Quantitative methods are the use of mathematical analysis or complex mathematical measurement to solve problems or puzzles. These methods generally involve the use of statistical techniques, particularly when analyzing datasets constructed from surveys. Datasets consists of data points generated from cases. Cases can include people, or decisions made by people. Data can be measured differently, using four scales - nominal scales, ordinal scales, interval scales, ratio scales.
Summary of Section 8.2: Making Sense of Data
The initial step is to organize the raw data into a more manageable format. Afterwards, there are various ways that the data can be presented: frequency table, histogram, bar graph, scatterplot, time-series plot. Datasets all have a central tendency, which locates the center of the data, which then allows for an analysis to take place. The mode, median, and the mean can help us determine the central tendency. From this, we can determine the range and interquartile range, the deviation, the variance, and the standard deviation.
Summary of Section 8.3: Introduction to Statistical Inference
Once we have established some elementary statistics, we can then begin to analyze the data. First, we look at the normal distribution of the data. It is often represented through a bell curve. with the exam scores peaking in the middle. If the value of the mean, median, and the mode is the same, and data near the mean are more frequent in occurrence, we can refer to this curve as a normal distribution. Understanding the distribution of the data then allows us to begin comparing. Using a z-score, we can determine if a particular data point falls above or below the mean, and how many standard deviations as well. With these techniques, we can begin developing statistical hypotheses. The two most common are the null hypothesis and the alternative hypothesis. To determine if we can accept or reject the null and/or alternative hypotheses, we have to establish the level of statistical significance we are interested in, or the alpha level. At times we mistakenly reject the null-hypothesis that was true. This type of error is called a type-I error. However, when a researcher fails to reject the null hypothesis that is false, the researcher has committed a type-II error.
Summary of Section 8.4: Interpreting Statistical Tables in Political Science Articles
Political scientists often use regression analyses to understand relationships between variables. These regression results are often represented in table format. In these tables, there are three numerical expressions that every student should understand, regardless of their skill levels. The first is the coefficient, which is a numerical expression of the relationship between the outcome and explanatory variables. The second is the standard error, defined as the estimate of the standard deviation of the coefficient. The third is the confidence level, which communicates the statistical significance of the correlation between the variables. Researchers use asterisks (*) to report the level of significance in the table.
