The Beginner’s Guide to Statistical Analysis

Statistical analysis uses quantitative data and explores trends, patterns, and relationships. Thus, it is an indispensable instrument for researchers, states, firms, and many others. This article offers introductory knowledge on statistical analysis for students and researchers. After discussing descriptive and inferential statistics, it covers various research designs.

19.06.2022

The Beginner’s Guide to Statistical Analysis

Statistical analysis uses quantitative data and explores trends, patterns, and relationships. It is an indispensable instrument because researchers, states, firms, and many other organizations must resort to it. What we need is to use quantitative data.

When you start the research process, you must do careful planning involving statistics. Otherwise, your conclusions may be invalid and futile. Thus, begin the process by specifying your hypotheses, deciding your experimental design, and meticulously choosing your sample size and sampling procedure.

You need to collect data from your sample. Then, you can use descriptive statistics to organize and summarize your data. What follows is to make inferences. Therefore, using sample statistics, you must employ inferential statistics to test research hypotheses and estimate population parameters. Only then can you interpret and generalize your results.

This article offers introductory knowledge on statistical analysis for students and researchers. Then, we will make it easy for you by giving two study questions. The first will address the cause-and-effect relationship. In contrast, the second explores the possible correlation between variables. 

Question 1) Can practice reduce exam stress on students? It is a causal question. It aims to gather whether practice helps reduce exam anxiety or not.

Question 2) Is there a relationship between wealth and recovery from COVID-19? It is a correlational research question. It does not imply causality. Now, we may move to the first step of statistical analysis.

1. How can you write your hypotheses and plan your research design?

Lay out your research hypotheses and design your experiment. Then, you can gather valid data for statistical analysis.

2. How can I write statistical hypotheses?

The research usually aims to explore a relationship between variables for a given population. All you need is, to begin with, a prediction and resort to statistical analysis to check its validity.

You may formally build a statistical hypothesis to estimate a prediction about a population. For every research, two hypotheses are a must: Null and alternative hypotheses. You need sample data when deciding which one is valid.

The null hypothesis suggests no effect or relationship between variables. On the contrary, the alternative or research hypothesis implies an effect or relationship.

Shall we give an example? It is a statistical hypothesis to test a treatment effect (cause and effect). Here it goes.

Null hypothesis: Two percent salt will not change the flavor of crackers.

Alternative hypothesis: Two percent salt will enhance the flavor of crackers. 

Here is another example to test a correlation

Null hypothesis: Income level and life insurance premium are not correlated.

Alternative hypothesis: Income level and life insurance premium are correlated.

3. How to plan your research design?

What do we mean by research design? In a nutshell, research design reflects our wholesome strategy exclusively used for collecting and analyzing data. It also allows you to decide on the tests to check your hypotheses.

The first step includes deciding what design you will use in your study. Your research may involve descriptive, correlational, or experimental design. You may experience the treatment effect directly in experiments, while descriptive and correlational design only deals with measuring variables of interest.

a. Experimental design 

Experimental design covers a cause-and-effect relationship (the effect of salt on the flavor of crackers). You may use any statistical comparison test (t-test, ANOVA, etc.) or regression to test the treatment effect.

b. Correlational design 

Correlational design merely explores relationships between variables (e.g., income level and life insurance premium), assuming no causality, and employs correlation coefficients and significance tests.

c. Descriptive design

Descriptive research design is a research design that systematically describes a phenomenon, situation, or population to get information. It specifically addresses the what, when, where, and how questions concerning the research problem instead of the why. Then, the next critical thing is to comprehend the level of comparison. Your design may involve group or individual level comparison. However, some designs may require both.

When the participants are subjected to varied treatments, what you have is the between-subjects design where you can make comparisons.

Should you make repeated measures on the participants irrespective of treatment, then what you have is radically different: the within-subjects design.

d. Mixed (factorial) design

mixed (factorial) design involves one variable, changed between subjects and another within-subjects (e.g., pretreatment and posttreatment cholesterol levels from participants who received cholesterol drug or not).

4. What are dependent and independent variables?

The next crucial thing is to define variables. In an experiment, we have independent and dependent variables. What we measure is the independent variable or response variable. The variable affecting the independent variable is the dependent variable. Suppose you have used three different drugs to reduce patients' cholesterol levels. Then, the cholesterol level is the dependent variable (y), and the drugs are the independent variable (x).

5. How can you measure variables?

You will decide on how to operationalize and measure the variables. In any statistical analysis, the most critical point is to determine the level of measurement of your variables as it tells you the data type it comprises:

  • Categorical data mean groups. They may be nominal (e.g., color) or ordinal (e.g., rank).

They may fall on an interval scale (e.g., IQ score) or a ratio scale (e.g., height).

  • Quantitative data implies amounts.

We can measure variables at varying levels of accuracy. For instance, age data can be quantified, such as 11 years old, or it may belong to a category (young or old). However, the data may have a numeric code (level of satisfaction from 1 to 5), but it does not assure that it is quantitative, not categorical.

After specifying the measurement level, we must select proper statistics and hypothesis tests. An excellent comparison involves the arithmetic mean, which is relevant for quantitative data but not categorical. 

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