Reasoning in Psychology Using Statistics Psychology 138 2018

Reasoning in Psychology Using Statistics Psychology 138 2018

• Moved the due date for Quiz 5. Now it is due Tue. Mar. 27 at midnight Announcements Reasoning in Psychology Using Statistics

• Hypothesis testing: a five step program – – – Hypothesis Step 1: State your hypotheses HH 0 Null A Alternative Hypothesis Step 2: Set your decision criteria � Alpha level Step 3: Collect your data from your sample Step 4: Compute your test statistics Distribution of Sample Means 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 • Statistics How To: Hypotheses (~4 mins) • Stats. Lectures: Hypotheses and Error types (~4 mins) • Hypothesis testing and Error types (~7 mins) Testing Hypotheses Reasoning in Psychology Using Statistics

5 4 3 2 1 2 In long run, the random selection of tiles leads to a predictable pattern The distribution of sample means 3 4 5 6 7 8 (DSM) means mean 2 2 4 6 8 2 2 5 5 2 4 4 8 8 4 3 6 6 2 8 6 4 4 7 2 8 6 4 8 8 5 5 8 4 2 6 6 3 6 4 4 6 8 4 7 All 16 samples of n=2 from 4 6 8 Population: 2 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 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+6+4+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 μ X 3 X 1 X 2 X 3 X 1 μ X 2 – 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 - 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 MEMORIZE THIS – For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will approach a normal distribution with a mean of μ and a standard deviation of as n approaches infinity (good approximation if n > 30). Properties of the distribution of sample means Reasoning in Psychology Using Statistics Central Limit Theorem (~13 mins)

• 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 with chance (it is our estimate of the sampling error) your notation Population Distribution of sample means Sample σ s μ 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 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 person, etc. Could be difference between a sample and a population, or between different samples Both of these parts change as a function of the design 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

• 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 Test statistic Using the distribution of sample means Reasoning in Psychology Using Statistics

Old z-formula New z-formula • 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 New z-formula • 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 population mean raw score population standard deviation New z-formula sample mean standard error One sample z-test statistic Reasoning in Psychology Using Statistics mean of the distribution of sample means

Old z-formula New z-formula • 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 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: z(2. 6) =. 0047 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 Memory. Test μ & σ known Compare these two means Conclusions: H 0: • 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’) H 0: is true (no treatment effect) H 0: 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 H 0, 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 H 0, 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 H 0 If test statistic is here Fail to reject H 0 “Generic” statistical test Reasoning in Psychology Using Statistics

• The alpha level gives us the decision criterion Two -tailed α = 0. 05 Reject H 0 0. 025 split up into the two tails Fail to reject H 0 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 α = 0. 05 all of it in one tail Reject H 0 0. 05 Fail to reject H 0 Reject H 0 Fail to reject H 0 • 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 α = 0. 05 Reject H 0 all of it in one tail Reject H 0 0. 05 Fail to reject H 0 Reject H 0 Fail to reject H 0 • 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 z-test Reasoning in Psychology Using Statistics – 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

• 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 • Step 3: Collect your data • Step 4: Compute your test statistics • Step 5: Make a decision about your HA: null hypothesis One -tailed μTreatment > μpop = 60 H 0: the memory treatment 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 α = 0. 05 • Step 3: Collect your data • Step 4: Compute your test statistics • Step 5: Make a decision about your null hypothesis H 0: 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 H 0: μTreatment > μpop = 60 HA: μTreatment < μpop = 60 One -tailed α = 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 H 0: μTreatment > μpop = 60 HA: μTreatment < μpop = 60 One -tailed α = 0. 05 n = 16, X = 55 = -2. 5 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 H 0: μTreatment > μpop = 60 HA: μTreatment < μpop = 60 One -tailed α = 0. 05 n = 16, X = 55 = -2. 5 5% Reject H 0 - 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 Memory. Test is NOT known m is known Compare these two means Hypotheses: H 0: • 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 Memory. Test is NOT known m is known Compare these two means Hypotheses: H 0: • 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 Memory. Test is NOT known m is known Compare these two means Hypotheses: H 0: • 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 Memory. Test is NOT known m is known Compare these two means Hypotheses: H 0: • 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 Memory. Test is NOT known m is known Compare these two means Hypotheses: H 0: • 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 – Population mean (m) 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 H 0: 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 H 0: 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 H 0: 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 t-test can be used when: – 1 sample – Two scores per subject 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: H 0: 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 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 – 2 samples Compare these two means Hypotheses: H 0: 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 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 – 2 samples – Samples are matched with one score per subject Compare these two means Hypotheses: H 0: 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 t-test can be used when: – 2 samples – Samples are matched with one score per subject 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 Compare these two means Hypotheses: H 0: 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 Compare these two means Hypotheses: H 0: 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 Compare these two means Hypotheses: H 0: 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 independent – One score per subject Compare these two means Hypotheses: H 0: 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 – 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