In a comment to this post, please discuss each of the graphs below. Be sure to address the questions under each graph. Please don't copy the questions or number your answers, rather, you should write a paragraph or two in complete sentences so your reader knows what you are talking about. Be sure to sign in as "anonymous" but put your first name and last initial in the post so I know to whom to give the credit. If you have any questions please e-mail me. Review the "how to e-mail a teacher" post on my blog before you send your e-mail.(click on the graphs to enlarge)
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| Hair Length v. Height - Correlation Coefficient = -0.47 |
What can we see from the above scatter plot of hair length vs. height? Is there a correlation? How strong is it? If so, is it positive or negative; strong or weak? What information about the students in our class does this graph give you? Are there a few "outliers" or extreme data points that seem unusual? If you throw them out of the data set what does the correlation look like? What other information would be helpful to interpret the data?
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| Height v. Shoe Size - Correlation Coefficient = +0.73 |
Above is the data we collected about our shoe sizes vs our heights. Can you see a relationship? Is there a correlation? If so, is it positive or negative? How strong is it? Does shoe size cause height to change? Does height cause shoe size to change?
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Finally, the above graph shows the relationship between shoe size and hair length. Is there a correlation? If so, is it positive or negative? How strong is it? What third variable which is not shown on the graphs might be causing the relationship between shoe size and hair length? Does correlation imply causation? Why or why not?
And a video about ice cream and polio...
11 comments:
Yes there is a correlation because you can assume that the taller a person is the longer there hair might be. But you can’t know for sure it could be the other way around as well. The graph shows us many points were the taller the person is the longer the hair length but also shows us that theirs certain people that are taller but their hair length is short. Other information that would be helpful to understand the data better will knowing who are girls and boys. Yes there is a correlation between shoe size vs our height. You can say that the taller the person the bigger their shoe size. I think the correlation is positive because it would be unusual to see a tall person with small feet it’s a strong correlation. I think the height causes the shoe size to change because the taller the person the bigger the shoe size. I don’t think there is a correlation between hair vs shoe size. The variable that might be causing a relationship between hair vs shoe size will be if the person is a girl or boy if there a girl most likely that they will have longer hair that boy and probably smaller shoe sizes than boys
L.g
From the hair length vs height graph we can see that there seems to be no relationship between them two. The data collected between them is a zero correlation. The data is splattered randomly on the graph. The information that the graph gives us about the students in our class is that there seem to be a connection between the students that are 160-175 height have the lowest hair length. There does seem to be extreme data plots on the graph were dots touch each other; like those that are 165 cm tall almost have the same hair length. If we were to eliminate their data than the graph will still be the same. However, the students that are 160-175 cm tall data points would increase in hair length than decrease. I think if we were able to know the differences in boy’s and girl’s data from our classroom would be helpful and that way we can see does gender play a role in any of our data collection.
In the shoe size vs height graph there seems to be a relationship for the most part between the two variables. The correlation between them seems to be positive, but it’s a weak positive correlation because the two variables at times don’t always increase together at the same time. Like for example from shoe size 18, 20, and 22 you can see that both shoe size and height are increasing. But if you look closely at the points in between them there is some that as the shoe increases the height decreases. This makes it a weak positive correlation between the two variables. I think shoe size causes height to change.
In the shoe size vs hair length graph there is some kind of relationship between the two variables. The correlation between them is a weak negative one because as hair length increases shoe size decreases but it’s not always consistent. The third variable that is not shown that could be a factor can be height. Correlation does not imply causation. Correlation is to examine the relationships between two variables at the same time and how they relate to each other. While causation is the cause of things to happen. Just because things happen at the same doesn't always mean that one causes the other. In the graphs there wasn't always consistency with data between two variables correlation.
First graph
Students that are taller have shorter hair in a way. I think there is no correlation in this graph. Yes there are a few “outliers” in our data. One student who is fairly shorter than another has a very big hair length difference than all he other students. If we were to throw them out of the data, I think the data would have a low negative correlation because the line is sloping down.
Second graph
The relationship is perfect in this graph. There definitely is a high positive correlation going on. It is very strong. I think the shoe size causes the height to change because as the shoe size increases, so does the height.
Third graph
The correlation In this graph is low negative. It’s strong but not that strong as graph two. The third variable that is not shown in this graph is the height of each student. I think correlation does not imply causation. Correlation is the mutual relationship between two or more things and causation is how one variable influences or other variables to have an effect on one another. There isn’t really any evidence to me that the correlation that happened in the graph does not imply what causation does. For example, if causation would have been true for graph one, then there wouldn’t be that outlier. All the data would have been almost the same. As in the person who has the longest hair, would be the shortest.
April Ayala
The scatter plot of Hair Length vs. Height shows us a correlation. It is a low negative correlation that is for the most part a very weak one. I can say that maybe the height of the students in my class might have gotten their numbers correct but we might have gotten a hit or miss with the hair length. Our class has quite a bit of people who have curly hair and we weren't really able to figure out the exact measurement of the strand of hair to the root. That could have affected our end results. One of the dots seemed outrageous because it was way from the other dots and their results were that he/she was 168 cm. tall with a hair length of 60 cm. If I were to throw away that dot it wouldn't make much of a difference but the graph would be less weak. Another way to interpret the data in the graph is to look at the line and how it only has two dots that are on the line. Meaning that the data might not necessarily be accurate.
The Shoe Sizes vs. The Height graph shows us that there is a relationship. There is also indeed a correlation that is a high positive correlation. The correlation is not strong but it isn't weak either. We can’t really assume that shoe size causes height to change and that height causes shoe size to change because the students could have measured wrong. Maybe our height wasn't well measured because some students didn't take of their shoes and our shoe size wasn't exactly accurate for the measurements that we used in the classroom.
The Hair Length vs. Shoe Size has a correlation. The correlation is a low negative correlation that is weak but not extremely weak. The third variable that might be causing the graph to look the way it does is height. I believe that correlation is causing the graphs to look as they appear. If the correlation is negative, the scatter plot seems to be weak. As oppose to when the correlation is positive the dots seem to be more aligned with each other. The data collected seems to make more sense when the correlation is positive.
http://youtu.be/lbODqslc4Tg
Jacqueline E.
In the “Hair length vs Height graph we can see can see a weak negative correlation, where as height increases hair length decreases. This graph suggests that the taller you are in our psychology class the shorter hair you tend to have, but this isn’t always true. There are a many outliers in this graph, per example there is someone who has the longest hair and measures 155 cm of height which is almost the mean of the height, 158.89.but if we got rid of a few of the extreme outliers then our correlation would probably increase significantly. Other information that could helpful to the graph could be the sex of the participant just to see if sex has anything to do with this.
On the height vs shoe size graph there seems to be very positive correlation, +0.73. The graph suggests that as shoe size increases then so does the height. And as the book states, “a correlation coefficient can’t tell us which variable is influencing which” (Bernstein, pg. 52) so I don’t know which variable cause which in this case.
On the final graph, you can see almost no correlation at all or if there is one it is a really weak one of -0.39. The third variable that is not shown on the graph and might be causing such a weak correlation is the height. On the first graph hair vs height there is negative correlation and on the second one there is a positive correlation making the third one have points all over the graph. And again correlation does not imply causation because correlation graphs can’t tell which variable is influencing which.
Leonardo M.
What I can see from the first scatter plot of hair length vs. height is that the data is skewed. Yes there is a correlation in this graph, it is not strong, but the correlation is negative. The information from the students in our class on the graph shows that there is no relationship between the heights of some students and their hair lengths. There are some outliers on this graph where some people will have the longest hair length, or the shortest. If I through them out of the data set, the correlation will become more grouped together and look more lucid.
There is a relationship in the data collected from the graph of shoe size vs. our heights. The correlation indicates that if the student’s height is larger, so is their shoe size. The correlation is positive, and it is strong because the data is very condensed. Shoe size does not cause a change in the height of students. The height of students does cause the shoe size of students to change.
There is a correlation in the final graph of shoe size vs. hair length. The correlation is negative, but it’s not strong. The third variable that is not shown could be the height of the student that causes the relationship between shoe size and hair length. Correlation does not imply causation, because the data between the two variables does not imply that one causes the other.
The hair length vs. height correlation is weak. However; there is a correlation. It's goes towards the negative direction. Based on the scatter plot graph, there seems to be no pattern. For example, at height 155(cm), the Hair length measured 78(cm) but at height 168(cm) hair length measured less than 10(cm) twice. The scatter plot graph may be more understanding if it specified the gender. Typically, females have longer hair length than males.
The shoe size vs. height correlation is stronger than the length vs. height. In this scatter plot graph, the correlation is positive. For the most part, as height(cm) increases, shoe size(cm) increases as well. When performing correlations, one cannot make the claim that shoe size causes height to change or vise-versa. That's the downfall of correlations. However, this seems to be the best scatter plot graph.
The hair length vs. shoe size correlation is weak and unreliable. The plot points are all over the place. The scatter plot graph is a negative one, but it is not strong at all. The third variable that may be causing the scatter plot graph to look as it does might be gender. As I mentioned in the hair length vs. height correlation, females typically have longer hair and smaller feet than males.
-Miguel Espinoza
In the hair length vs. height plot I see a correlation. This correlation appears to be negative because it is going downward. To me it seems fairly strong. This data is showing a connection between the hair length, and height showing that as the hair is shorter the taller you are. There is one outlier that stands out to me which is JR this person has long hair and is tall. So yes JR made an outlier in this data. But what I think is really showing from our class is that if the hair length is short and the height is tall it most likely means the person is a man and opposite for women; they usually have longer hair and happen to be shorter than men. Something that would of helped us interpret this data better would have been giving different color points to females and males in the data.
The correlation between height and shoe size is much stronger than the hair length vs. height. Because the correlation coefficient is +0.73. The relationship I see between height and shoe size is the taller you are the bigger feet you have. It’s true because this positive correlation shows a strong connection between height and shoe size. The connection is as your height goes up the size of your feet increase and that’s with every part of your body. Not just one of your body part grows its all of your body that grows with you. So yes I can say height causes your shoe size to change.
There is a slight correlation between shoe size and hair length. The relationship between them is that as hair length decreases shoe size increases. But this isn't constant of course it varies this plot is very scattered and isn't constant. This correlation is negative and slightly strong. This plot was weaker than the first one due to the inconsistency of it.
A.S
According to the hair length vs. height plot, I could see that the data is very random and inconstant. The data is everywhere on the plot, and difficult to actually understand on my part. On the other hand, I could see that as the hair length measurements decreases the height increases. Even though the data is going like a roller-coaster, I could see that once the data reaches to 160-180 cm of height, the dots decreases more than any other as well as the hair length decreases too, but the number of heights is greater. There is a weak and negative correlation, being -0.47 coefficient. I don’t see the relation between hair lengths with height. There’s small and tall people with long and short hair. That’s what I see in the data. For example there’s, more than one student in the data plot with the height of approximately 167 cm and all three have a variety of hair length measurements; one has 60 cm of hair length, then the other has 1 cm, the last one has 0 cm of hair length. It doesn’t matter how long the hair length of a person or how tall or short is the individual, everything varies. However the interesting part is that you could distinguish the female and male students in the data, by the measurements of the the hair lengths, since most females have the tendency to have long hair and most males tend to have shorter hair. Also its curious to see that the plot has a crowded section of dotted data, but then as the height measurements becomes greater the hair measurements becomes very small and the plot information ends up with a decrease finish. You could say from this data that people with shorter hair are taller, which means that this data may show masculine description. On other hand instead of assuming, the data could have been easier to interpret if the data was able to show the students sex.
As I saw the height v. shoe size plotted data, you could see the relationship of the two values. The plot started with a height of 145 cm as well as the shoe size of 18 cm and it ended with the data of 174 cm of height and approximately 27 cm of shoe size. With that information I could state that as height increase, shoe size also increases. There is a low positive correlation with a coefficient of +0.73. I could see the positive correlation on the data, but the quality of it is not very perfect nor high either. I could also come to determine that height causes shoe size to change. You never come across with a small person with a big foot, nor a tall person with a small foot. In most cases it all goes in hand, a small person has a small shoe size and a tall person has a bigger shoe size. A great example are basketball players, most basketball players are very tall and tend to have a very large foot, which means a big shoe size.
On the other hand, in the shoe size v. hair length plot, I see no correlation, it has a coefficient of -0.39. The variable that may be causing the relationship between shoe size and hair length could surely be the student’s sex orientation, which could show more of a comprehensive data. As well as the unknown number of female and male that are in the data. I could say that correlation does not always implies causation, because there could be two variables that may simply correlate but does have the cause of the relationship of the two variables. Like for example on the hair length v. Height data plot, it had a weak correlation, but just because it had some type of correlation it doesn’t mean that it was the casualty of the relation, it had an unknown third variable, or you could say missing data to actually come to a true conclusion, or to proof that it was a cause an effect thing. Sometimes it could be a coincidental data but may not amplify with each other.
-Daisy.R
We can see from the above scatter plot of hair length vs. height that there is some kind of relationship. There is a correlation but it’s a negative correlation because the line decreases. The correlation is in between because it’s not that strong or weak. The information that the graph gives about the students is that the taller the student are the shorter their hair is although there are some outliers that if remove the correlation would’ve been stronger. On the data about our shoe sizes vs. our heights there is a relationship. There’s a positive correlation and pretty strong. I think that the height made the shoe size change because if tall people had small feet they wouldn’t be able to walk. On the data of shoe size and hair length there is a negative correlation and it’s in between strong and weak. The third variable might be the gender of the students because girls usually have longer hair than boys. Correlation doesn’t imply causation because there might be a relationship but you don’t know exactly what cause that relationship or if there were confound variables.
Edmundo. s
Mariana D
In the hair length vs. height scatter plot we can see that there’s a weak correlation between this two variables, it is weak because the correlation coefficient is -0.74 which is further away from 1.oo which is the highest positive correlation and closer to -1.oo which is the lowest coefficient of correlation. This correlation is a negative one because as height increases the hair length decreases. This shows that the taller a student is the shorter his/her hair tends to be. There are a few extreme data points that seem odd and if this didn’t exist the correlation would probably be stronger.
In the second graph we can see that there’s a correlation between shoe size and height. The correlation is positive as it is shown in the graph when the shoe size increases the height increases too. It is a strong correlation because the correlation efficient is (o.73)which is closer to the highest correlation coefficient. Even thought evidence shows there’s a relationship between this variables we cannot infer that one affects the other.
The final graph shows a correlation between hair length vs. shoe size. The correlation is weak because the coefficient is -.39 which is closer to the lowest coefficient of correlation. Other variables that can be affecting the data are: if experiment was not sampled, if subjects cut their hair the day before or simple things such as the type of hair of the subjects. Correlation does not imply causation because other variables could have affected the results and the correlation wasn't exact.
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