Basic Statistics Michael Hylin

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

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)

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)

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

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

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

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

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.

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?

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

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

Mean

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

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

Variance Equation for Variance Where:

Variance Another Equation for Variance Where: &

Standard Deviation Equation for Standard Deviation Or

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

Example = = = = = Variance Standard Deviation

Mean & Standard Deviation

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

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

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

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)

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

Equation for Independent T- Test

GPA Group 2 (no techniques)Group 1 (study techniques)   X   X

Since our observed t = 3.04 which is greater than 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

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

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

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.)

Example

ANOVA Table Sum of Squaresdf Mean SquareFSig. Test Test * Group Error(Test) Group Error

Example

ANOVA Table Sum of Squaresdf Mean SquareFSig. Test Test * Group01001 Error(Test) Group Error

F-Score Equation

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