School of Psychology Queen‟s University, Belfast, BT7 1NN 1 Worked Examples of mathematics used in Psychology Worked Example 1: Level 1 Introductory Psychology I (PSY1001) Laboratory Demonstration Worked Example 1 draws from CCEA GCSE Mathematics Module T1 and T2, (Foundation Tier) – Statistics Component For these exercises, describe in detail what the results presented in the tables and graphs mean. Answer: This graph shows the mean extraversion and neuroticism scores for people grouped by the number of friends they have. It shows that people with no friends have similar levels extraversion and neuroticism, with a score of around 11 points. The trend for extraversion shows that as the level of extraversion increases, so does the number of close friends. This would be expected because extraversion is a personality trait associated with outgoingness and sociability, so you would expect people who have high levels of extraversion to have larger circles of friends. The opposite trend is found with neuroticism, where lower levels of neuroticism are associated with having more friends. This again is expected because neuroticism is a personality trait associated with anxiety and worry. You would expect people with lower levels of neuroticism to have larger circle of friends because people who are less prone to anxiety and worry are probably able to make and maintain friendships. NONE 1-2 3-5 5- 10+ 6 8 10 12 14 Mean EXTRA Mean NEUROT EXTRAVERSION AND NEUROTICISM WITH NUMBER OF CLOSE FRIENDS NUMBER OF CLOSE FRIENDS Mean Score
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School of Psychology
Queen‟s University,
Belfast, BT7 1NN
1
Worked Examples of mathematics used in Psychology
Worked Example 1: Level 1 Introductory Psychology I (PSY1001) Laboratory
Demonstration
Worked Example 1 draws from CCEA GCSE Mathematics Module T1 and T2,
(Foundation Tier) – Statistics Component
For these exercises, describe in detail what the results presented in the tables and
graphs mean.
Answer:
This graph shows the mean extraversion and neuroticism scores for people grouped
by the number of friends they have. It shows that people with no friends have similar
levels extraversion and neuroticism, with a score of around 11 points. The trend for
extraversion shows that as the level of extraversion increases, so does the number
of close friends. This would be expected because extraversion is a personality trait
associated with outgoingness and sociability, so you would expect people who have
high levels of extraversion to have larger circles of friends. The opposite trend is
found with neuroticism, where lower levels of neuroticism are associated with having
more friends. This again is expected because neuroticism is a personality trait
associated with anxiety and worry. You would expect people with lower levels of
neuroticism to have larger circle of friends because people who are less prone to
anxiety and worry are probably able to make and maintain friendships.
NONE 1-2 3-5 5- 10+ 6
8
10
12
14
Mean EXTRA
Mean NEUROT
EXTRAVERSION AND NEUROTICISM
WITH NUMBER OF CLOSE FRIENDS
NUMBER OF CLOSE FRIENDS
Me
an
Score
School of Psychology
Queen‟s University,
Belfast, BT7 1NN
2
EXTRAVERSION
NEUROTICISM
MEAN S.D. MEAN S.D.
MALE 12.20 5.30 7.27 4.38
FEMALE 11.53 4.34 10.36 5.00
Answer:
This table shows males are, on average, more extraverted compared to females with
males having a mean extraversion score of 12.2 and females having a score of
11.53. There is more variance in male extraversion scores, as males have a larger
standard deviation (5.3) compared to females (4.34). Females seem to be more
neurotic on average compared to males with a mean score of 10.36 compared to
7.27 for males. Neuroticism scores varied more for females, who have a larger
standard deviation compared to males.
8 12 16 20 24 28
0
10
20
30
FREQUENCY DISTRIBUTION
LIFE SATISFACTION INDEX - Z
LSI-Z SCORES
FR
EQ
UE
NC
Y
Answer:
This graph shows the distribution of standardised scores from the life satisfaction
questionnaire from a sample of approximately 100 people. The modal score on the
questionnaire was 24 with 29 people obtaining this score. The range of scores was
20 (with scores from 8 to 28). The shape of the distribution approximates a normal
distribution, with some evidence of negative skew seen in the tail to the left hand
side of the distribution.
School of Psychology
Queen‟s University,
Belfast, BT7 1NN
3
Most Enjoyed Least Enjoyed
1. Time spent with spouse (32%)
2. Doing things with children (22%)
3. Recreational activities/hobbies (18%)
4. Getting together with friends (13%)
1. Time spent alone (51%)
2. Taking care of the house (48%)
3. Recreational activities/hobbies (1%)
Answer:
This table shows a list of most and least popular past-times. The most popular
activity was spending time with spouse where 32% of respondents indicated they
most enjoyed this activity. Spending time alone was the least enjoyed activity with
51% of respondents indicating this. There appears to be some missing activities
rated as most enjoyed because the percentages of this group only adds up to 85%
meaning 15% o responses are unknown.
Background to this experiment: Participants were presented with a list of twenty
words and asked to remember as many words as possible. Each word was
presented one at a time on a computer screen for 5 seconds. Every participant saw
exactly the same list of words. After all 20 words were presented, the participants
were asked to write down as many words as they could remember from the list in
any order. The graph shows the percentage of participants who remembered each
word, depending on where the word appeared in the list. E.g. the word in word-
position 1 was presented first in the list, word position 10 is the middle word of the
list, and word position 20 was the final word presented.
School of Psychology
Queen‟s University,
Belfast, BT7 1NN
4
Answer:
This line graph shows the accuracy of recall for words presented as part of a list,
depending on each word‟s position in the list. It seems that the group were better at
remembering words presented at the start and the end of the list, compared to words
located in the middle of the list. Words at the end of the list were remembered better
than any other word positions, which would be expected because these words would
have been most recent in the participants‟ memory. Accuracy for words in the middle
of the list (approx. 40%) were approximately half that of the accuracy of recall for
words at the end of the list (approx. 80%).
Source: Questions based on level 1 laboratory handbook exercises, 2010/11.
School of Psychology
Queen‟s University,
Belfast, BT7 1NN
5
Worked Example 2: Level 1 Introductory Psychology 1 (PSY1001) Laboratory
Class Work
Worked Example 2 draws from CCEA GCSE Mathematics Modules:
T1 and T2, (Foundation Tier) – Mathematics & Algebra and Statistics