Thursday, May 8, 2008

IB Math Studies IA project example

I kind of handed this sucker in two weeks late, so I probably got a 0/2 for commitment. Still, I scoured the net for examples and couldn’t find anything that our teacher didn’t give us, so I thought a sample project would be appreciated. I got 14/20, by the way, and my topic is "First Period Leads in National Hockey League Games and the Effect on the Final Score."



Plan of Investigation

While watching National Hockey League (NHL) games, I often heard the play-by-play announcer mention at the start of the third and final period how it would be tough for a team to come back from a one goal deficit. This led me to wonder just how difficult it was mathematically, and how much previous periods affected the final one. In this project, I will investigate whether the scores at the end of the first period affect the final score of NHL games.
I will gather the scores of 200 hockey games between 2005-2008 from the nhl.com website. I chose these years because the type of hockey before and after the new Collective Bargaining Agreement is different in terms of goals scored per game, with more goals scored per game on average before than after.
After gathering this data, I will analyze and compare the data. I will make scatterplots, plotting the scores of both losing and winning teams at the end of the first period on the Y-axis and the final score on the X-axis. This will let me see visually whether previous scores affect the amount of goals scored in the third period. I will also use Pearson’s correlation coefficient to see whether there appears to be a correlation between the score at the end of the first period and the final score. I will also try to describe the strength of association by using the coefficient of determination. I will then create a bar graph showing teams who won at the end of the first period and won at the end of the third and teams who lost at the end of the first period and won at the end of the third. Using information from the bar graph, I will use the chi-squared test of independence to see whether the score at the end of the first period and the score at the end of the third period are independent.


Procedure

1. For the dates of the 200 games, I placed slips of paper into a three boxes. In one box were four slips of paper, one for each year between 2005-2008, in another box were 31 slips with the numbers 1-31, and in the final box were 9 slips with the months January-June, October-December

2. Took one slip of paper from each hat and noted the scores of all games played that day. I put the slips of paper back into the box after I noted the scores

3. Repeated this process until I reached 200 games

4. Made two scatterplots, one of the score of the winning team at the end of the first period and the score at the end of the third, and one of the score of the losing team at the end of the first period and at the end of the third

5. Found the line of best fit

6. Used Pearson’s correlation coefficient on the numbers used in the scatterplots

7. Used the coefficient of determination on the numbers used in step 5

8. Made bar graph of teams who won at the end of the first period and won at the end of the third versus teams who lost at the end of the first period and won at the end of the third

9. Concluded whether there appears to be a correlation between the score at the end of the first and the score at the end of the third



Raw data

Uh, I had 100+ trials, I put the number into tables, you guys don't need to see this.



Data Analysis

After collecting the data, two scatter plots were created using Microsoft Excel, one of the scores of Team A, the winning team at the end of the first period, and one of the scores of Team B, the losing team at the end of the third period.

[GRAPH] [GRAPH...if you really want to see them, send me an email/leave a comment or something and I can send it over]

To make this graph, I placed the data into Microsoft Excel, used XY (scatter) using the Chart Wizard. I made sure the maximums, minimums and scales were the same for the two graphs so a better comparison could be made between them. I next added a linear trend line. Under the Add Trendline Option, I elected to display the equation on the chart. --> NOTE: I don't think you're supposed to use Microsoft Excel, but I had lost my calculator, I was across the continent, I was really, really desperate

The scatter plot is a graph that shows the correlation between the two variables. The trendline, known as the line of best fit or the least squares regression line, shows the linear equation which best explains the sums up the data’s trend. The formula on the right is the formula of the line of best fit.

As can be observed from these plots, teams who win at the end of the first period have a much larger range of data, with 26 separate points versus 14 separate points on Team B’s graph. Since the scatter plot does not use a thicker dot when numerous teams share one place on the plot, this suggests that teams who lose at the end of the first period tend to have similar scores, as they have twelve fewer points than teams who win.

If a team loses in the first period, this means that its X-range must be smaller than that of the winning team. Since 9/26, or almost 35%, of Team A’s points are on 3 or 4 on the X-axis, it is logical for Team A to have a larger range. However, even disregarding 3 and 4 on the X-axis, Team A’s range is still larger than that of Team B’s. There is a greater spread of data on the Y-axis of Team A, as well.

Note that when Team A scores one goal in the first period, there are instances of them ending the third period with five or six goals. However, when Team B scores one goal in the first period, the most goals they ended up with is only four. This pattern is repeated when the teams score two goals in the first period. With Team A, there are instance(s) when they end up with seven; with team B, the most they have ended up with is six, one less than with Team A. This suggests that having a lead in the first does increase scoring slightly in the later periods.

I then used Pearson’s correlation coefficient. When necessary, I rounded numbers to three significant digits. Again, I used Microsoft Excel to find r, by placing data from Team A into A1 to A110 and B1 to B110. Next, I imputed =CORREL(A1:A110,B1:B110). This gave me r, +0.452. I repeated this process with data from Team B, although I imputed data into C and D columns and imputed =CORREL(C1:C110,D1:D110). The r for Team B was +0.436.

The purpose of r is to find the degree of linearity between the two variables. This allows me to evaluate the strength of the correlation between goals scored in the first period and third period by each time.

The Pearson’s correlation coefficient for Teams A and B suggests a weak positive correlation, with a slightly weaker correlation for Team B. This means that generally, the higher the score in the first period for both teams, the higher the score at the end of the third period. Team A is more likely than Team B to have a higher score in the third period given that it has a higher score in the first. Thus, Team A appears more likely to win because it either widens the difference in goals-scored between it and team B, or scores more goals in response to Team B trying to launch a comeback. However, this connection is quite weak. While this trend exists, it does not often occur. This suggests that if a higher score at the end of the first period does not frequently result in a higher score in the third period, then having a lead in the first period will aid the winning team, but only slightly.

Next, I squared r to find the coefficient of determination, r2.

Team A
r = 0.452
r2 = 0.204

Team B,
r = 0.436
r2 = 0.190

The coefficient of determination allows me to better describe the strength of association. It shows a very weak correlation between goals scored in the first period and the third period with both Team A and Team B. This means that although goals scored in the first period may help both teams, it does not do so significantly. This corroborates with r, which showed a weak link between goals scored in the first and third periods. As discussed with the results of r, this lead helps Team A more than Team B.

My final step was to make a bar graph of when Team A won at the end of the third versus when Team B won at the end of the third.

[GRAPH]

This shows clearly that Team A is more likely than Team B to win at the end of the third period. Team A won 88 times, while Team B won only 22 times, meaning that Team A won 80% of the time. This is quite a significant difference and shows that while the goals scored during the first period may not make a large difference in the goals scored at the end of the third period, a win at the end of the first period usually results in a win at the end of the third.



Discussion and Evaluation of Results

From the data collected for this experiment, as well as analysis of this data, it appears that a team winning at the end of the first period is generally more likely to win at the end of the third period. Note that the bar graph shows that teams who win at the end of the first period go on to win at the end of the third period 80% of the time, which strongly supports this idea. However, goals scored in the first period only slightly affect the score at the end of the third period. This suggests that many games are very close, with one team winning by one or two goals.
This naturally results in something I noticed during the investigation – that a great many ties occurred. It makes sense that with so many close games, many end up going into overtime. This partially explains the application of the shootout in hockey after 2006, which eliminated ties and ensured that one team won every game, which results in a clear outcome for the audience.
Something interesting I noticed in the data was that on the occasions Team B won, they tended to score more goals than needed for them to win. Team B often scored up to four goals during the second and third periods, even if only one was needed to catch up to Team A. Another trend I noticed was that Team A either played defensively and did not score another goal, or they scored up to four or five more goals. Both of these trends are results of individual coaching styles and team motivation. This was not reflected in my scatter plot because as mentioned, my scatter plot did not have a thicker dot for an event happening more frequently. Thus, even if Team A winning by three goals was more common than Team A winning by one, both are represented the same way on the scatter plot. This misrepresentation is one of the fallibilities in my experiment. It could perhaps be remedied by creating another graph which shows how often each score occurred.
I also noticed that it is uncommon for teams to score more than 4 goals in a period. In most games, teams score between 0 to 3 goals per period. Going by this generalization, a team which leads by one or two goals in the first period is not advantaged by much, as Team B should be able to catch up by scoring one or two goals in the second and third periods. However, once a team leads by four or more goals in the first period, it should be harder for Team B to catch up, as it will be forced to score more goals than it usually does.
This generalization is supported by my scatter plot and data. Teams who score three or four goals in the first period can end up with seven or eight goals by the third period, while there are no instances of teams losing in the first period scoring more than six goals. This suggests that more goals are scored overall when a team scores more goals in the first period. My data shows that in almost every instance when a team scores three or four goals in the first period, this team wins the hockey game. Thus, although Team A usually wins, it has a higher chance of doing so when it scores more goals in the first period.
Several factors prevent this study from being perfectly valid. Although I deliberately chose the dates randomly, games are affected by a myriad of factors outside of simply scores. The scheduling can affect the scores as teams playing three games in four nights, or back to back games, are liable to being more fatigued and possibly scoring fewer goals. Scheduling could also affect scores in that during late season games, as some teams who will not make the playoffs stop trying to win, while others who wish to improve their position try harder. It is difficult to judge the former whether they score more or fewer goals in the first, as when they score, they are not as motivated to hold onto their lead, and when they do not score, they are not as motivated to catch up. Meanwhile, the latter are eager to score as much as possible, since sometimes ranking between similar teams is based on goals scored for and against.
I think that this problem could be helped by collecting more data. Although I randomly chose 110 games, it may not be enough to cover all the factors that can affect games throughout two and a half seasons considering 2460 games are played each season. Doubling or even tripling the number of games would better encompass these changes.
The reliability of the analysis stems from the fact that since the data is gathered throughout the regular season, it can be compared accurately, as opposed to data collected during regular season, preseason and the playoffs, when different types of hockey are played. It was also randomly gathered, reducing the chance of a bias resulting in games chosen from one circumstance.
Although goals scored in the first period do not affect goals scored in the third period in a major fashion, my investigation shows a strong correlation between winning in the first period and winning in the third period.

253 comments:

1 – 200 of 253   Newer›   Newest»
ibbb said...

n how much did u get for this?

Anonymous said...

Thank you, this helped me so so so much with my own MS Project (which was about high-heels)!

miranda said...

can you send me some of your data like how it looked so i can see how mine should look like please i would appreciate it greatly.

Anonymous said...

can you please send me some of your data information, i mean the graphs on scatter and chisquared as well as the pearson's? thanks

Anonymous said...

can you please send me some of your data information, i mean the graphs on scatter and chisquared as well as the pearson's? thanks

Anonymous said...

u just saved my life=] i did something very similar to urs but with football instead, hope u dont mind! thanks again=]

Anonymous said...

hi, please send mr ur graph. thanks so much

Anonymous said...

Hi, very similar idea to my project, interested in how the graphs look... greatly appreciated if you would have the time to send me the graphs, for me to get an idea of the direction to take! thanks!

oskar_hall@hotmail.com

kris said...

hii. can you please send me any data you have recieved. i am doing my project on how basketball shots are affected by height. i would really appreciate this so much!!!
sashaamirzanjani@yahoo.com

Anonymous said...

Hi my project has the same concept as yours. Can you please send me the graphs and data so i can have an idea of how to organize my data. I would really appreciate it and it would be of much more ease to me.

rippedtex@yahoo.com

Anonymous said...

This was sooo helpful!!! thanks.

Anonymous said...

Thank you for the information posted. If you could please e-mail me the graphs it would mean the world.

lacrosseinfo@gmail.com

GraceJM said...

Thank you! I lost my packet telling me the sections i needed and this is a life saver!

Anonymous said...

Im doing something really similar with soccer...could you send me your charts please, like your graph and chi squared tests? it would be greatly appriciated.

georgette.leau@gmail.com

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Anonymous said...

I'm doing a project with a similar concept, except I'm doing it with basketball. It would be greatly appreciated if you could send me some of the graphs and data you used.

Cheers,
miron_128@hotmail.com

Anonymous said...

hi im doing something similar but with nba do you think you could send me your charts to
jbernal_626@hotmail.com

Anonymous said...

Hey.. Awesome job man. Also, can you send me your graphs and chi squared. It would be much appreciated. Thank you.

My topic is to see if there is any correlation between one's favorite sport to watch and their favorite sport to play. Pretty interesting!


armswideopen2692@aol.com

Anonymous said...

my email is aka_panchal@yahoo.com

can you send me the graphs

John said...

Hi, how were you able to complete the graphs without a calculator? can you send me the pearsons formula you used and how you used it? Thanks!
dodgersjohn2010@gmail.com

John said...

Hi, how were you able to complete the graphs without a calculator? can you send me the pearsons formula you used and how you used it? Thanks!
dodgersjohn2010@gmail.com

Sofia said...

Hey! This was very good! It would be great if I could take a look at the graphs and equations! :)

Please send them to me at sassan-91@hotmail.se

Thank you!

Anonymous said...

hey im basically doing the same exact project. do u think u can send me the word file of the completed paper? That would be totally awesome
My email is Jluvhockey@aol.com

Reetu said...

This is really helpful, can u please send me the word document or the pdf of this pleaseee!!!
tasnim.rahman@gmail.com

Anonymous said...

Can you send me your charts/graphs and a pdf of your final paper? I just need to make sure I'm doing everything correctly. Thanks!
jennam110@gmail.com

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darius said...

i really need the charts for dis project jokaz_rme@yahoo.com

Anonymous said...

is it possible for you to send me the graphs so i can get an idea of the overall paper? thanks. tkdcrazy451@aol.com

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marwa =) said...

Can you please send me your graphs and other data you didnt include? THANK YOU SOOOO MUCH :) :)
my project is due next week....
aaahhhhhhhhh

marwa898@hotmail.com

Heath said...

could you send me the actual project? im not lookin to copy it, i just wanna see how you formatted it and such. it would be greatly appreciated!

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Anonymous said...

Hey, i was planning on doing something similar for my IB studies math project, i was wondering if you could send your raw data for the 200 games that would be super!

my email is mebbe_@hotmail.com

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email: kemjibemji_3000@hotmail.com

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aleksander_vedvik@hotmail.com, if you could send it to me that would be awesome!!! =D I really need a good example to go after for my own Math Studies project, THANKS!!

Anonymous said...

hi, i would just like to say thank you for writing this and if it was possible could you send me either raw data or just the whole IA cause i was wondering how you put it together. i.e structured/formatted the project.

thank you so much

email: fredbrick2000@yahoo.com

Anonymous said...

Hi,
I wanna thank you for this! it reeeeally helped me out of my hopeless case :P
And i was wondering if u could please send me the whole IA document just to get an idea of how to present it, but if u can't, the graphs and chi squared alone would be fine :)
thnx
jannatd_93@hotmail.com

Anonymous said...

hey! could you send me your data, please? That would be so amazing, thanks so much :)

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Anonymous said...

Thanks! As much as a help as this has been I'm still confused with bits of it. Can you please send me your data and graphs?

the.next.vah@gmail.com

Anonymous said...

THanks a bunch this is really helping me! could you please please please send me your data, the scatterplots and pearson's formula? Plss send to kyladurrett@yahoo.com Thank you!

Shivya said...

Hey! This a great project and im doing something similar.
Could you please email me the final bar graph as I am confused about how to go about mine
Thank you so much!

email id: shivya.kochar@gmail.com

Anonymous said...

This helped me sooooo much for my project as I didnt know what I should include and what I shouldn't.
Thanks for the help :)

Anonymous said...

could you email me the graph!
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Anonymous said...

You. Just. Saved. My. Life. Thank you!!! My teacher literally has mentioned this project in passing like 3 times and informed us today that he expected us to have already collected our data. O.O This is the best example I've found, it was really really really really helpful!

Alex M said...

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Anonymous said...

So far your IA has been the only example I have to go off of in creating my own, which is due in a modest fourteen hours, and I could not be more grateful to have access to it. Especially seeing as the only guidance our teacher gave us was something along the lines of "as long as you have the criteria, you should be able to figure it out." I would have piggy-backed off of my older brother's, but I don't think he actually ever did his.
By the way, my topic was to what extent being knowledgeable in current events is dependent on being in IB. Definitely couldn't predict the outcome of that one....

Anonymous said...

fiona_brisland@hotmail.com
could you please send me your graphs and so on? It would be a HUGE help...thank you!!

Anonymous said...

Hi this was very very helpful, could you please send me the word doc for this project at mfk.797@gmail.com please? Also how much did you get for this project?

Anonymous said...

Thanks for posting this man, but i was just wondering if you could send like a word or pdf version of the project so that i can see if i formatted mine right. Im doing mine on whether or not being in IB affects the amount of sleep a student gets on average per night lol. My email is nkemick44@yahoo.com. thanks in advance!

Please help said...

ok so im pretty much done with mine except i would like to see how you setup the tables and the rest of the project, so if you dont mind can you please send me the full project? thanks so much in advance mam. my email is (mohamed.a.nouri@gmail.com)

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OE said...
This comment has been removed by the author.
OE said...

Thanks a lot for this man, but I'd love to see the graphs and possibly the data u got. I gave mine in, but I did mine for the NBA. It'll be great to see your results and data. If you do feel like letting me see your results, fire me an email to oediri@gmail.com..thanks.

Anonymous said...

hey, thanks for this. if u can, can u send me your data like the graphs. it will really help mine...thanks.

my email is meljo192@gmail.com

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Kaitlin said...

I'm in my first year of DP and the guidelines I was given are so vague. I've just turned in Criterions A&B (after changing my topic twice because the teacher shouldn't have approved the others..) late and I can't afford to mess up again. I don't understand what I need to do for Criterion C.

I took a survey and got 76 pieces of data, split into two data tables and two scatterplot graphs (made on MS Excel), and I can't find any good explanations of where to go from here. The form is so confusing.

An email would be much appreciated. Thanks so much!
anon_jones@hotmail.com

Anonymous said...

This is great! I'm doing something similar (as I am a hockey fan too) but do you think you could email me the graphs/data just to be sure if I'm headed in the right direction? Thanks!
email:nicolefinstar95@aol.com

Anonymous said...

this is really great! im doing something similar, football scores.

i would really like to get a look at the graphs, and the data table

if u can please send me an email, i would really appreciate it, thanks again =]

mr.BS77@live.com

Zack_21 said...

Can u send me your graphs please? I would like to compare them to mine

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Anonymous said...

I'm doing a project with a similar concept, except I'm doing it with basketball. It would be greatly appreciated if you could send me some of the graphs and data you used.

Thanks,
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Grant said...

Hey i know everybody else asked, but you think you could send me the data and graphs? It would be a HUGE help
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anonymouse said...

i thank your so much ,

can you please send me the full project i mean the graphs and scatter and chisquared thing ? i mean the mathematical processs ?

on my email : ajaber1094@hotmail.com

many thanks

anonymouse said...

i thank your so much ,

can you please send me the full project i mean the graphs and scatter and chisquared thing ? i mean the mathematical processs ?

on my email : ajaber1094@hotmail.com

many thanks

patrick said...

Hey can u please send me ur graphs? It would be really helpful. Thanks.
gwoodpatrick@gmail.com

annonymous said...

can you send your graphs and scatterplots and chisquared and pearsons to dompdx@gmail.com ? many thanks

Tomasz Zalewski said...

Hey,
I know its been like 2 or 3 years since you did this, but i was just wondering if you could post the data and the graph to me ? Im doing something similar about soccer scores, but its how likely is a 3-0 comeback in the second half and just dont know how to set it out.
Cheers :)

tomasz_z54@hotmail.com

Darksider13 said...

Regardless of how long ago this happened, thank you oh so very much for this guide. I'm totally cramming last minute (as is probably everyone who's ever used this guide) on this IA just to get it done and out of the way and the fact that you got a 14/20 on this and doing such a similar topic to mine makes me feel a little bit more confident about my score on this. Thanks so much again for the help and seeing as this is my last IA for ANY CLASS (WOOOOOOOT!) I won't be using this for help anymore but regardless thank you for doing what most in the IB community wouldn't!!!! :D

Anonymous said...

thankyouu this helped me so much with my project! there's also a great project on slideshare that got a level 7 which helped a lot when i was writing mine... http://www.slideshare.net/BillyEgg/ib-math-studies-internal-assessment-final-draft
taaa again :)

SHAKER.2013 said...

Can You Please Send Me Your GRAPHS...? I'd Love To Take A Look @ Them :) Thnx For This GREAT Resource...

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MY E-Mail - Shaker.2013@Gmail.com :)

Anonymous said...

Hey do you think you could send me your graphs and raw data please?? :)

My email is ryan_16_3@hotmail.com

Anonymous said...

can you please send me the graphs, tables and chisquared tests please :)

email: ssyed.17.jm@gmail.com
thank you once again :D

Anonymous said...

could you send it to me as well? im just looking through mine and wasnt sure exactly how it should be formated. Thanks a lot :))

ibanezjoe12@yahoo.com

SHAKER.2013 said...

I STILL Haven't Received ANY GRAPHS & Information. Can You Please Send IT To Me...? :) Thankz....

Anonymous said...

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Anonymous said...

What was your soccer IA topic?

Anonymous said...

Thankyou so much! this helped me heaps!

Bebeto Goenha said...

Could you please send me the graphs
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Could you send me your graph for this?
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busty milf said...

you guys are dumb as shit..... you are all gonna basically go copy the thing but i think IB would know if you copied someone's shit and you wont get a good score because its not different. they will clearly realize that the same fucking project is being done again and again. thats what my teacher told us dont judge me.

Anonymous said...

wow this is extremely helpful! can you please send me the graphs and the chi-squared because i want to see how you set them up? i would appreciate it alot!
thanks soo much :D

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i know it had been 2 years since u post this sample..but can u pliz email me the graph..here is my email
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Hey i really like ur ia am doing similar stuff with soccer can you send me the graph and other important info by my email freshprins-@hotmail.com

Anonymous said...

love your stuff can you please send me your graphs my e-mail is shadowofthepast@hotmail.com

Anonymous said...

Hi! you just saved my life
i'd appreciate it if you could send me your graph so i can compare it to mine? i did a similar IA but i used english premier league football rather than NFL

could you please send it to:
taymourihno@live.com
thanks again!

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