Homework 12: Part 2, Problem 3

How Math Relates to My Field of Study

My field of study is psychology. I decided to major in it last year and I was well aware that math was going to be involved. Statistics are an integral part of psychology, and this almost stopped me from studying psychology. My classmates who are also majoring in it were very anxious to learn we needed a statistics course to complete our degree. I doubt any of them were taking an actual math course, so I feel better prepared for courses involving statistics.

Math is an important part of psychological research because psychologists must quantify their data and results into numbers so that people can understand phenomena occurring in the population. Using the scientific method, psychologists are constantly measuring aspects of human behaviour that can be conceptual and abstract or they can be primarily biological. People are asked to quantify how depressed they have felt, how much anxiety they feel or how happy they are on interval scales. Cognitive processes, and physiological responses can also be measured and expressed in graphs or as functions. The goals of the scientific method in psychology are to describe, predict, explain and determine the cause of behaviour. These findings concerning behaviour are important to companies, governments and may help people's general well-being. Of course, in order to attain results and test hypotheses, we need math to score and code observations and compile this data into a few figures. Psychology would be an even bigger joke without statistics helping to boost research credibility!

Something I thought was neat from my psychology class last semester was called integrative complexity. It goes back to the idea of taking an abstract concept, and scoring it and turning it into helpful data. In archival research, psychologists can examine old archives of politicians' speeches after a crisis for example. Scoring integrative complexity means assigning a number from 1 to 7 to a speech based on how many different point of views the individual who made the speech is holding in his/her mind at one time. The higher the integrative complexity, the more diplomatic the outcome was between two conflicting countries.

Correlational relationships are expressed in coefficients and can be summarized in informative graphs. A number will quickly give you an idea about a particular relationship and whether it is strong enough to be important. This threshold is about 0.37 and above in psychology. The graph of a correlation will indicate the direction of the relationship, and whether it's negative or positive. relationship (if it is linear) or an absence of a relationship. The shape of the graph matters too. Curvilinear graphs are more interesting to me because the relationship between variables reaches an optimal point and then one variable decreases as the other increases.

Inferential statistics are preferable to simple correlations. Psychologists try to keep their samples as random as possible and they must use math to determine whether their results are statistically significant. This goes back to analyzing graphs and functions. Psychologists also use math to test the reliability and validity of their measures. This could be tests, indexes or surveys they give to participants in their studies. Cronbach's Alpha and Cohen's Kappa show how well questions on a test correlate to each other and the correlation between raters' observations in a study. These are single numbers that vary with each test. For example, the BFI44 (Big Five Index), which is a measure of personality traits has test reliability of 0.85 and a Cronbach's alpha of 0.88. Because these numbers are correlations, this tells us that it is a very reliable test! When psychologists use statistics, the are always looking at measures of central tendency, such as the mean, the mode and the median. They can be represented as curves and distributions on graphs.

As far as calculus is concerned, maybe I have not delved deeply enough into into its applications to psychology in my academic career. If I do want to be a psychologist one day I will have to embrace math and it's countless uses in the field!

Term 1 Homework

The Pythagorean Theorem

a2 + b2 = c2. This is the equation that got you through grade eight math. It is called the Pythagorean equation. What our teachers did not tell us back then was that the Pythagoras' equation has many more complex uses in math. Pythagoras was a Greek philosopher who lived from c.570 to c. 490 BCE. His equation refers right triangles. It states that the square of the hypotenuse in a right triangle is equal to the sum of the two squares of each of the sides. The Pythagorean theorem applies to trigonometry and helps us solve for the other angles in the right triangle, which are referred to as "theta". One can use trigonometric ratios to solve for the sides if theta is known. A handy acronym is "SOHCAHTOA", where the S, C and T represent sine, cosine and tangent. The values found by using the Pythagorean equation are represented by O, H and A (opposite, hypotenuse, adjacent) and the order in which they are read is their ratio. Solving right triangles has real-life applications, and is relevant in physics. The Pythagorean theorem is very ancient but has been very important to mathematics.