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Basic Statistics Michael Hylin

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Scientific Method Start w/ a question Gather information and resources (observe) Form hypothesis Perform experiment and collect data Analyze data Interpret data & draw conclusions form new hypotheses Retest (frequently done by other scientists) i.e. replicate & extend

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Example Pavlov noticed that when the dogs saw the lab tech they salivated the same as when they saw meat powder (Observation) Predicted that other stimuli could elicit this response when paired w/ meat powder (Hypothesis)

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Example Pavlov found that when a bell was paired w/ the presence of meat powder an association occurred (Experimentation) Concluded that pairing of US w/ CS could lead to CR (Interpretation) Research since Pavlov has demonstrated the mechanism of how CC works (e.g. Aplysia)

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Basics of Experimental Design Types of Variables Types of Comparisons Types of Groups

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Types of Variables Independent Variable Manipulated by the experimenter May have several Dependent Variable Dependent upon the IV The data IV → DV

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Types of Comparisons Between-subjects Comparing one group to another Within-subjects Comparing a subject’s results at one point to another point Usually referred to as repeated-measures

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Types of Groups Experimental Group Receives experimental manipulation Control Group “controls” for the effect of manipulation

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Example A researcher has a new drug (M100) that improves semantic memory in normal individuals. The researcher decides to test M100’s effectiveness by giving the drug to participants and testing their ability to memorize a list of words. Other participants are given a sugar pill and told to memorize the list as well.

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Example What is the IV? the DV? Additional IVs & DVs What was the control? What type of comparison was being done? Could it be different?

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What about statistics? Why do we need statistics? Cannot rely solely upon anecdotal evidence Make sense of raw data Describe behavioral outcomes Test hypotheses

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Measures of Central Tendency Mode Frequency, most common ‘score’ Median Point at or below 50% of scores fall when the data is arranged in numerical order Used typically w/ non-normal distributions Mean (Often expressed ) Sum of the scores divided by the number of scores

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Mean

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Example Data for number of words recalled 8, 14, 17, 10, 8 Mode = 8 Median = 10 (8, 8, 10, 14, 17) Mean = 8+14+17+10+8 = 11.4 5

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Measures of Variability Range Difference between highest and lowest scores Variance (s 2 ) Standard Deviation (s) Standard Error of the Mean (S.E.M.)

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Variance Equation for Variance Where:

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Variance Another Equation for Variance Where: &

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Standard Deviation Equation for Standard Deviation Or

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Example Data for number of words recalled 8, 14, 17, 10, 8 Range = 17 – 8 = 9 Variance = 15.8 Standard Deviation = 3.97

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Example 11.488 - 11.4 = -3.411.56 1414 - 11.4 = 2.66.76 1717 - 11.4 = 5.631.36 1010 - 11.4 = -1.41.96 88 - 11.4 = -3.411.56 63.2 Variance Standard Deviation

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Mean & Standard Deviation

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Null Hypothesis Start w/ a research hypothesis “Manipulation” has an effect e.g. Students given study techniques have a higher GPA Set up the null hypothesis “Manipulation” has NO effect e.g. Students w/ techniques are no diff. than those w/o techniques

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Null Hypothesis Does the manipulation have an effect Use a critical value to test our hypothesis Usually 0.05

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Hypothesis Testing Type II Error p = β Correct decision p = 1 - α Accept H 0 Correct decision p = 1 – β = Power Type I Error p = α Reject H 0 H 0 FalseH 0 TrueDecision True State of the World

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Hypothesis Testing Not truly ‘proving’ our hypothesis In reality we are setting up a situation where there is no relationship between the variables and then testing whether or not we can reject this (null hypothesis)

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Independent T-Test Test whether our samples come from the same population or different populations

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Equation for Independent T- Test

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2.803.26 2.402.95 2.102.98 3.103.16 2.543.41 GPA Group 2 (no techniques)Group 1 (study techniques) 76.15 1 X94.12 2 X

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Since our observed t = 3.04 which is greater than 2.306 we can reject the null hypothesis Therefore the probability of the difference we observed occurring when the null hypothesis is true is less than 0.05 (5%) As a result our effect is likely due to the training

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Degrees of Freedom 6, 8, 10 Mean = 8 If we change two numbers the other is determine if we want to keep Mean = 8 6 7 & 10 13 then the final number is 4

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IV with more than two levels Sometimes we want to compare more that just two groups Cannot just due multiple t-tests Increase alpha Simple analysis of variance 1-way ANOVA

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Multiple IVs Factoral ANOVA Allow for comparison of more than one IV IVs can be between or within If both its called mixed ANOVA (repeated measures) Interaction of IVs E.g. 2x2 ANOVA IV 1 Study group (no study vs. study) IV 2 Time at testing (pre. vs. post.)

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Example

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ANOVA Table Sum of Squaresdf Mean SquareFSig. Test0.54451 36.30.00 Test * Group0.84051 56.033330.00 Error(Test)0.1280.015 Group0.76051 5.8275860.04 Error1.04480.1305

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Example

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ANOVA Table Sum of Squaresdf Mean SquareFSig. Test0.0021 0.1481480.710342 Test * Group01001 Error(Test)0.10880.0135 Group0.0021 0.0172410.898775 Error0.92880.116

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F-Score Equation

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What about further group comparisons Significant main effects with more than 2 levels Post hoc comparisons Significant interactions Simple effects

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