAT Example: = 500, = 100You find out you are at 63rd percentileConsult z table as long as 13% z = .33 X = .33(100) + 500 = 533UMD & GRE ExampleHow do UMD students measure up on the older version of the verbal GRE We know that the population average on the old version of the GRE (from ETS) was 554 with a st in addition to ard deviation of 99. Our sample of 90 UMD students had an average of 568. Is the 14 point difference in averages enough to say that UMD students per as long as m better than the general populationGiven in problem: M = = 554, = 99 M = 568, N = 90Remember that if we use distribution of means, we are using a sample in addition to need to use st in addition to ard error.UMD & GRE ExampleGiven in problem: M = = 554, = 99 M = 568, N = 90Consult z table as long as z = 1.34

THIS z Table lists the percentage under the normal curve, between the mean (center of distribution) in addition to the z statistic.z = 1.34Assumptions of Hypothesis TestingAssumptions of Hypothesis TestingThe DV is measured on an interval scaleParticipants are r in addition to omly selectedThe distribution of the population is approximately normalRobust: These hyp. tests are those that produce fairly accurate results even when the data suggest that the population might not meet some of the assumptions.Parametric Tests (we will discuss)Nonparametric Tests (we will not discuss)

Testing HypothesesIdentify the population, comparison distribution, inferential test, in addition to assumptionsState the null in addition to research hypothesesDetermine characteristics of the comparison distributionWhether this is the whole population or a control group, we need to find the mean in addition to some measure of spread (variability).Testing Hypotheses (6 Steps)Determine critical values or cutoffsHow extreme must our data be to reject the nullCritical Values: Test statistic values beyond which we will reject the null hypothesis (cutoffs).How far out must a score be to be considered extremep levels (): Probabilities used to determine the critical valueCalculate test statistic (e.g., z statistic)Make a decisionStatistically Significant: Instructs us to reject the null hypothesis because the pattern in the data differs from what we would expect by chance alone.The z Test: An ExampleGiven: = 156.5, = 14.6, M = 156.11, N = 97Populations, distributions, in addition to assumptionsPopulations:All students at UMD who have taken the test (not just our sample)All students nationwide who have taken the testDistribution: Sample distribution of meansTest & Assumptions: z testData are intervalWe hope r in addition to om selection (otherwise, less generalizable)Sample size > 30, there as long as e distribution is normal

The z Test: An ExampleState the null (H0) in addition to research (H1)hypothesesIn Symbols In Words H0: 1 2H1: 1 > 2ORH0: 1 = 2H1: 1 2H0: Mean of pop 1 will be less than or equal to the mean of pop 2H1: Mean of pop 1 will be greater than mean of pop 2 H0: Mean of pop 1 will be less equal to the mean of pop 2 H1: Mean of pop 1 will be different from the mean of pop 2The z Test: An ExampleDetermine characteristics of comparison distribution.Population: = 156.5, = 14.6Sample: M = 156.11, N = 97The z Test: An ExampleDetermine critical value (cutoffs)In Behavioral Sciences, we use p = .05p = .05 = 5% 2.5% in each tail50% – 2.5% = 47.5%Consult z table as long as 47.5% z = 1.96

THIS z Table lists the percentage under the normal curve, between the mean (center of distribution) in addition to the z statistic.95% / 2 = 47.5%zcrit = 1.96The z Test: An ExampleCalculate test statisticMake a DecisionDoes sample size matter

Increasing Sample SizeBy increasing sample size, one can increase the value of the test statistic, thus increasing probability of finding a significant effectWhy Increasing Sample Size MattersOriginal Example: Psychology GRE scoresPopulation: = 554, = 99Sample: M = 568, N = 90Why Increasing Sample Size MattersNew Example: Psychology GRE scores as long as N = 200Population: = 554, = 99Sample: M = 568, N = 200

Feel com as long as table yetCould you complete a similar problem on your ownCould you per as long as m the same steps as long as a one-tailed test (i.e., directional hypothesis)Are you com as long as table with the concept of p-value (alpha level) in addition to statistical significanceCan you easily convert back in addition to as long as th between raw scores, z scores/statistics, in addition to percentagesIf you answered No to any of the above then you should be seeking extra help (e.g., completing extra practice problems, attending SI sessions, coming to office hours or making appt. with professor).

## Ruelas, Richard Features Profiles Reporter

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