## Table of Contents

## Introduction

How are statistical research questions for quantitative analysis written? This article provides five examples of statistical research questions that will allow statistical analysis to take place.

In quantitative research projects, writing statistical research questions requires a good understanding and the ability to discern the type of data that you will analyze. This knowledge is elemental in framing research questions that shall guide you in identifying the appropriate statistical test to use in your research.

Thus, before writing your statistical research questions and reading the examples in this article, read first the article that enumerates the four types of measurement scales. Knowing the four types of measurement scales will enable you to appreciate the formulation or structuring of research questions.

Once you feel confident that you can correctly identify the nature of your data, the following examples of statistical research questions will strengthen your understanding. Asking these questions can help you unravel unexpected outcomes or discoveries particularly while doing exploratory data analysis.

## Five Examples of Statistical Research Questions

In writing the statistical research questions, I provide a topic that shows the variables of the study, the study description, and a link to the original scientific article to give you a glimpse of the real-world examples.

### Topic 1: Physical Fitness and Academic Achievement

A study was conducted to determine the relationship between physical fitness and academic achievement. The subjects of the study include school children in urban schools.

#### Statistical Research Question No. 1

*Is there a significant relationship between physical fitness and academic achievement?*

Notice that this study correlated two variables, namely 1) physical fitness, and 2) academic achievement.

To allow statistical analysis to take place, there is a need to define what is physical fitness, as well as academic achievement. The researchers measured physical fitness in terms of *the number of physical fitness tests* that the students passed during their physical education class. It’s simply counting the ‘number of PE tests passed.’

On the other hand, the researchers measured academic achievement in terms of a passing score in Mathematics and English. The variable is the *number of passing scores* in both Mathematics and English.

Both variables are ratio variables.

Given the statistical research question, the appropriate statistical test can be applied to determine the relationship. A Pearson correlation coefficient test will test the significance and degree of the relationship. But the more sophisticated higher level statistical test can be applied if there is a need to correlate with other variables.

In the particular study mentioned, the researchers used *multivariate logistic regression analyses* to assess the probability of passing the tests, controlling for students’ weight status, ethnicity, gender, grade, and socioeconomic status. For the novice researcher, this requires further study of multivariate (or many variables) statistical tests. You may study it on your own.

Most of what I discuss in the statistics articles I wrote came from self-study. It’s easier to understand concepts now as there are a lot of resource materials available online. Videos and ebooks from places like Youtube, Veoh, The Internet Archives, among others, provide free educational materials. Online education will be the norm of the future. I describe this situation in my post about Education 4.0.

The following video sheds light on the frequently used statistical tests and their selection. It is an excellent resource for beginners. Just maintain an open mind to get rid of your dislike for numbers; that is, if you are one of those who have a hard time understanding mathematical concepts. My ebook on statistical tests and their selection provides many examples.

Source: Chomitz et al. (2009)

### Topic 2: Climate Conditions and Consumption of Bottled Water

This study attempted to correlate climate conditions with the decision of people in Ecuador to consume bottled water, including the volume consumed. Specifically, the researchers investigated if the increase in average ambient temperature affects the consumption of bottled water.

#### Statistical Research Question No. 2

*Is there a significant relationship between average temperature and amount of bottled water consumed?*

In this instance, the variables measured include the *average temperature in the areas studied* and the *volume of water consumed*. Temperature is an *interval variable,* while volume is a *ratio variable*.

In this example, the variables include the *average temperature* and *volume of bottled water*. The first variable (average temperature) is an interval variable, and the latter (volume of water) is a ratio variable.

Now, it’s easy to identify the statistical test to analyze the relationship between the two variables. You may refer to my previous post titled Parametric Statistics: Four Widely Used Parametric Tests and When to Use Them. Using the figure supplied in that article, the appropriate test to use is, again, Pearson’s Correlation Coefficient.

Source: Zapata (2021)

### Topic 3: Nursing Home Staff Size and Number of COVID-19 Cases

An investigation sought to determine if the size of nursing home staff and the number of COVID-19 cases are correlated. Specifically, they looked into the number of unique employees working daily, and the outcomes include weekly counts of confirmed COVID-19 cases among residents and staff and weekly COVID-19 deaths among residents.

#### Statistical Research Question No. 3

Is there a significant relationship between the number of unique employees working in skilled nursing homes and the following:

- number of weekly confirmed COVID-19 cases among residents and staff, and
- number of weekly COVID-19 deaths among residents.

Note that this study on COVID-19 looked into three variables, namely 1) number of unique employees working in skilled nursing homes, 2) number of weekly confirmed cases among residents and staff, and 3) number of weekly COVID-19 deaths among residents.

We call the variable *number of unique employees* the **independent variable**, and the other two variables (*number of weekly confirmed cases among residents and staff* and *number of weekly COVID-19 deaths among residents*) as the **dependent variables**.

This correlation study determined if the number of staff members in nursing homes influences the number of COVID-19 cases and deaths. It aims to understand if staffing has got to do with the transmission of the deadly coronavirus. Thus, the study’s outcome could inform policy on staffing in nursing homes during the pandemic.

A simple Pearson test may be used to correlate one variable with another variable. But the study used multiple variables. Hence, they produced regression models that show how multiple variables affect the outcome. Some of the variables in the study may be redundant, meaning, those variables may represent the same attribute of a population. Stepwise multiple regression models take care of those redundancies. Using this statistical test requires further study and experience.

Source: McGarry et al. (2021)

### Topic 4: Surrounding Greenness, Stress, and Memory

Scientific evidence has shown that surrounding greenness has multiple health-related benefits. Health benefits include better cognitive functioning or better intellectual activity such as thinking, reasoning, or remembering things. These findings, however, are not well understood. A study, therefore, analyzed the relationship between surrounding greenness and memory performance, with stress as a mediating variable.

#### Statistical Research Question No. 4

Is there a significant relationship between exposure to and use of natural environments, stress, and memory performance?

As this article is behind a paywall and we cannot see the full article, we can content ourselves with the knowledge that three major variables were explored in this study. These are 1) exposure to and use of natural environments, 2) stress, and 3) memory performance.

Referring to the abstract of this study, *exposure to and use of natural environments* as a variable of the study may be measured in terms of the days spent by the respondent in green surroundings. That will be a ratio variable as we can count it and has an absolute zero point. Stress levels can be measured using standardized instruments like the Perceived Stress Scale. The third variable, i.e., memory performance in terms of short-term, working memory, and overall memory may be measured using a variety of memory assessment tools as described by Murray (2016).

As you become more familiar and well-versed in identifying the variables you would like to investigate in your study, reading studies like this requires reading the method or methodology section. This section will tell you how the researchers measured the variables of their study. Knowing how those variables are quantified can help you design your research and formulate the appropriate statistical research questions.

Source: Lega et al. (2021)

### Topic 5: Income and Happiness

This recent finding is an interesting read and is available online. Just click on the link I provide as the source below.

The study sought to determine if income plays a role in people’s happiness across three age groups: young (18-30 years), middle (31-64 years), and old (65 or older). The literature review suggests that income has a positive effect on an individual’s sense of happiness. That’s because more money increases opportunities to fulfill dreams and buy more goods and services.

Reading the abstract, we can readily identify one of the variables used in the study, i.e., money. It’s easy to count that. But for happiness, that is a largely subjective matter. Happiness varies between individuals. So how did the researcher measured happiness? As previously mentioned, we need to see the methodology portion to find out why.

If you click on the link to the full text of the paper on pages 10 and 11, you will read that the researcher measured happiness using a 10-point scale. The scale was categorized into three namely, 1) unhappy, 2) happy, and 3) very happy.

An investigation was conducted to determine if the size of nursing home staff and the number of COVID-19 cases are correlated. Specifically, they looked into the number of unique employees working daily, and the outcomes include weekly counts of confirmed COVID-19 cases among residents and staff and weekly COVID-19 deaths among residents.

#### Statistical Research Question No. 5

Is there a significant relationship between income and happiness?

Source: Måseide (2021)

Now the statistical test used by the researcher is, honestly, beyond me. I may be able to understand it how to use it but doing so requires further study. Although I have initially did some readings on logit models, ordered logit model and generalized ordered logit model are way beyond my self-study in statistics.

Anyhow, those variables found with asterisk (***, **, and **) on page 24 tell us that there are significant relationships between income and happiness. You just have to look at the probability values and refer to the bottom of the table for the level of significance of those relationships.

I do hope that upon reaching this part of the article, you are now well familiar on how to write statistical research questions. Practice makes perfect.

## References:

Chomitz, V. R., Slining, M. M., McGowan, R. J., Mitchell, S. E., Dawson, G. F., & Hacker, K. A. (2009). Is there a relationship between physical fitness and academic achievement? Positive results from public school children in the northeastern United States. *Journal of School Health*, *79*(1), 30-37.

Lega, C., Gidlow, C., Jones, M., Ellis, N., & Hurst, G. (2021). The relationship between surrounding greenness, stress and memory. *Urban Forestry & Urban Greening*, *59*, 126974.

Måseide, H. (2021). Income and Happiness: Does the relationship vary with age?

McGarry, B. E., Gandhi, A. D., Grabowski, D. C., & Barnett, M. L. (2021). Larger Nursing Home Staff Size Linked To Higher Number Of COVID-19 Cases In 2020: Study examines the relationship between staff size and COVID-19 cases in nursing homes and skilled nursing facilities. Health Affairs, 40(8), 1261-1269.

Zapata, O. (2021). The relationship between climate conditions and consumption of bottled water: A potential link between climate change and plastic pollution. Ecological Economics, 187, 107090.

© P. A. Regoniel 12 October 2021 | Updated 08 January 2024