There are two methods that we can use in research of Psychology Study of Mathematics.
1. Qualification methods is methods which use subjective value to take conclusion of the problems.
2. Quantitative methods is methods which use objective value in mathematical calculation to take conclusion of the problems
Statistical methods have found extensive application in the psychological and educational testing field and in the study of human ability. Since the time of Binet, who developed the first extensively used and successful test of intelligence. We can use quantitative prediction to research human behavior, human ability, personality characteristics, attitudes, etc.
In this paper, we will concern to quantitative methods, specially descriptive statistics in research of psychology study of mathematics.
A. Definition Of Descriptive Statistics
Descriptive statistics is the part of statistics which process, presenting data without taking conclusion for population. Descriptive Statistics are used to describe the basic features of the data gathered from an experimental study in various ways. A descriptive Statistics is distinguished from inferential statistics. They provide simple summaries about the sample and the measures.
We can use descriptive statistic in psychology research. Example, if we measure the IQ of the complete population of students in a particular university and compute the mean IQ, the mean is a descriptive statistic because it describes a characteristic of sample population. If, on other hand, we measure the IQ of a sample of 100 students and compute the mean IQ for the sample, that mean is also a descriptive statistic because it describes a characteristic of the sample.
B. Steps in Descriptive Statistics
- Collect data
- Summarize data
- Present data
- Proceed to inferential statistics if there are enough data to draw a conclusion
C. Univariate Analysis
Univariate analysis involves the examination across cases of one variable at a time. There are three major characteristics of a single variable that we tend to look at:
- the distribution
- the central tendency
- the dispersion
In most situations, we would describe all three of these characteristics for each of the variables in our study.
The Distribution
The distribution is a summary of the frequency of individual values or ranges of values for a variable. The simplest distribution would list every value of a variable and the number of persons who had each value. For instance, a typical way to describe the distribution of college students is by year in college, listing the number or percent of students at each of the four years. Or, we describe gender by listing the number or percent of males and females. For example, we will measure the student problems in mathematics. We can identification it from mathematics test scores. There are the mathematics test score of 10 students.
Table 1. Frequency distribution of mathematics test score of 10 students
|
One of the most common ways to describe a single variable is with a frequency distribution. Variable x is the mathematics test score and variable f is the frequency. Frequency distributions can be depicted in two ways, as a table or as a graph.
Table 2. Frequency distribution histograms.
|
|
Table 3. Frequency distribution polygons.
Central Tendency
The central tendency of a distribution is an estimate of the "center" of a distribution of values. There are three major types of estimates of central tendency:
- Mean
- Median
- Mode
The Mean or average is probably the most commonly used method of describing central tendency. To compute the mean all you do is add up all the values and divide by the number of values. For example, the mean or average quiz score is determined by summing all the scores and dividing by the number of students taking the exam. For example, The sum of 10 values in table 1 is 81, so the mean is 810/10 = 8,1
The Median is the score found at the exact middle of the set of values. One way to compute the median is to list all scores in numerical order, and then locate the score in the center of the sample. If we order the10 scores shown above, we would get:
60,60,70,80,80,80,90,90,100,100
There are 10 scores and score #5 and #6 represent the halfway point. Since both of these scores are 80, the median is 80. If the two middle scores had different values, you would have to interpolate to determine the median.
The mode is the most frequently occurring value in the set of scores. To determine the mode, you might again order the scores as shown above, and then count each one. The most frequently occurring value is the mode. In our example, the value 80 occurs three times and is the model. In some distributions there is more than one modal value. In a bimodal distribution there are two values that occur most frequently.
Dispersion refers to the spread of the values around the central tendency. There are two common measures of dispersion, the range and the standard deviation. The range is simply the highest value minus the lowest value. In our example distribution, the high value is 36 and the low is 15, so the range is 100 - 60 = 40.
The Standard Deviation is a more accurate and detailed estimate of dispersion because an outlier can greatly exaggerate the range. The Standard Deviation shows the relation that set of scores has to the mean of the sample. To compute the standard deviation, we first find the distance between each value and the mean. We know from above that the mean is 81. So, the differences from the mean are:
60 – 81 = -21
60 – 81 = -21
70 – 81 = -11
80 – 81 = -1
80 – 81 = -1
80 – 81 = -1
90 – 81 = 9
90 – 81 = 9
100 - 81 = 19
100 - 81 = 19
Notice that values that are below the mean have negative discrepancies and values above it have positive ones. Next, we square each discrepancy and then we :
-21 X -21 = 441
-21 X -21 = 441
-11 X -11 = 121
-1 X -1 = 1
-1 X -1 = 1
-1 X -1 = 1
9 X 9 = 81
9 X 9 = 81
19 X 19 = 361
19 X 19 = 361
Now, we take these "squares" and sum them to get the Sum of Squares (SS) value. Here, the sum is 1890. Next, we divide this sum by the number of scores minus 1. Here, the result is 1890 /9 = 210. This value is known as the variance. To get the standard deviation, we take the square root of the variance (remember that we squared the deviations earlier). The standard deviation is 14,49. Although this computation may seem convoluted, it's actually quite simple. To see this, consider the formula for the standard deviation:
In the top part of the ratio, the numerator, we see that each score has the the mean subtracted from it, the difference is squared, and the squares are summed. In the bottom part, we take the number of scores minus 1. The ratio is the variance and the square root is the standard deviation.
After we analysis the data by descriptive statistics, we can take a conclusion, for example: student who get score under mean value have problem in study mathematics, etc.
D. References
http ://en.wikipedia.org/wiki/Descriptive_statistics
http://www.socialresearchmethods.net/kb/statdesc.php
Tidak ada komentar:
Posting Komentar