Correlation or Causation - Solutions 1 There is a positive correlation between the amount of sugar and the number of calories in breakfast cereals. Might be causal. One might directly cause the other. Although other ingredients may add to the calorie count. Eg, there is an outlier, Kellogg’s Crunchy Nut Clusters. This high calorie reading could be to do with this cereal containing nuts which are high in calories. Also note the vertical axis does not start at zero so any correlation may be exaggerated. 2 It is reported, based on a sample of students aged between 11 and 16, that taller children have a better vocabulary. Might not be causal. The variable that is probably causing this correlation is age. 3 There is a positive correlation between the time spent running on the treadmill and the number of calories the person burns. Likely to be causal as we know exercise uses up calories. 4 A news story starts "Scottish neighbourhoods with the most licensed premises have the highest rates of alcohol-related illness and deaths, according to a new study." Open for discussion: Might be causal - if there were fewer places selling alcohol, it is possible that alcohol-related illnesses would drop. Does supply create demand or demand cause supply? Might not be causal - discuss other variables that could affect either alcohol-related illnesses or most licensed premises. Unemployment, investment in medical care, education on risks of drinking alcohol, interest in sport (shown on the big screens in pubs). 5 Between 1992 and 2006 there is a negative correlation between the number of first time marriages for women and life expectancy in England and Wales. Might not be causal. The variable that is probably causing this correlation is the year. There were more marriages 1992 but female life expectancy was lower. 6 Organic food may be the cause of the increase in the number of cases of autism in the USA. Not causal - the graph only shows that both variables increase in a similar way over the time period. It offers no scientific explanation of why this may happen.
Transcript
Correlation or Causation - Solutions
1 There is a positive correlation between the amount of sugar and the number of calories in breakfast cereals. Might be causal. One might directly cause the other. Although other ingredients may add to the calorie count. Eg, there is an outlier, Kellogg’s Crunchy Nut Clusters. This high calorie reading could be to do with this cereal containing nuts which are high in calories. Also note the vertical axis does not start at zero so any correlation may be exaggerated.
2 It is reported, based on a sample of students aged between 11 and 16, that taller children have a better vocabulary. Might not be causal. The variable that is probably causing this correlation is age.
3 There is a positive correlation between the time spent running on the treadmill and the number of calories the person burns. Likely to be causal as we know exercise uses up calories.
4
A news story starts "Scottish neighbourhoods with the most licensed premises have the highest rates of alcohol-related illness and deaths, according to a new study." Open for discussion: Might be causal - if there were fewer places selling alcohol, it is possible that alcohol-related
illnesses would drop. Does supply create demand or demand cause supply?
Might not be causal - discuss other variables that could affect either alcohol-related illnesses or most licensed premises. Unemployment, investment in medical care, education on risks of drinking alcohol, interest in sport (shown on the big screens in pubs).
5 Between 1992 and 2006 there is a negative correlation between the number of first time marriages for women and life expectancy in England and Wales.
Might not be causal. The variable that is probably causing this correlation is the year. There were more marriages 1992 but female life expectancy was lower.
6 Organic food may be the cause of the increase in the number of cases of autism in the USA.
Not causal - the graph only shows that both variables increase in a similar way over the time period. It offers no scientific explanation of why this may happen.
Correlation or Causation?
1
Relationship State what you think the evidence is trying to suggest
Give a reason why you agree or disagree with what the evidence is suggesting
Do you think the relationship is probably causal or probably not causal?
Example
There is a positive correlation between the number of ice-creams sold and the
number of drownings.
Suggests eating ice-cream causes
drowning.
When the weather is hot more people swim and more people eat ice-cream. There is a third variable affecting both, the outside temperature.
Probably causal
Probably not causal
1 There is a positive correlation between the amount of sugar and the number of calories in breakfast cereals
Probably causal
Probably not causal
X
403020100
450
425
400
375
350
Sugar per 100g (g)
Kcal/
10
0g
Kcal per 100g vs Sugar per 100g for breakfast cereals
Correlation or Causation?
2
Relationship State what you think the evidence is trying to suggest
Give a reason why you agree or disagree with what the evidence is suggesting
Do you think the relationship is probably causal or probably not causal?
2 It is reported, based on a sample of students aged between 11 and 16, that taller children have a better vocabulary
Probably causal Probably not causal
3 There is a positive correlation between the time spent running on the treadmill and the number of calories the person burns
Probably causal Probably not causal
4 A news story starts "Scottish neighbourhoods with the most licensed premises have the highest rates of alcohol-related illness and deaths, according to a new study”
Probably causal Probably not causal
Correlation or Causation?
3
Relationship State what you think the evidence is trying to suggest
Give a reason why you agree or disagree with what the evidence is suggesting
Do you think the relationship is probably causal or probably not causal?
5 Between 1992 and 2006 there is a negative correlation between the number of first time marriages for women and life expectancy in England and Wales
Probably causal Probably not causal
6 Organic food may be the cause of the increase in the number of cases of autism in the USA
Data obtained from the Organic Trade Association Survey 2011
Organic Industry Survey. US Department of Education Office for Special Education Program
Probably causal Probably not causal
3400032000300002800026000240002200020000
82.0
81.5
81.0
80.5
80.0
79.5
79.0
Number of first time marriages
Fem
ale
lif
e e
xp
ecta
ncy a
t b
irth
(years
)
Female life expectancy vs number of females marrying
If a scatter graph is used to show how 20 people scored on 2 variables, the scatter diagram will have 2 axes and 20 points plotted.
True or False
This season, every time Jim has worn his blue scarf his team has won. His friend says that if Jim wears his blue scarf to the next game the team Jim supports will definitely win.
True or False
Some islanders noticed that whenever they were sick they didn't have lice whereas they did have lice whenever they were healthy. So, as long as you have lice you will be healthy.
True or False
If you are the tallest student in your class and there is a positive relationship between height and another variable, your point will be plotted in the top right of a scatter graph of height against this other variable.
True or False
Correlation always implies causation.
True or False
If two variables are negatively correlated high values for one variable suggests low values for the other variable.
Spearman's rank correlation coefficient
Country Actual Rank
X
Student Rank
Y
R
a
n
d
(
Actual Rank
X
Social Sciences 7 6 1
Physical
Sciences
59 -4
Medical Related 3 8 -5
Medicine and
Dentistry
83 5
Computer
Science
91 8
Law 10 4 6
Engineering 1 10 -9
Biological Studies 27 -5
Creative Arts and
Design
42 2
Business and
Admin Studies
65 1
Means 5.5 5.5 Sum
r =
Spearman's rank correlation coefficient
Student Rank
Y
1
16
25
25
64
36
81
25
4
1
278
-0.685
0
2
4
6
8
10
12
0 2 4
Stu
den
t ra
nk
Student Rank vs Actual Rank
6 8 10 12
Actual rank
Student Rank vs Actual Rank
12
A macro is included in this spreadsheet. Press Ctrl c: this will randomly order the student rank s, plot a scatter graph and calculate Spearman's rank correlation coefficient for the new student ranks. Each time you press Ctrl c put into column G any values of r you consider far enough away from zero to convince you that there is an associationbetween the populations of student ranks and actual ranks.
Press Ctrl c: this will randomly order the student rank s, plot a scatter graph and calculate Spearman's rank correlation coefficient for the new student
you consider far n association
True of False – Solutions
Statement True or False
1 If a scatter graph is used to show how 20 people
scored on 2 variables, the scatter diagram will have 2 axes and 20 points plotted.
True
2
This season, every time Jim has worn his blue scarf his team has won. His friend says that if Jim wears
his blue scarf to the next game the team Jim supports will definitely win.
False This is just luck and nothing to do with the way Jim’s team plays.
3
Some islanders noticed that whenever they were sick they didn't have lice whereas they did have lice whenever they were healthy. So, as long as you
have lice you will be healthy.
False Lice leave unhealthy people.
4
If you are the tallest student in your class and there is a positive relationship between height and
another variable, it is certain that your point will be plotted in the top right of a scatter graph of height
against this other variable.
False. This could be an outlier.
5 Correlation always implies causation.
False We have just seen several examples of this not being true.
6 If two variables are negatively correlated high values
for one variable suggests low values for the other variable.
True
True of False
Statement True or
False
1 If a scatter graph is used to show how 20 people
scored on 2 variables, the scatter diagram will have 2 axes and 20 points plotted.
2
This season, every time Jim has worn his blue scarf his team has won. His friend says that if Jim wears
his blue scarf to the next game the team Jim supports will definitely win.
3
Some islanders noticed that whenever they were sick they didn't have lice whereas they did have lice whenever they were healthy. So, as long as you
have lice you will be healthy.
4
If you are the tallest student in your class and there is a positive relationship between height and another variable, it is certain that your point will be plotted in the top right of a scatter graph of height against this
other variable.
5 Correlation always implies causation.
6 If two variables are negatively correlated high values
for one variable suggests low values for the other variable.
