IB Math Studies IA
Criterion C – Further Mathematical Processes
You must have at least one further mathematical process in your IA. To be considered a “further” process, you must work the process out by hand, showing full work. While there are many processes that count as “further” (including differential calculus, mathematical modeling, optimization, analysis of exponential functions, statistical tests and distributions, and compound probability), the two below processes may be easiest to consider.
1. Chi squared test of independence
a. Collect at least 100 data points
b. Do not use percentages; instead, use counts.
i. Show sums or conversion from % to counts for each category (if applicable).
c. Do not use expected values less than 5.
i. If necessary, combine data.
d. Use Yates’ continuity correction if testing with a 2 x 2 contingency table.
e. Include bar graph (counts as simple process).
f. Include all steps for Chi squared test of independence.
g. Useful formulas:
i. χ2calc=f0-fe2fe where f0 is an observed frequency and fe is an expected frequency.
ii. Yates’ continuity correction: χ2calc=(f0-fe-0.5)2fe
h. Textbook reference pages: 334-344
2. Linear regression analysis
a. Can only be used as long as the correlation coefficient is high. (It does not make sense to calculate the equation of linear regression line if the scatterplot and value of r indicate there is no correlation.)
b. Collect at least 30 data points.
c. Include scatterplot with line of best fit by eye (counts as simple process).
d. Include calculations of r and r2, with interpretation of both.
i. Useful formulas:
1. r=(x-x)(y-y)(x-x)2(y-y)2 where x and y are the means of x and y respectively, and Ʃ is the sum over all the data values.
2. r2=(r)2
e. Include equation of regression line.
i. Useful formulas:
1. y-y=sxysx2(x-x) where x and y are the means of x and y respectively, sx is the standard deviation of the x data values, and sxy is the covariance.
2. sx=x-x2n
3. sxy=(x-x)(y-y)n
f. Textbook reference pages: 316-332