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Personal Response System (PRS).
Revision session
Dr David Field
Do not turn your
handset on yet!
Interactive revision session
• Multiple choice questions will be displayed on
the projector
• You use the radio transmitter handset to make
an anonymous response
• The projector will show how many people chose
each answer
• The correct answer will be then be highlighted,
or I may ask you to discuss the answer with your
neighbours and answer again
Interactive revision session
• The purpose of the session is to
– allow you to find out how familiar you are with
the course material
– give you practice for the Week 10 statistics
test
– provide an opportunity for me to explain topics
further if there is confusion
1. Turn ON your handset - slide the Power Switch up (I = ON)
2. Enter the number _ and press
to join the class
3. The ANS: field will appear – you are ready to respond to questions
4. To respond, enter your answer and press
to send it
5. You may change your mind by entering a new answer to replace your
original answer
WARNING:
Your handset will go to SLEEP when not in use.
Press ANY KEY to WAKE UP your handset.
Which of these variables has an ordinal
level of measurement?
1)
2)
3)
4)
reaction time measured in seconds?
place in class exam (e.g., 1st , 2nd, 3rd)
gender
percentage score in a maths exam
What is a dependent variable?
1) something which you measure in an
experiment
2) something that varies which is continuous
3) something which you manipulate in an
experiment
4) none of the above
Which of these is likely to have the
largest SD?
1) The heights of a sample of men
2) The heights of a sample of men and
women
3) The heights of a sample of women
A person’s height is 2SD > the mean of a
sample. What % of participants are shorter?
1)
2)
3)
4)
5)
68%
5%
2.5%
97.5%
95%
The formula for computing a z score is:
1.
2.
3.
4.
(score – mean) / standard deviation
(mean – score) / variance
mean / standard deviation
score / variance
If a frequency histogram shows a normal distribution, which
of the following are true? To select multiple answers you
enter the corresponding numbers in any order, without any
separating spaces or commas.
1)
2)
3)
4)
The mean and the median will have similar values
The tallest histogram bar shows the interval with more
scores in it than any other interval
95% of scores will fall within 1.96 * the SD of the mean
68% of scores will fall within 1 * the SD of the mean
If a frequency histogram shows a skewed
distribution, which of the following are true?
You may choose more than 1 answer
1)
2)
3)
4)
The mean and the median will have similar values
The tallest histogram bar shows the interval with more
scores in it than any other interval
47.5% of scores will lie in the range defined by the
mean plus 1.96 * the SD
34% of scores will fall within the range defined by the
plus 1 * the SD of the mean
Which of the following are true? You may select
more than one answer.
1.
2.
3.
4.
5.
Taking many samples of the same size from a
population and plotting a frequency histogram of the
sample means produces a “sampling distribution”
For sample sizes > 1, the SD of a sampling distribution
(called the SE) is always less than the SD of the
population
The SE is smaller when the size of the individual
samples making up the distribution is larger
It is 68% likely that any sample will have a mean that
falls within 1SE of the mean of its sampling distribution,
and therefore when the SE is smaller the sample mean
is probably closer to the population mean
When calculating test statistics such as t the SE can be
used as an estimate of measurement error due to
sampling
A type I error is when…
1. We fail to reject the null hyp, but it is
actually false in the population
2. We support the null hypothesis
3. We reject the null hypothesis, but it is
actually true in the population
4. the p value is > 0.05
Imaginary experiment
• 30 myopic volunteers undergo eye surgery
– volunteers selected to have similar acuity pre surgery
• 15 are randomly selected to undergo modern laser
surgery
• The other 15 undergo a traditional operation, in which
the top of the cornea is removed with a knife
– Which procedure produces better post-op vision?
• After recovery from surgery visual acuity is measured
• Visual acuity is measured in normalised units of
“LogMAR”
– after normalisation of the scale, the average score for young
adults with typical vision is 0
– negative numbers indicate acuity worse than average
– positive numbers indicate better than average acuity
Choose the type of research design and
likely statistical test.
1) Repeated measures experiment - test the null
hypothesis with an independent samples t test
2) Independent samples experiment - test the null
hypothesis with a paired samples t test
3) Correlational design - test the null hypothesis
with an independent samples t test
4) Independent samples experiment - test the null
hypothesis with an independent samples t test
95% CI normalised logMAR (typical vision = 0)
Look at the Figure 1 on the handout
0.50
• This is an error
bar chart of the
experimental
results. Acuity is
plotted on the y
axis.
0.40
0.30
0.20
0.10
0.00
-0.10
-0.20
-0.30
-0.40
-0.50
knife
laser
group
Which of the following statements are true?
You may select more than one answer.
1)
2)
3)
4)
5)
The knife surgery group end up with better vision than the laser
group
The null hypothesis is that for all the patients in the world who
undergo these two types of surgery there will be no difference in
the resulting acuity between the two types of surgery
This error bar chart allows the null hypothesis to be rejected
Based on the error bar chart we can say that this experiment has
failed to reject the null hypothesis
If the experiment was repeated, this time using 30 participants in
each condition instead of 15, we can be 95% sure that the mean
acuity of the new laser group would lie somewhere between -0.26
and 0.02 normalised LogMar
Look at the Figure 2 on the handout
Group Statistics
normalised logMAR
(typical vision = 0)
group
knife
las er
N
15
15
Mean
.0598
-.1225
Std. Error
Mean
.04706
.06617
Std. Deviation
.18226
.25629
Independent Samples Test
Levene's Test for
Equality of Variances
F
normalised logMAR
(typical vision = 0)
Equal variances
as sumed
Equal variances
not ass umed
.826
Sig.
.371
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
2.245
28
.033
.18227
.08120
.01594
.34861
2.245
25.277
.034
.18227
.08120
.01513
.34942
For this t test, you should report the df and Sig.
from the “equal variance not assumed” row
1) True
2) False
The t test is statistically significant and the null
hypothesis can be rejected
1) True
2) False
If the researchers had predicted that the
knife group would have a better outcome,
which option below is correctly reported?
1)
2)
3)
4)
t(28) = 2.2, p = 0.033
t(28) = 1.1, p = 0.016
t(28) = 2.2, p = 0.016
t(28) = 1.1, p = 0.033
What is the effect size?
1)
2)
3)
4)
5)
0.83
0.24
1.67
0.56
none of the above
Effect size (Cohen’s d )
d=
Condition 1 mean – Condition 2 mean
SD Condition 1 + SD condition 2
2
Effect size in the acuity experiment
d=
(knife mean)0.06 – –0.12 (laser mean)
(Knife SD) 0.18 + 0.26 (laser SD)
2
Remember that two minuses make a plus!
Effect size in the acuity experiment
0.18
d=
0.44
2
• d is 0.18 / 0.22 = 0.83
Cohen (1988) would describe this effect
size as…
1)
2)
3)
4)
5)
enormous
significant
large
medium
small
Imaginary repeated measures experiment
• 15 participants have their reaction time
measured in the afternoon and then again in
the evening
• Half of them are tested in the afternoon and
then the evening, and half vice versa
• Look at Figure 4 of the handout
Did it take longer to react in the
afternoon or the evening?
1) It took longer in the evening
2) It took longer in the afternoon
Given a two-tailed hypothesis, can the null
hypothesis of no time of day effects be rejected?
1) yes
2) no
Look at Figure 5 on the handout
• This is a scatter plot of the data from the
afternoon versus evening reaction time
experiment
• Each circle on the graph represents the two data
points collected from each participant
• For each participant, the value of rtm in the
evening is plotted against the value of rtm in the
afternoon
– evening is on the x axis
• A scatter plot is a way of visualising the strength
of correlation between two variables
Most of the variation in the scores on
the scatter plot is determined by…
1) The difference in rtm between afternoon
and evening
2) Differences between participants
3) Neither of the above
How helpful did you find this interactive
PRS session?
1)
2)
3)
4)
Very helpful
Helpful
A bit helpful
Not very helpful
Would you like more PRS sessions in the
future (for statistics or other courses)?
1) Yes
2) Maybe
3) No
If the mean and the median of a
variable are similar…
1) The data is probably measured on an interval
or ratio scale
2) A frequency histogram of the variable probably
will not show a normal distribution
3) The data is probably measured on an ordinal
scale
4) A frequency histogram of the variable will
probably show a normal distribution