Statistical Analysis of Research The math behind research

What is Statistics? Statistics is the study of the collection, analysis, interpretation, and organization of data. In other words, it is how we gather, look at, and display the numerical data we gather on the topic we are researching. Statistics, while not glamorous, is key to proper research, as it allows us to be certain of trends in our data. It can be used to both plot and analyze existing data, as well as predict future data (extrapolation).

Two Types of Statistics In psychology, like most other sciences, two different types of statistics are used. The first, descriptive statistics, does what it says: describes data. The second type, inferential statistics, helps scientists make inferences about what the data mean. An inference is a conclusion made based on evidence and reasoning. So, really, they both do what they say in their name.

Important Statistical Terms If you’ve had a math class, you probably know these. Important Statistical Terms

Statistical Terms Mode: The mode is the “measure of central tendency that is the value or score that occurs most frequently in a data set.” In other words, it’s the number that pops up most often in the set. Median: The median is the “measure of central tendency that is the halfway point in a set of data.” When you organize a data set from smallest to greatest number, half the scores fall above the median, half the scores fall above the median, half the scores fall below. With an odd number of data, it will be one of the datum. With an even number, it will be a new number that falls exactly between the two middle data.

Statistical Terms, continued Mean: The mean is “a measure of central tendency that is the arithmetic average of the scores in a set of data.” Also known as the average. You add up then data, then divide by the number of data. Range: The range is “a measure of variability that is the difference between the highest and the lowest scores in a data set”. More simply, it’s a list of all the numbers in a set, from least to greatest.

Standard Deviation In statistics, an important number needed to properly analyze data is called the Standard Deviation. The standard deviation measures the average difference between each score and the mean for that data set. In other words, it measures how closely related the data points are to each other. When applied to a bell curve, 68% of the data should fall within one standard deviation above or below the mean. For example, the average (mean) height of adult males in the U.S. is about 70 inches (5’10”). The standard deviation for this statistic is 3 inches. That means 68% of the adult male population in the U.S. falls between the 67 (5’7”) and 73 (6’1”) range. If a datum falls outside of this 68%, this means that they are more than 1 standard deviation away from the mean.

Correlation Correlation is the degree to which one variable is related to another (co-relation). The two variables are often plotted on a scatterplot, and then measured based on the direction and strength of their relation. They can be positively or negatively related, and strongly or weakly related. If the scatterplot shows no obvious relation, then they have no correlation. A number, often represented by an r, is called a correlation coefficient, will show the relationship between the two points. This number ranges from -1.00 to 1.00. For instance, r=.95 shows a strong positive relationship, and -.4 shows a weak negative one.

Statistical Significance By using correlation scatterplots, we can determine if two variables have statistical significance. This mean it is determined that two variables have a stronger relation than may be expected by chance alone. Although, it’s important to remember that CORRELATION IS NOT CAUSATION