1 / 44

PSYM021 Introduction to Methods Statistics

Last week's assignment. All designs were between-subjects (non-repeated measures)Contrast coefficients?Questions ?. This week. Polynomial contrasts

Antony
Download Presentation

PSYM021 Introduction to Methods Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. PSYM021 Introduction to Methods & Statistics Week Four: Statistical techniques II

    2. Last week’s assignment

    3. This week

    4. Polynomial contrasts

    5. Polynomial contrasts

    6. Polynomial trends

    7. Two-way ANOVA: Driving study

    8. Results of Two-way ANOVA: Driving study

    9. Implications This means that you can use ANOVA to examine the independent effects on your data of 2, 3, 4 or more different independent variables In the SPSS output from such analyses, the so-called main effects tell you whether each variable has an independent effect (by itself) on the dependent variable The interactions tell you how the effect of each independent variable is itself altered by the influence of the others

    10. Interpreting main effects and interactions What does it actually mean to say that “the TIME main effect was significant”, “the WEATHER main effect was significant” And “that the TIME by WEATHER interaction was significant”? To answer this, it helps to plot the results...

    12. Graphs of possible non-interactions (parallel graphs)

    13. Graphs of possible interactions (non-parallel graphs)

    14. Plots in ANOVA

    15. Describing main effects and interactions (1) Distance estimates are affected by whether people are driving during day or at night (the TIME main effect) (2) Distance estimates are affected by whether people are driving in foggy or clear conditions (the WEATHER main effect) (3) The average difference in Day compared with Night estimates is itself affected by whether people are driving in foggy or clear conditions (the TIME*WEATHER interaction)

    16. Be clear! For example, it is wrong to describe the interaction as showing that: “distance estimates are affected by both WEATHER and TIME of day at which the test is done” This could easily be a description of a completely different experimental outcome: (1) “estimates are affected by WEATHER”; (2) “estimates are affected by TIME of day” but (3) No interaction.

    17. Summary Main effects tell you something about the differences in performance that occur when an independent variable is manipulated (e.g. effect of day vs. night, or of foggy vs. clear) The interaction tells you about differences between differences (or more generally between the profiles of the effects of an independent variable).

    18. Repeated-measures ANOVA

    19. Problems with Sphericity Only relevant to repeated measures Not necessary for contrasts (not even contrasts using repeated measures variables)

    21. Assessing Sphericity One approach is to use “Mauchly’s test of Sphericity” A significant Mauchly W indicates that the sphericity assumption has been violated “Significant W = trouble” But… Mauchly’s test is innaccurate Routinely given as the first step of SPSS output Ignore Mauchly’s test table because it is not accurate What do we do instead? Greenhouse-Geisser or “lower bound” test

    22. Dealing with departures from Sphericity assumptions Worst Case Scenario: This assumes that the violation of sphericity is as bad as it could possibly be In other words, each participant is affected entirely differently by the manipulation This is known as the “Lower Bound” test or Greenhouse-Geisser Conservative test For ANOVA procedures with Repeated-measures IVs, four different F-ratios and p-values are reported.

    23. Dealing with departures from Sphericity assumptions

    24. Dealing with departures from Sphericity assumptions

    25. Undergraduate lectures Sphericity will be covered in more detail in PSYM022 But … Undergraduate lectures on ‘Sphericity’ take place on: Tuesday Nov 14th and 21st Location: Newman E, 2:00-3:00pm You are advised to attend these !

    26. Summary Non-parametric tests are limited in their ability to provide the experimenter with grounds for drawing conclusions - parametric tests provide more detailed information ‘Tests of difference’ use a statistic that reflects a ‘signal to noise’ ratio, or how much variance in the DV is accounted for by the IV, compared with the what is left The only fundamental difference between a t-test and ANOVA is the number of levels in the Independent Variable (IV) T-tests: IV has two levels; ANOVA: IV has three or more levels (or two or more IVs with 2+ levels) We can combine a number of IVs together in the same ANOVA procedure (two-way, three-way etc.), identifying their individual and combined (interaction) effects on the DV

    27. Break If I needed a drink last week, today I need a swim… Five minutes – please be prompt

    28. Test of association - Correlation A correlation measures the “degree of association” between two variables (interval or ordinal) Associations can be positive (an increase in one variable is associated with an increase in the other) or negative (an increase in one variable is associated with a decrease in the other) Correlation is measured in “r” (parametric, Pearson’s) or “?” (non-parametric, Spearman’s)

    29. Test of association - Correlation Compare two continuous variables in terms of degree of association e.g. attitude scale vs behavioural frequency

    30. Test of association - Correlation Test statistic is “r” (parametric) or “?” (non-parametric) 0 (random distribution, zero correlation) 1 (perfect correlation)

    31. Test of association - Correlation Test statistic is “r” (parametric) or “?” (non-parametric) 0 (random distribution, zero correlation) 1 (perfect correlation)

    32. Correlation: Height vs Weight Strong positive correlation between height and weight Can see how the relationship works, but cannot predict one from the other If 120cm tall, then how heavy?

    33. Example: Symptom Index vs Drug A Strong negative correlation Can see how relationship works, but cannot make predictions What Symptom Index might we predict for a standard dose of 150mg?

    34. “Best fit line” Allows us to describe relationship between variables more accurately. We can now predict specific values of one variable from knowledge of the other All points are close to the line Example: Symptom Index vs Drug A

    35. We can still predict specific values of one variable from knowledge of the other Will predictions be as accurate? Why not? “Residuals” Example: Symptom Index vs Drug B

    36. Simple Regression How best to summarise the data?

    37. Establish equation for the best-fit line: y = bx + a General Linear Model (GLM) How best to summarise the data?

    38. Establish equation for the best-fit line: y = bx + a Simple Regression Terminology

    39. For simple regression, R2 is the square of the correlation coefficient Reflects variance accounted for in data by the best-fit line Takes values between 0 (0%) and 1 (100%) Frequently expressed as percentage, rather than decimal High values show good fit, low values show poor fit

    40. R2 = 0 (0% - randomly scattered points, no apparent relationship between X and Y) Implies that a best-fit line will be a very poor description of data

    41. R2 = 1 (100% - points lie directly on the line - perfect relationship between X and Y) Implies that a best-fit line will be a very good description of data

    43. Simple regression uses a t-test to establish whether or not the model describes a significant proportion of the variance in the data This tests is reported in the SPSS output

    44. R2 is reported in the first table in the SPSS output Expressed as a decimal, but can be reported as a percentage 0.520 = 52%

    45. SPSS output table entitled Coefficients Column headed Unstandardised coefficients - B Gives regression coefficient for each regressor variable (IV) Coefficient for AGE = -0.162 Constant = 68.285 DEPRESS = -0.162 AGE + 68.285

More Related