ARA0103 Aðferðafræði Rannsókna Fyrirlestur 15 Factorial designs/Þáttasnið factor/þáttur 21/09/2018 Dr Andy Brooks

Factorial Designs/Þáttasnið True experimental design/Hrein tilraun Factorial Designs/Þáttasnið True experiments can consider more than one independent variable. We could consider the effects of mattress cover and the frequency of patient turning on the number of bedsores. tvær óháðar breytur We could consider the effects of mattress cover, the frequency of patient turning, and nutritional supplements on the number of bedsores. þrjár óháðar breytur háð breyta : fjöldi legusára 21/09/2018 Dr Andy Brooks

4 hópar -> margir sjúklingar Dæmi: þáttasnið, 2x2 snið mattress cover Usual mattress M1 Sheepskin M2 Usual frequency of patient turning F1 M1 F1 M2 F1 x2 frequency of patient turning F2 M1 F2 M2 F2 að snúa sjúklingum The two factors are: mattress cover and frequency of patient turning. Factors must have two or more levels. This is a 2x2 design. 4 hópar -> margir sjúklingar 21/09/2018 Dr Andy Brooks

Multiple hypotheses/Margar tilgátur Factorial designs allow the testing of many hypotheses in a single experiment. Do sheepskin covered mattresses reduce bedsores? (main effect/megináhrif) Does doubling the frequency of patient turning reduce bedsores? (main effect/megináhrif) Are sheepskin mattresses more effective at a particular frequency of patient turning? (interaction effect/samvirkniáhrif) 21/09/2018 Dr Andy Brooks

One-way ANOVA test Eins þáttar ANOVA próf Not a factorial design. One-way ANOVA test Eins þáttar ANOVA próf analysis of variance fervikagreining t-próf, tveir hópar eins þáttur ANOVA próf, þrír eða fleiri hópar dæmi: There are 3 groups of 10 patients. The patients have memory problems. Ég man ekki... Each group is given a different intervention (inngrip A, B, or C) which should help them remember things. After the intervention, the patients are given a memory test/minnispróf and their scores recorded. The null hypothesis is that the means for the three groups are the same. Núlltilgátan – meðaltöl eru jöfn/áhrif er ekki til 21/09/2018 Dr Andy Brooks

Árangur minnisprófa A B C 3 10 20 5 8 15 14 2 9 4 11 17 6 16 7 18 19 21/09/2018 Dr Andy Brooks

One-way ANOVA results Við getum hafnað núlltilgátunni (p < 0,01). Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 10 53 5,3 8,011111 Column 2 118 11,8 13,06667 Column 3 147 14,7 16,01111 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 463,4 2 231,7 18,74146 7,87E-06 3,354131 Within Groups 333,8 27 12,36296 Total 797,2 29   0,00000787 Við getum hafnað núlltilgátunni (p < 0,01). 21/09/2018 Dr Andy Brooks Hin tilgátan er rétt.

Eins þáttar ANOVA árangur Hin tilgátan er rétt, en samt, við vitum ekki: Er A betri en B? Er B betri en C? Er A betri en C? Special follow-up tests can be performed. Do not perform several t-tests as this effects the alpha levels (0,05 and 0,01). Special follow-up tests are an advanced topic. So plot a graph/Svo teikna graf You may get the answer you seek by looking at boxplots. 21/09/2018 Dr Andy Brooks

Boxplot/Kassarit Inngrip B og C eru betri en A. 50% of the data lies in the box. lágmark miðtala hámark Inngrip B og C eru betri en A. En B og C skarast mikið. 21/09/2018 Dr Andy Brooks

Two-way ANOVA test tveggja þátta ANOVA próf hayfever/heymæði Two-way ANOVA test tveggja þátta ANOVA próf skor í bílprófshermi A new drug is a good remedy for hay fever, but it may effect performance when driving a car. It is possible that the effects on people who have been drinking alcohol are different to those who have not been drinking alcohol. Factor 1: placebo, usual drug, new drug gervilyf, venulegt lyf, nýtt lyf Factor 2: no alcohol, alcohol án áfengis, áfengi Háð breyta: skor í bílprófshermi. Hver flokkur með 10 þátttakendum. 3 x 2 snið Factorial Design/Þáttasnið 21/09/2018 Dr Andy Brooks

Experimental Data (Excel format) placebo usual drug new drug No alcohol 24 18 27 25 8 14 13 9 19 22 29 16 23 15 6 17 20 26 Alcohol 21 12 11 4 3 2 Experimental Data (Excel format) 21/09/2018

Two-way ANOVA results The null hypotheses are rejected (p < 0,01). Source of Variation SS df MS F P-value F crit Sample 201,6667 1 8,712 0,004669 4,019541 Columns 190 2 95 4,104 0,021917 3,168246 Interaction 763,3333 381,6667 16,488 2,58E-06 Within 1250 54 23,14815 Total 2405 59   Sample is Factor 2 Columns is Factor 1 The null hypotheses are rejected (p < 0,01). Núlltilgáturnar eru hafnað (p < 0,01). 21/09/2018 Dr Andy Brooks

Anova: Two-Factor With Replication SUMMARY placebo usual drug new drug Total No alcohol   Count 10 30 Sum 210 120 220 550 Average 21 12 22 18,33333 Variance 18,44444 19,55556 24,44444 40,29885 Alcohol 100 180 160 440 18 16 14,66667 32 21,55556 22,88889 35,67816 20 310 300 380 15,5 15 19 55,73684 28,94737 31,89474 21/09/2018

Line graph showing averages Línurit sýna meðaltöl teikna graf Line graph showing averages Línurit sýna meðaltöl no alcohol alcohol 21/09/2018 Dr Andy Brooks

Preliminary conclusions from the experiment preliminary conclusions/drög að niðurstöðum Preliminary conclusions from the experiment The usual drug has a bad effect on driving performance for drivers who have not been drinking alcohol. Both the usual and new drugs have a good effect on driving performance for drivers who have been drinking alcohol. Overall the new drug outperforms the usual drug. Assuming it is as good a remedy for hay fever as the old drug. 21/09/2018 Dr Andy Brooks

Caution/Viðvörun It can be very complicated analysing factorial designs bigger than 3x3. ...gæti verið afar flókið að greina þáttasnið stærri en 3x3 From a statistical point of view, follow-up tests are required if you have significant main and interaction effects. Plotting the data as boxplots or line charts of averages can allow preliminary conclusions to be made. 21/09/2018 Dr Andy Brooks