PSYC 2101Exam # 3 Study GuideOne Sample Tests• Z-scores– Review• What is the formula for a z-score?– Z=x-mu/standard deviation• What is the formula for a z test?– Z=mean-mu of mean/ standard deviation of mean• Why do we care about z scores?– What about the standard normal distribution?• We can use the z table to find the area under the curve• Hypothesis testing – 5 steps– Making a probability, based on our observed value what’s the probability of the null hypothesis– Used with a z testa. Identify populations, test we’re using & any assumptions1. Comparing two populationsb. State/specify the null & research hypotheses1. Identify null & research hypothesis; In words & symbolically; p=0 à no relationshipc. Determine critical values/p values1. Critical value à threshold; below or above a certain # we determine if we are oraren’t going tor eject the null2. After determining if we reject it or not we relate what it means back to the original variable; this there a relationship?d. Calculate test statistics (used with a z test)e. Make a decision• Determining Critical Values– Remember when testing hypotheses we are making a probability judgment about H0• Probability to reject the null is small– Before collecting our data we need to determine the minimum probability that H0 is true we are willing to accept.• Called alpha level or significance level (also is probability of making a Type 1 error)• Usually we use alpha= .05; 5% chance that if we reject the null, the null is actually true– Finally this has to be translated to the distribution we are working with.• Determining Critical Values – Z test; Example: z-test– Loren Michaels wants to find out if the “new” ‘Tonight Show’ with Jimmy Fallon is getting as many laughs as the original ‘Tonight Show’ with Jay Leno– Fallon• N = 4• M = 1.2• SD = .4– Leno• μ = .8• σ = .6• Normally distributed– Fallon: N=4 / M=1.2 / SD=.4– Leno: μ = .8 / σ = .6 / Normally distributed– Step #1: Identify populations, test we’re using & any assumptions• Population: “Tonight show with Leno” & “Tonight show with Fallon”• Test: Z test Ζ = Μ - μ ÷ σ √Ν– Step #2: State/specify the null & research hypotheses• Ho μF = μLà population mean for Fallon = population mean for Leno/Equal # of laughts between each• H1 μF ≠ μL– Step #3: Determine critical values/p values• Critical value: zcrit = +/- 1.96 (always the CV)– Step #4: Calculate test statistics Ζ = Μ - μ ÷ σ √Ν • Z = 1.2 − .8 ÷ (.6/ √4) à Z = .4 / .3 à Z = 1.33– Step #5: Make a decision• “Fail to reject the null” H1 μF ≠ μL• Hypothesis tests: Single Samples– One tailed test (one group)• One critical value• Only have a critical values on one side of the distribution• Effects our hypothesis & our critical values– Two tailed test (comparing two groups)• Two critical values• Example we just did• Has 2 critical values• Is there a difference between the two groups?– How would this work with a z-test?• Another Example z test– One tailed test (single group = one tailed)– Human short term memory can hold 7 plus or minus 2 pieces of information.• Does intensive shock based memory training improve memory?• M = 7.6• SD = 4.1• N = 35– One tailed test (single group = one tailed)– Human short-term memory can hold 7 plus or minus 2 pieces of information. Does intensive shock based memory training improve memory?• M = 7.6 / SD = 4.1 / N = 35– Step #1: • Population: “People without shock training” & “People with shock training” • Test: Z Test– Step #2: • Ho μF ≤ μL– “People with shock would have worse or equal memory compared to no shock”• H1 μF > μL– “People would remember more with shock compared to no shock”– Step #3:• Zcrit = 1.65 (only one critical value when it’s one tailed)• Interested in the highest 5% of the distribution– Step #4: Ζ = Μ – μ ÷ σ √Ν• Z = 7.6 – 7 ÷ (2 / √35) à Z = .6 / .34 à Z = 1.77– Step #5:• “Reject the Null” Ho μF ≤ μL• T-tests– Allows us to compare means when we don’t know the standard deviations– What happens when we don’t know the standard deviation of a population?– Or when we want to compare two samples?– We need a new tool!– The t-test• Types of T-tests– Three types of t-tests• One sample– Similar to z-test but we don’t know the population SD• Dependent Samples– Comparing two sample & don’t have the population means• Independent Samples– Comparing two samples• T-tests– What do we do if we do not have the population SD?• Use the sample SD– If we don’t know the population SD• What is the difference between the population & sample SD?– N & N-1• T Distributions– With sample standard deviations we are less sure about the shape of the population distribution– The T distribution takes this into account• There’re different T distribution for each sample size– Slightly different shape at different sample sizes• We have to make a guess on the population parameter• Sample size increasing T Distributions– As ample size increases the sample SD approaches o & the T distribution approaches the z distribution– The size of the distribution is most important for determining our critical values– Our critical values comes from the distribution• Using the T table– To find Critical Values we need to use the T table (appendix E Table E.6)• One or two tailed test & look at alpha level & where they are in the column depends on the sample size– We do not look up sample size, instead we look up in the column Degrees of Freedom (df)• The number of scores that are free to vary when estimating a population parameter from a sample– Certain # of scores that can take any values & a certain #of values that have a constraint• One sample T test: df = N-1• One sample t-test– Indicates the distance of a sample mean from a population mean– Work through the 5 steps• Doing a T test– Use the same 5 steps of hypothesis testing we used with a z test– When finished, write your results in the following format:• t(df) = #.##, p <(or >) .05– Refer to APA format document under Lab 6 to understand more about this format• I did a t test with this many degrees of freedom (which you can find the critical values with df) which equals our test statistic ; P presents the