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Reasoning in Psychology Using Statistics Psychology 138 2015 • Don’t forget Quiz 5 is due Fri. Mar. 20 at midnight Announcements Reasoning in Psychology Using Statistics • Hypothesis testing: a five step program – – – – – Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data from your sample Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis Note: In the labs I combine steps 1 & 2, so it is described as a 4 step program Testing Hypotheses Reasoning in Psychology Using Statistics • Hypothesis testing: a five step program – – – – – Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data from your sample Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis Testing Hypotheses Reasoning in Psychology Using Statistics • A simpler case – Population: 2 4 6 8 – All possible samples of size n = 2 mean mean 2 2 4 6 2 5 2 4 2 6 2 8 4 2 4 4 3 4 5 4 8 6 2 6 4 3 4 6 6 6 8 6 4 5 There are 16 of them mean 8 2 5 8 4 8 6 8 8 6 7 Distribution of sample means Reasoning in Psychology Using Statistics 6 7 8 5 4 3 2 1 In long run, the random selection of tiles leads to a predictable pattern The distribution of sample means 2 3 4 5 6 7 8 means 2 mean 2 2 4 mean 6 5 8 mean 2 5 2 4 3 4 5 4 8 8 4 2 6 6 2 8 6 2 8 6 4 8 8 4 2 3 4 6 6 4 4 6 8 6 4 5 6 7 Distribution of sample means Reasoning in Psychology Using Statistics 6 7 8 5 4 3 2 1 Using the distribution of sample means • Finding out how likely is a particular sample 2 3 4 5 6 7 8 means X f p 8 1 0.0625 7 2 0.1250 6 3 0.1875 5 4 0.2500 4 3 0.1875 3 2 0.1250 • Sample problem: – What is the probability of getting a sample (n = 2) with a mean of 6 or more? P(X > 6) = .1875 + .1250 + .0625 = 0.375 • Same as before, except now we are asking about sample means rather than single scores 2 1 0.0625 Distribution of sample means Reasoning in Psychology Using Statistics • Distribution of sample means is a “virtual” distribution between the sample and population – Note: There is a different one for each sample size Population Distribution of sample means Sample • Shape • Center • Spread Distribution of sample means Reasoning in Psychology Using Statistics • Shape – If population is Normal, then the dist of sample means will be Normal – If the sample size is large (n > 30), the DSM will be approximately Normal (regardless of shape of the population) Distribution of sample means Population n > 30 Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Center – The mean of the dist of sample means is equal to the mean of the population Population m Distribution of sample means same numeric value different conceptual values Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Center – The mean of the dist of sample means is equal to the mean of the population – Consider our earlier example Population 2 4 6 Distribution of sample means 8 μ= 2+4+6+8 4 =5 5 4 3 2 1 2 3 4 5 6 7 8 means = 2+3+4+5+3+4+5+6+4+5+6+7+5+6+7+8 16 =5 Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Spread – The Stand. Dev. of the Distrib. of Sample Mean depends on 2 things • Standard deviation of the population • Sample size Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Spread • Standard deviation of the population X3 X1μ X2 X3 X1μ X2 – The smaller the population variability, the closer the sample means are to the population mean, so the smaller the spread of sample means Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Spread • Standard deviation of the population • Sample size n=1 μ X Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Spread • Standard deviation of the population • Sample size n = 10 μ X Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Spread • Standard deviation of the population • Sample size n = 100 - The larger the sample size the smaller the spread of sample means μ X Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Spread • Standard deviation of the population • Sample size – Putting them together we get the standard deviation of the distribution of sample means sX = s n - The smaller the population variability, … the smaller the spread - The larger the sample size the smaller the spread – Commonly called the standard error Properties of the distribution of sample means Reasoning in Psychology Using Statistics • All three of these properties are combined to form the Central Limit Theorem sX = MEMORIZE THIS s n – For any population with mean μ and standard deviation , the distribution of sample means for sample size n will approach a normal distribution with a mean of μ and a standard deviation of s as n approaches infinity n (good approximation if n > 30). Properties of the distribution of sample means Reasoning in Psychology Using Statistics • The standard error is the average amount that you’d expect a sample (of size n) to deviate from the population mean Keep your distributions – In other words, it is an estimate of the error that you’d expect by straight by taking care chance (it is our estimate of the sampling error) with your notation Population Distribution of sample means sX = μ s n Sample s X Properties of the distribution of sample means Reasoning in Psychology Using Statistics • Hypothesis testing: a five step program – – – – – Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data from your sample Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis Testing Hypotheses Reasoning in Psychology Using Statistics • How do we know which test to use? – The design of the research: how many groups, how many scores per person, etc. Start here Statistical test decision tree Reasoning in Psychology Using Statistics • How do we know which test to use? – The design of the research: how many groups, how many scores per person, etc. Could be difference between a sample and a population, or between different samples observed difference test statistic = difference expected by chance As a result, the test statistic changes Based on standard error or an estimate of the standard error Generic statistical test Reasoning in Psychology Using Statistics Both of these parts change as a function of the design test statistic = observed difference difference expected by chance • Transform the distribution of sample means into the appropriate standardized distribution (as determined by the design features) Distribution of sample means Test statistic distribution We will use 2: z’s & t’s sX Test statistic Using the distribution of sample means Reasoning in Psychology Using Statistics test statistic = observed difference difference expected by chance Old z-formula z= New z-formula X -m s zX = X - mX sX • Same as before,with two differences: – Uses the distribution of sample means – Ask questions about samples rather than individual scores One sample z-test statistic Reasoning in Psychology Using Statistics test statistic = observed difference difference expected by chance Old z-formula population mean raw score z= sample mean X -m population standard deviation New z-formula s zX = standard error One sample z-test statistic Reasoning in Psychology Using Statistics mean of the distribution of sample means X - mX sX test statistic = observed difference difference expected by chance Old z-formula z= New z-formula X -m s zX = X - mX sX • Same as before,with two differences: – Uses the distribution of sample means – Ask questions about samples rather than individual scores One sample z-test statistic Reasoning in Psychology Using Statistics Old z-formula What is the probability of getting a 630 or better on the SAT? From the table: μ = 500, σ = 100, Normal z(1.3) =.0968 z= X -m s 630 - 500 = =1.3 100 So the probability is 0.0968 New z-formula What is the probability of getting a sample of n = 4 students with an average of 630 or better on the SAT? μ = 500, σ = 100, Normal From the table: s 100 sX = = = 50 z(2.6) =.0047 n 4 X - m X 630 - 500 = = 2.6 zX = 50 sX So the probability is 0.0047 One sample z-test statistic Reasoning in Psychology Using Statistics • Hypothesis testing: a five step program – – – – – Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data from your sample Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis Testing Hypotheses Reasoning in Psychology Using Statistics • What are we doing when we test the hypotheses? – Consider a variation of our memory experiment example Memory patients We test this one Memory treatment Memory Test X Population of memory patients MemoryTest μ & known Compare these two means Conclusions: H0: • The memory treatment sample are the same as those in the population of memory patients. HA: • They aren’t the same as those in the population of memory patients Performing your statistical test Reasoning in Psychology Using Statistics • What are we doing when we test the hypotheses? Real world (‘truth’) H0: is true (no treatment effect) H0: is false (is a treatment effect) One population Two populations XA The memory treatment sample are the same as those in the population of memory patients. XA They aren’t the same as those in the population of memory patients We test this one Performing your statistical test Reasoning in Psychology Using Statistics • The generic test statistic distribution (a transformation of the distribution of sample means) – To reject the H0, you want a computed test statistics that is large • The probability of having a sample with that mean is very low – What’s large enough? • The alpha level gives us the decision criterion Distribution of the test statistic α-level determines where these boundaries go “Generic” statistical test Reasoning in Psychology Using Statistics • The generic test statistic distribution (a transformation of the distribution of sample means) – To reject the H0, you want a computed test statistics that is large • The probability of having a sample with that mean is very low – What’s large enough? • The alpha level gives us the decision criterion Distribution of the test statistic If test statistic is here Reject H0 If test statistic is here Fail to reject H0 “Generic” statistical test Reasoning in Psychology Using Statistics • The alpha level gives us the decision criterion Two -tailed = 0.05 Reject H0 0.025 split up into the two tails Fail to reject H0 0.025 z .00 .01 … -3.4 -3.3 : -1.9 : 0 : : 1.0 : 1.9 : 3.4 0.0003 0.0005 : 0.0287 : 0.5000 : : 0.8413 : 0.9713 : 0.9997 0.0003 0.0005 : 0.0281 : 0.5040 : : 0.8438 : .9719 : 0.9997 … … .06 .0250 .9750 • Go to the table (unit normal table for z-test) and find the z that has 0.050 in the tails. Zcritical = ±1.96 “Generic” statistical test Reasoning in Psychology Using Statistics • The alpha level gives us the decision criterion Two -tailed One -tailed = 0.05 all of it in one tail Reject H0 Reject H0 0.05 Fail to reject H0 Reject H0 Fail to reject H0 Fail to reject H0 • Go to the table (unit normal table for z-test) and find the z that has 0.050 in the tail. Zcritical = +1.645 “Generic” statistical test Reasoning in Psychology Using Statistics • The alpha level gives us the decision criterion Two -tailed One -tailed = 0.05 Reject H0 all of it in one tail Reject H0 0.05 Fail to reject H0 Reject H0 Fail to reject H0 Fail to reject H0 • Go to the table (unit normal table for z-test) and find the z that has 0.050 in the tail. Zcritical = -1.645 “Generic” statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. Memory patients Memory treatment Memory Test X Compare these two means 1-sample z-test Reasoning in Psychology Using Statistics Population of memory patients Memory Test σ is known μ is known • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. Memory patients Memory treatment Memory Test X Compare these two means 1-sample z-test Reasoning in Psychology Using Statistics – 1 sample Population of memory patients Memory Test σ is known μ is known • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. Memory patients Memory treatment Memory Test X Compare these two means 1-sample z-test Reasoning in Psychology Using Statistics – 1 sample – 1 score per subject Population of memory patients Memory Test σ is known μ is known • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. Memory patients Memory treatment Memory Test X Compare these two means – 1 sample – 1 score per subject – Population mean (μ) and standard deviation (σ) are known (assume Normal dist) Population of memory patients Memory Test σ is known μ is known 1-sample z-test zX = 1-sample z-test Reasoning in Psychology Using Statistics X - mX sX • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using = 0.05. • Step 1: State your hypotheses • Step 2: Set your decision criteria • Step 3: Collect your data • Step 4: Compute your test statistics • Step 5: Make a decision about your HA: null hypothesis One -tailed H0: the memory treatment μTreatment > μpop = 60 sample are the same as those in the population of memory patients (or even worse). the memory treatment sample μTreatment < perform better (fewer errors) than those in the population of memory patients Performing your statistical test Reasoning in Psychology Using Statistics μpop = 60 • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. • Step 1: State your hypotheses • Step 2: Set your decision criteria = 0.05 • Step 3: Collect your data • Step 4: Compute your test statistics • Step 5: Make a decision about your null hypothesis H0: μTreatment > μpop = 60 HA: μTreatment < μpop = 60 One -tailed Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages 60 errors, with a σ = 8). Test using α = 0.05. • Step 1: State your hypotheses • Step 2: Set your decision criteria • Step 3: Collect your data n = 16, X = 55 • Step 4: Compute your test statistics • Step 5: Make a decision about your null hypothesis H0: μTreatment > μpop = 60 HA: μTreatment < μpop = 60 One -tailed = 0.05 Performing your statistical test Reasoning in Psychology Using Statistics • • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages 60 errors, with a σ = 8). Test using α = 0.05. Step 1: State your hypotheses • Step 2: Set your decision criteria • Step 3: Collect your data • Step 4: Compute your test statistics • Step 5: Make a decision about your null hypothesis zX = X - mX sX = H0: μTreatment > μpop = 60 HA: μTreatment < μpop = 60 One -tailed = 0.05 n = 16, X = 55 55 - 60 æ8 ö ç ÷ è 16 ø = -2.5 Performing your statistical test Reasoning in Psychology Using Statistics • • H0: μTreatment > μpop = 60 HA: μTreatment < μpop = 60 Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages 60 errors, with a σ = 8). Test using α = 0.05. Step 1: State your hypotheses • Step 2: Set your decision criteria • Step 3: Collect your data • Step 4: Compute your test statistics • Step 5: Make a decision about your null hypothesis zX = X - mX sX = One -tailed = 0.05 n = 16, X = 55 55 - 60 æ8 ö ç ÷ è 16 ø = -2.5 5% Reject H0 - Support for our HA, the evidence suggests that the treatment decreases the number of memory errors Performing your statistical test Reasoning in Psychology Using Statistics If time allows: The following pages give examples of situations that require different statistical tests. Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). Memory patients Memory treatment Memory Test X Population of memory patients MemoryTest is NOT known is known Compare these two means Hypotheses: H0: • the memory treatment sample are the same as those in the population of memory patients. HA: • they aren’t the same as those in the population of memory patients Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). Memory patients Memory treatment Memory Test X – 1 sample Population of memory patients MemoryTest is NOT known is known Compare these two means Hypotheses: H0: • the memory treatment sample are the same as those in the population of memory patients. HA: • they aren’t the same as those in the population of memory patients Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). Memory patients Memory treatment Memory Test X – 1 sample – One score per subject Population of memory patients MemoryTest is NOT known is known Compare these two means Hypotheses: H0: • the memory treatment sample are the same as those in the population of memory patients. HA: • they aren’t the same as those in the population of memory patients Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). Memory patients Memory treatment Memory Test X – 1 sample – One score per subject – Population mean (μ) is known Population of memory patients MemoryTest is NOT known is known Compare these two means Hypotheses: H0: • the memory treatment sample are the same as those in the population of memory patients. HA: • they aren’t the same as those in the population of memory patients Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). Memory patients Memory treatment Memory Test X – 1 sample – One score per subject – Population mean (μ) is known – Population standard deviation () is NOT known Population of memory patients MemoryTest is NOT known is known Compare these two means Hypotheses: H0: • the memory treatment sample are the same as those in the population of memory patients. HA: • they aren’t the same as those in the population of memory patients Performing your statistical test Reasoning in Psychology Using Statistics • The single sample t-test can be used when: – 1 sample – One score per subject X - mX t= sX – Population mean () is known – Population standard deviation () is NOT known Which test do we use? Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. His sample averaged 60 errors before the treatment and 55 errors after the treatment. Pre-test Memory patients Memory Test X Post-test Memory treatment Memory Test X Compare these Hypotheses: two means H0: Memory performance at the post-test is equal to memory performance at the pre-test. HA: Memory performance at the post-test is NOT equal to memory performance at the pre-test Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. His sample averaged 60 errors before the treatment and 55 errors after the treatment. Pre-test Memory patients Memory Test X – 1 sample Post-test Memory treatment Memory Test X Compare these Hypotheses: two means H0: Memory performance at the post-test is equal to memory performance at the pre-test. HA: Memory performance at the post-test is NOT equal to memory performance at the pre-test Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. His sample averaged 60 errors before the treatment and 55 errors after the treatment. Pre-test Memory patients Memory Test X – 1 sample – Two scores per subject Post-test Memory treatment Memory Test X Compare these Hypotheses: two means H0: Memory performance at the post-test is equal to memory performance at the pre-test. HA: Memory performance at the post-test is NOT equal to memory performance at the pre-test Performing your statistical test Reasoning in Psychology Using Statistics • The related sample ttest can be used when: – 1 sample – Two scores per subject D - mD t= sD Which test do we use? Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and matches them to a sample of similar individuals. He then gives them one sample the new treatment (but not the other). Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his matched sample averaged 60 errors over the same time period. No Memory treatment Memory patients related Memory treatment On a pair-by-pair basis every person in the No Treatment group is related to or matched to a person in the Memory Treatment group Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and matches them to a sample of similar individuals. He then gives them one sample the new treatment (but not the other). Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his matched sample averaged 60 errors over the same time period. No Memory treatment Memory patients Memory Test X related Memory treatment Memory Test X Compare these two means Hypotheses: H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. HA: Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and matches them to a sample of similar individuals. He then – 2 samples gives them one sample the new treatment (but not the other). Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his matched sample averaged 60 errors over the same time period. No Memory treatment Memory patients Memory Test X related Memory treatment Memory Test X Compare these two means Hypotheses: H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. HA: Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and matches them to a sample of similar individuals. He then – 2 samples gives them one sample the new treatment (but not the other). Following the treatment period he gives both groups a memory test. His treatment sample – Samples are averaged 55 errors after the treatment and his matched sample averaged 60 matched with errors over the same time period. one score per No Memory treatment Memory patients Memory Test X related Memory treatment Memory Test X subject Compare these two means Hypotheses: H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. HA: Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. Performing your statistical test Reasoning in Psychology Using Statistics • The related sample ttest can be used when: – 2 samples – Samples are matched with one score per subject D - mD t= sD Which test do we use? Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 50 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his control sample averaged 60 errors over the same time period. No Memory treatment Memory patients Memory treatment Memory Test X Memory Test X Compare these two means Hypotheses: H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. HA: Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 50 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a – 2 samples memory test. His treatment sample averaged 55 errors after the treatment and his control sample averaged 60 errors over the same time period. No Memory treatment Memory patients Memory treatment Memory Test X Memory Test X Compare these two means Hypotheses: H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. HA: Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 50 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a – 2 samples memory test. His treatment sample averaged 55 errors after the treatment and – Samples are his control sample averaged 60 errors over the same time period. independent No Memory treatment Memory patients Memory treatment Memory Test X Memory Test X Compare these two means Hypotheses: H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. HA: Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. Performing your statistical test Reasoning in Psychology Using Statistics • Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn’t certain what impact, if any, it will have. To test it he randomly assigns 50 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a – 2 samples memory test. His treatment sample averaged 55 errors after the treatment and – Samples are his control sample averaged 60 errors over the same time period. No Memory treatment Memory patients Memory treatment Memory Test X Memory Test X independent – One score per subject Compare these two means Hypotheses: H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. HA: Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. Performing your statistical test Reasoning in Psychology Using Statistics • The independent sample ttest can be used when: – 2 samples – Samples are independent (X A - X B ) - (mA - mB ) t= sX A -X B – One score per subject Which test do we use? Reasoning in Psychology Using Statistics • In lab – Make hypotheses (both null & alternative) – Test hypotheses using 1-sample z-test • Questions? Wrap up Reasoning in Psychology Using Statistics