Quantitative Data Analysis PDF

Quantitative Data Analysis Descriptive Statistics | Inferential Statistics What is Quantitative Data Analysis? Simply, analyzing data that is NUMBERS-BASED. Data that can be converted into number without losing its meaning. Gender, Ethnicity, Native Language (Categorical variables) Quant...

Quantitative Data Analysis Descriptive Statistics | Inferential Statistics What is Quantitative Data Analysis? Simply, analyzing data that is NUMBERS-BASED. Data that can be converted into number without losing its meaning. Gender, Ethnicity, Native Language (Categorical variables) Quantitative analysis is generally used for three purposes. 1. Firstly, it’s used to measure differences between groups. For example, the popularity of different clothing colours or brands. 2. Secondly, it’s used to assess relationships between variables. For example, the relationship between weather temperature and voter turnout. 3. And third, it’s used to test hypotheses in a scientifically rigorous way. For example, a hypothesis about the impact of a certain vaccine. How does it work? Statistical analysis methods form the engine that powers quantitative analysis, and these methods can vary from basic calculations (for example, averages and medians) to more sophisticated analyses (for example, correlations and regressions). 2 Branches of Quantitative Analysis DESCRIPTIVE STATISTICS Descriptive statistics serve a simple but critically important role in your research – to describe your data set – hence the name. In other words, they help you understand the details of your sample. Descriptive statistics don’t aim to make inferences or predictions about the entire population – they’re purely interested in the details of your specific sample. What kind of statistics to use? Mean – this is simply the mathematical average of a range of numbers. Median – this is the midpoint in a range of numbers when the numbers are arranged in numerical order. If the data set makes up an odd number, then the median is the number right in the middle of the set. If the data set makes up an even number, then the median is the midpoint between the two middle numbers. Mode – this is simply the most commonly occurring number in the data set. Standard deviation – this metric indicates how dispersed a range of numbers is. In other words, how close all the numbers are to the mean (the average). In cases where most of the numbers are quite close to the average, the standard deviation will be relatively low. Conversely, in cases where the numbers are scattered all over the place, the standard deviation will be relatively high. Skewness. As the name suggests, skewness indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph, or do they skew to the left or right? Example Why do these numbers matter? While these descriptive statistics are all fairly basic, they’re important for a few reasons: 1. Firstly, they help you get both a macro and micro-level view of your data. In other words, they help you understand both the big picture and the finer details. 2. Secondly, they help you spot potential errors in the data – for example, if an average is way higher than you’d expect, or responses to a question are highly varied, this can act as a warning sign that you need to double-check the data. 3. And lastly, these descriptive statistics help inform which inferential statistical techniques you can use, as those techniques depend on the skewness (in other words, the symmetry and normality) of the data. 2 Branches of Quantitative Analysis INFERENTIAL STATISTICS Inferential statistics aim to make inferences about the population. In other words, you’ll use inferential statistics to make predictions about what you’d expect to find in the full population. Two common types of predictions that researchers try to make using inferential stats: 1. Predictions about differences between groups – for example, height differences between children grouped by their favourite meal or gender. 2. Relationships between variables – for example, the relationship between body weight and the number of hours a week a person does yoga.  In other words, inferential statistics (when done correctly), allow you to connect the dots and make predictions about what you expect to see in the real-world population, based on what you observe in your sample data. For this reason, inferential statistics are used for hypothesis testing – in other words, to test hypotheses that predict changes or differences. What Statistics to use? Correlation Tests Correlation tests check whether two variables are related without assuming cause-and-effect relationships. These can be used to test whether two variables you want to use in (for example) a multiple regression test are auto-correlated. Comparison Tests Comparison tests look for differences among group means. They can be used to test the effect of a categorical variable on the mean value of some other characteristic. T-tests are used when comparing the means of precisely two groups (e.g. the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g. the average heights of children, teenagers, and adults). Regression tests Regression tests are used to test cause- and-effect relationships. They look for the effect of one or more continuous variables on another variable. NONPARAMETRIC TEST Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests. How to choose the right statistical method? To choose the right statistical methods, you need to think about two important factors: 1. The type of quantitative data you have (specifically, level of measurement and the shape of the data). And, 2. Your research questions and hypotheses Factor 1: Data Type Factor 2: Research Question The next thing you need to consider is your specific research questions, as well as your hypotheses (if you have some). The nature of your research questions and research hypotheses will heavily influence which statistical methods and techniques you should use. If you’re just interested in understanding the attributes of your sample (as opposed to the entire population), then descriptive statistics are probably all you need. For example, if you just want to assess the means (averages) and medians (centre points) of variables in a group of people. On the other hand, if you aim to understand differences between groups or relationships between variables and to infer or predict outcomes in the population, then you’ll likely need both descriptive statistics and inferential statistics.