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PSYM201 ADVANCED STATISTICS

创建日期：2024-06-01 15:28:39

所属分类：统计学statistics

标签： PSYM201

ADVANCED STATISTICS

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PSYM201

ADVANCED STATISTICS
Duration: 3 hours
This is an Open Book exam
Materials to be supplied:
Data files potent-potions.csv, soothing-pets.csv and thirsty-bees.csv
Additional materials:
Statistical software R, RStudio, rstudio.cloud
R packages psych, car, pwr, ggplot2, multcomp, emmeans, ppcor, afex, GPArotation, corpcor, lavaan,
rockchalk, lme4, lattice, ResourceSelection, mlogit, arm, MASS, brms
Part A (35 marks)
Evil mastermind Professor Leigh Hogwarts is busy in his underground laboratory, concocting potions that he
believes will boost his cognitive powers and enable him to take over the world. He has developed four different
types of potion—WombleJuice, GutterSlime, BurpleGoo and FibbleJelly—and now wishes to test their
effectiveness alongside an inert placebo solution. He buys 100 guinea-pigs and measures their performance in
a radial arm maze (maze1), with higher numbers representing better performance. He then randomly allocates
the guinea-pigs to five groups of 20, gives each group a different potion or the placebo, and tests them in the
radial arm maze a second time (maze2). His data are in the file potent-potions.csv.
A1. (2 marks) Report the mean and standard error for the change in performance between the first and second
maze attempts.
mean = 6.78 (1), s.e. = 0.53 (1)
potions$change <- potions$maze2 - potions$maze1
library(psych)
describe(potions$change)
A2. (5 marks) Nine guinea-pigs sadly died between their first and second maze tests (indicated as ‘NA’ for
maze2). Is there evidence that this pattern was non-random with respect to the potion they received? Report
the results of a statistical test to support your answer, and remember to check the assumptions.
Pattern is significantly non-random (1) (Fisher’s exact test: P < 0.001) (3). There were excess deaths in the
GutterSlime group (1).
Binomial logistic regression also fine if comparing to null model (χ24 = 25.6, P < 0.001), but max. 1 mark if
only reporting parameter estimates (as standard errors unreliable).
Max. 3 marks for chi-squared test (half of expected counts < 5): χ24 = 29.8, P < 0.001.
Max. 1 mark for Kruskal–Wallis test on dead/alive DV: χ24 = 29.5, P < 0.001.
potions$died <- ifelse(is.na(potions$maze2),1,0)
fisher.test(potions$died,potions$potion)
table(potions$died,potions$potion)
A3. (4 marks) Professor Hogwarts notices that the variables maze1 and maze2 are not normally distributed.
Identify suitable transformations for each variable and report whether these have corrected the problem, using
either plots or a statistical test.
Plots indicate strong positive skew (1), so log transformation (or square-root transformation) (1) is
appropriate. Q-Q plots or Shapiro–Wilk tests indicate that log-transformed variables are normally distributed
(2).
library(car)
qqPlot(potions$maze1)
hist(potions$maze1)
shapiro.test(potions$maze1)
qqPlot(potions$maze2)
shapiro.test(potions$maze2)
hist(potions$maze2)
potions$log.maze1 <- log10(potions$maze1+1)
qqPlot(potions$log.maze1)
shapiro.test(potions$log.maze1)
potions$log.maze2 <- log10(potions$maze2+1)
qqPlot(potions$log.maze2)
shapiro.test(potions$log.maze2)
A4. (4 marks) Report Pearson’s correlation coefficient between the maze1 and maze2 scores and test its
significance, using the transformed variables if appropriate. What is the percentage of shared variance?
r = 0.933 (1), t89 = 24.46, P < 0.001 (2). Shared variance = 100*(0.933
2) = 87% (1).
Max. 1 mark if using untransformed data or a non-parametric alternative.
with(potions,cor.test(log.maze1,log.maze2))
100*(0.9330068^2)
A5. (4 marks) Professor Hogwarts is excited to discover that the 11 guinea-pigs with the lowest maze1 scores
all performed better in their second maze attempt. Give two reasons why this does not provide convincing
evidence that his potions improve maze performance.
Performing the same task a second time may lead to improvement, even if the potions are ineffective (2). And
even with no overall improvement, the lowest scores are statistically likely to increase on the second
measurement because of regression towards the mean (2).
A6. (3 marks) The bumbling professor wants to analyse his data using a repeated-measures ANOVA, to test
whether the repeated measurements of maze performance (maze1, maze2) differ between the potion
treatments. Explain why instead it would be more logical to use an ANCOVA to test whether maze2 differs
between the potion treatments, with maze1 as a covariate.
maze1 is measured before the guinea-pigs have received the potion treatment, so it cannot conceivably affect
their performance (3) [or something else along these lines].
A7. (8 marks) Use an ANCOVA to compare the maze performance (maze2) of the guinea-pigs after their
potion treatment, including maze1 as a covariate to control for pre-existing differences in cognitive ability and
using the transformed versions of these variables if appropriate. For both the fixed factor and the covariate,
report the results of a statistical test and a brief interpretation of the effect.
Using log10(maze2+1)~potion+log10(maze1+1):
Maze performance after the potion treatment was significantly positively associated with pre-treatment maze
performance (1) (F1,85 = 619.9, P < 0.001) (3), but was not significantly affected by potion treatment (1) (F4,85
= 1.8, P = 0.136) (3).
potions$potion <- factor(potions$potion)
potions$potion <- relevel(potions$potion,"placebo")
model1 <- lm(log.maze2~log.maze1+potion,data=potions)
anova(model1)
summary(model1)
par(mfrow=c(2,2))
plot(model1)
A8. (5 marks) Test whether pre-treatment maze performance is independent of potion type, remembering to
check the assumptions of your analysis. Report the test statistic, degrees of freedom, P value and your
conclusion.
Need to use log-transformed data (1).
Pre-treatment maze performance is independent of potion type (1) (F4,95 = 0.677, P = 0.610) (3).
model2 <- aov(log.maze1~potion,data=potions)
summary(model2)
par(mfrow=c(2,2))
plot(model2)
A9. UPLOAD YOUR R SCRIPT
Part B (40 marks)

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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