Field Work and Latin Square Design
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1 Field Work and Latin Square Design Chapter 12 - Factorial Designs (covered by Jason) Interactive effects between multiple independent variables Chapter 13 - Field Research Quasi-Experimental Designs Program Evaluation Surveys Latin Square Design
2 Quasi-Experimental Designs Experimental design in natural environment Nonequivalent control-group design Two natural groups, measure pre and post treatment/placebo Interrupted time-series designs Within-group, measure/treat over time
3 Program Evaluation Research Evaluating programs like Head Start Ethical issues Randomized control-group designs Waitlist control group: treatment after serving as control Nonequivalent control-group design Single group, time-series designs Pretest-Posttest design: weak
4 Surveys Types:Status survey,survey research Instruments define, pretest and refine Questionnarie (phone:interview schedule) Demographic questions (factual, verifiable) Content items (opinion, attitude, knowledge, behavior) Sampling Nonprobable: unplanned Probable: random, stratified Confidence interval: improved with heterogeneous Cross sectional design Longitudinal/panel design
5 Within-Subjects design Each subject given each experimental condition. Controls individual differences. Sequence Effects "Experiences with earlier conditions effect responses to later conditions" Positive and negative practice effects. Carryover effect. Example Each subject plays/interprets 5 mini-games "ABCDE". Interpretation of E systematically confounded by all having experienced ABCD.
6 Counterbalancing Controls sequence effect by modifying order that subjects are presented with conditions. Complete Counterbalancing All possible sequences are tested an equal number of times. Latin Square Controls sequence effect with fewer subjects
7 Latin Square Design Sequence 1 Sequence 2 Sequence 3 Sequence 4 Player 1 A B C D Player 2 B C D A Player 3 C D A B Player 4 D A B C Mini-games: A,B,C,D
8 Latin Square Designs
9 Latin Square Designs Selected Latin Squares 3 x 3 4 x 4 A B C A B C DA B C DA B C DA B C D B C A B A D CB C D AB D A CB A D C C A B C D B AC D A BC A D BC D A B D C A BD A B CD C B AD C B A 5 x 5 6 x 6 A B C D E A B C D E F B A E C D B F D C A E C D A E B C D E F B A D E B A C D A F E C B E C D B A E C A B F D F E B A D C
10 A Latin Square
11 Definition A Latin square is a square array of objects (letters A, B, C, ) such that each object appears once and only once in each row and each column. Example - 4 x 4 Latin Square. A B C D B C D A C D A B D A B C
12 In a Latin square You have three factors: Treatments (t) (letters A, B, C, ) Rows (t) Columns (t) The number of treatments = the number of rows = the number of colums = t. The row-column treatments are represented by cells in a t x t array. The treatments are assigned to row-column combinations using a Latin-square arrangement
13 Example A courier company is interested in deciding between five brands (D,P,F,C and R) of car for its next purchase of fleet cars. The brands are all comparable in purchase price. The company wants to carry out a study that will enable them to compare the brands with respect to operating costs. For this purpose they select five drivers (Rows). In addition the study will be carried out over a five week period (Columns = weeks).
14 Each week a driver is assigned to a car using randomization and a Latin Square Design. The average cost per mile is recorded at the end of each week and is tabulated below: Week D P F C R P D C R F Drivers F C R D P R F D P C C R P F D
15 yij The Model for a Latin Experiment = µ + τ + ρ + γ + ( k ) k i j ij ( k ) ε i = 1,2,, t j = 1,2,, t k = 1,2,, t y ij(k) = the observation in i th row and the j th column receiving the k th treatment µ = overall mean τ k = the effect of the i th treatment ρ i = the effect of the i th row γ j = the effect of the j th column ε ij(k) = random error No interaction between rows, columns and treatments
16 A Latin Square experiment is assumed to be a threefactor experiment. The factors are rows, columns and treatments. It is assumed that there is no interaction between rows, columns and treatments. The degrees of freedom for the interactions is used to estimate error.
17 The Anova Table for a Latin Square Experiment Source S.S. d.f. M.S. F p-value Treat SS Tr t-1 MS Tr MS Tr /MS E Rows SS Row t-1 MS Row MS Row /MS E Cols SS Col t-1 MS Col MS Col /MS E Error SS E (t-1)(t-2) MS E Total SS T t 2-1
18 The Anova Table for Example Source S.S. d.f. M.S. F p-value Week Driver Car Error Total
19 Using SPSS for a Latin Square experiment Rows Cols Trts Y
20 Select Analyze->General Linear Model->Univariate
21 Select the dependent variable and the three factors Rows, Cols, Treats Select Model
22 Identify a model that has only main effects for Rows, Cols, Treats
23 The ANOVA table produced by SPSS Dependent Variable: COST Source Corrected Model Intercept DRIVER WEEK CAR Error Total Corrected Total Tests of Between-Subjects Effects Type III Sum of Mean Squares df Square F Sig a a. R Squared =.952 (Adjusted R Squared =.905)
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