Vocabulary List

• Descriptive: Providing details or characteristics about something. 
  
• Median: The middle value in a set of data arranged in numerical order.
  
• Skewed: Uneven or asymmetrical distribution of data. 
  
• Coefficient: A number or factor in an equation that represents the relationship between variables.
  
• Incidence: The rate of occurrence or new cases of a particular event, such as a disease, within a population over a specified period of time. 
  
• Scatterplots: Graphical representations of data points on a two-dimensional plane, where each point represents the values of two variables. In public health, scatterplots are used to visualize relationships between variables, such as the correlation between smoking and lung cancer rates.
  
• Regression: A statistical technique used to analyze the relationship between one dependent variable and one or more independent variables.
  
• Histogram: A type of bar graph that displays the distribution of data by dividing it into intervals, or bins, and showing the frequency of values within each interval.

4.1 Introduction

(Brigham Young University-Idaho, Pryor, 2024)

The Results section is one of the most important parts of your research paper. In this section you will report your important findings using words, tables, and figures. The Results section should start with your participants. Explain any demographics and if any participants were excluded from the study and why. You should also restate your research question, what you found, including explanations, and then summarize your findings.

4.2 Results Section Tips

(Brigham Young University-Idaho, Pryor, 2024)

• Start with a brief description of your population and why you excluded any participants.

• What was the mean age?

• What percentage was male and female?

• Discuss ethnicity if it is relevant.

• What specific question are you trying to answer? (state it clearly)

• Include tables or figures that support what you found. For example, if my question is "Do males drink more energy drinks than females?" I want to include a specific table or graph that shows, on average, how many energy drinks males drink compared to females.

• Mention any figures or tables in your writing as follows:

• “These results are displayed in Figure 1.”

• “These results are shown in Table 1.”

• Provide a brief explanation of what you found.

• For example, “The average per day energy drink consumption for males was 2.9, and the average per day energy drink consumption for females was 1.3.”

• Do not interpret the results in this section; save that for the Discussion.

• Avoid phrases like “This means that…” or “This shows that…”

4.3 Descriptive Statistics

(Brigham Young University-Idaho, Pryor, 2024)

The most common ways to describe the results of your research are the central tendency and variability. These can be calculated in Excel.

Central tendency describes a typical data point using one of the following methods:

• Mean: The total sum of all numbers in the data set divided by the total number of data points. This is usually called the average and is the most common form of central tendency.

• Median: The middle value of a data set. It is useful to describe data sets that are skewed or have extreme values.

• Mode: The most commonly occurring value in the data set. It is often used to indicate the most frequent response, especially if the data is not numeric. 

Variability refers to the dispersion of the data from the central point.

• Range: The difference between the lowest value and the highest value. It shows how far apart the most extreme values are.

• Standard Deviation: The average distance that individual data points are from the mean. 

4.4 Correlation Coefficient

(Brigham Young University-Idaho, Pryor, 2024)

A correlation coefficient is a number that tells how two variables are related and how strong the relationship is. The most common way to calculate it is with Pearson r, which is possible within Excel. The calculation gives a number between -1 and 1.

How to interpret the Pearson r correlation coefficient:

Example: If we want to know if malaria risk increases with age, we can look at data showing both malaria incidence and age, and calculate the correlation coefficient for those two variables. 

• If Pearson r = 0.9 then there is a strong positive association of age with malaria incidence, meaning as age increases, risk of malaria increases.
• If Pearson r = -0.9 then there is a strong negative association of age with malaria incidence, meaning as age increases, risk of malaria decreases.
• If Pearson r = 0.1 then there is a weak association of age with malaria incidence, meaning as age increases, risk of malaria increases only slightly.
• If Pearson r = 0 then there is no association of age with malaria incidence, meaning age is not related to risk of malaria.

4.5 How to Find the Pertinent Information in Your Data

After collecting your data, the values need to be organized and listed in columns and rows on a spreadsheet. If the data is saved in comma delimited (.csv) form, the data set can be used in Excel and many other statistical applications. 

4.5.1 How to Clean Your Data Set

(Brigham Young University-Idaho, 2024)

Since you will be using Google Forms to construct your data, this section will show you how to download and clean your data set using Google Forms.

1. After your survey is complete, you will be able to see the number of responses that you have received. 

2. Select the Responses tab to see a visual of your responses. 

3. You will need to select the Link to Sheets button on the right to open up your data in Google Sheets. It will ask you if you want to create a new spreadsheet or select existing spreadsheet. Choose Create a new spreadsheet and the select Create.

4. Your data will look something like the following:

5. Next, you will need to find any rows where participants may not have answered all the questions. If there are rows where there are many blank answers, delete those rows.

6. You will have to assign your data numerical values in order for you to perform a statistical analysis. For example, Males can equal one and Females can equal two. You can replace these values in your spreadsheet by selecting Edit, Find and Replace. Type in Male in the Find box and 1 in the Replace box. Also select the box that says Match entire cell contents. Then select Replace All. Continue doing this until you have replaced all of your data with numbers.

7. Your dataset should look like the following when you are done:

Make sure that you write down what your numbers mean before you make any changes.

8. You are now ready to use this data with the Stats Toolbox.

4.6 Expressing Your Results

(Price et al., 2017)

Once you have conducted your descriptive statistical analyses, you will need to present them to others in writing, in graphs, and in tables.

4.6.1 Presenting Descriptive Statistics in Writing

APA style has guidelines for writing numbers.

• One to nine: Spell out the word, unless it is a statistic.
• Numbers 10 and higher: Use numerals.
• If the number is a statistical result: Use numerals and round to two decimal places. Below are some examples:
  • The mean age of the participants was 22.43 years with a standard deviation of 2.34.
  • The participants with a positive mood were more compliant with medications (M = 4.05, SD = 2.32) than those in a negative mood (M = 2.15, SD = 2.27).
  • The treatment group had a mean of 23.40 (SD = 9.33), while the control group had a mean of 20.87 (SD = 8.45).

Notice that in the narrative, the terms mean and standard deviation are written out, but within parentheses the abbreviations M and SD are used instead. 

4.6.2 Presenting Descriptive Statistics in Graphs

A large number of results can be reported more clearly and efficiently with a graph. General APA style guidelines for graphs:

• First, the graph should always add important information rather than repeat information that already appears in the text or in a table. If the graph presents information more clearly, then keep the graph and eliminate the text or table. 
• Second, graphs should be as simple as possible, usually without color.
• Third, a graph should be understandable with its caption and should not have to refer to the text for an explanation.
• Layout
• The graph should be slightly wider than it is tall.
• The independent variable should be plotted on the x-axis and the dependent variable on the y-axis.
• Values should increase from left to right on the x-axis and from bottom to top on the y-axis.
• Axis Labels and Legends
  • Axis labels should be clear and concise and include the units of measurement if they do not appear in the caption.
  • Axis labels should be parallel to the axis.
  • Legends should appear within the boundaries of the graph.
  • Text should be in the same simple font throughout and differ by no more than four points.
• Captions should briefly describe the figure, explain any abbreviations, and include the units of measurement if they do not appear in the axis labels.

4.6.3 Bar Graphs

Bar graphs are used to present the mean scores for two or more groups. The bar graph in Figure 12.11 conforms to all the guidelines listed. The smaller vertical bars that extend both upward and downward from the top of each main bar are error bars. They represent the variability in each group. A bar graph with error bars shows whether a difference is statistically significant.

Figure 12.11 Sample APA-Style Bar Graph, With Error Bars

4.6.4 Line Graphs

Line graphs are used when the independent variable is measured in a more continuous manner (such as time) or when the independent variable has a relatively small number of distinct levels. Each point in a line graph represents the mean score on the dependent variable for participants at one level of the independent variable. Figure 12.12 includes error bars representing the standard error.

Figure 12.12 Sample APA-Style Line Graph

4.6.5 Scatterplots

Scatterplots are used to present correlations between quantitative variables when the independent variable on the x-axis has a large number of levels. Each point in a scatterplot represents an individual and there are no lines connecting the points. The straight dotted line that best fits the points in the scatterplot is called the regression line.

Figure 12.13 Sample APA-Style Scatterplot

4.6.6 Expressing Descriptive Statistics in Tables

Like graphs, tables can be used to present large amounts of information clearly and efficiently. The same general principles apply to tables as apply to graphs. They should add important information to the presentation of your results, be as simple as possible, and be understandable on their own. 

One common use of tables is to present several means and standard deviations for complex research designs with multiple independent and dependent variables. 

Another common use of tables is to present correlations, measured by Pearson’s r. The following is an example of their use:

Researchers in San Diego, California studied the relationship of social determinants of health to COVID-19 case rates during different pandemic stages (Embury et.al., 2022). Table 1 below is an excerpt of the Pearson r values found. The table shows that education below ninth grade had a strong positive correlation to COVID-19 (r = 0.71), while a bachelor’s degree or higher had a medium negative correlation (r = -0.53). Low household income had a medium positive correlation to COVID-19 (r = 0.56), and a high household income had a medium negative correlation (r = -0.40). (Embury et al., 2022)

Table 1

Pearson Correlation Coefficients Between Social Determinants of Health and COVID-19

4.7 Using the Statistics Tool

(Brigham Young University-Idaho, Pryor, 2024)

For this course, you will be using an Excel statistics tool called the Statistics Toolbox. There are many statistical tests that you can use with this tool, but we will only be using a few of them.

4.7.1 Descriptive Stats

The first tab in the tool is called Descriptive Stats. This tab will let you calculate sample size, mean, standard deviation, and variance for a single variable. You would use this tab to calculate the mean age of your sample, as well as means of other variables you are measuring (such as mean sleep time). Paste your data in the left hand column and the tool will calculate the mean and sample size for you.

Example:

This is an example of 20 data points (age). The important tables and figures that you could use in this example are the Quantitative Summaries Table and the Histogram.

4.7.2 Two Sample T-Test

The next test you could run on your data is a Two Sample T-Test. This test will tell you if your data is statistically different between two groups. For example, if you had two groups, male and female, and you wanted to know if their test scores were statistically different between the groups you would use this test. You would paste the data for males in one column and paste the data for females in another column.

Example:

This is a sample of 12 different test scores from males and females. The male test scores are on the left and the female test scores are on the right.

The Statistics box is used if you have already calculated the sample size, mean and standard deviation for each variable. In this case, you would ignore this box. If you examine the Summary of Data table, you will notice that the mean for Data 1 (males) is 57.956 and the mean for Data 2 (females) is 64.9. Next, if you examine the table Hypothesis Test you will see that the P-value is 0.000, which is less than 0.05. This means that our two samples are statistically significantly different: Females scored higher on the test than males. Another useful figure that you could include in your paper is the Comparison of Data 1 and Data 2. This figure shows graphically the difference between the data (males are red, females are blue).

Tip: You can change the labels of the data to make it easier for you. Simply select the Data 1 and Data 2 boxes where they appear in the sheet (there are three separate places) and change the names. Below is how the charts looks after the change.

4.7.3 ANOVA

Another way you can compare data is with an ANOVA (Analysis of Variance) test. You would use this test if you are comparing 3–6 variables. For example, you have five different age groups (19–22, 23–26, 27–30, 31–34, 35–40). You want to know if there is a difference in the number of hours slept each night between the groups. (Note: I changed the labels of the Data to reflect the age groups.)

In the Summary of Data Table you will notice the Sample Means of each age group. Age group 35–40 has the highest mean (7.750) and age group 23–26 has the lowest mean (5.000). In the table labeled Hypothesis Test the P-value is 0.000. This means that there are significant differences between the groups. Unfortunately, you cannot tell from this test which groups are different, but you could compare each pair of age groups using a two-sample t-test.

This figure can also be useful in your paper because it shows a plot of the means of each group.

4.7.4 Correlation

A Correlation tells you if two variables are linearly related (meaning that they change together at a constant rate). Correlations are described using a correlation coefficient (r) which ranges from -1 to +1. The closer that r is to zero, the weaker the correlation. Positive r values indicate a positive correlation (both values tend to increase together). Negative r values indicate a negative correlation (one variable tends to increase, while the other decreases). See Correlation Coefficient above for more information.)

To run a Correlation in the Statistics Toolbox, select the Correlation Tab. Copy the data that you want to compare in the columns labeled Data 1 and Data 2. The Correlation will automatically be calculated for you. In the example below, the correlation coefficient (r) is 0.796, indicating a strong correlation between the two variables. The p-value is 0.001, which is statistically significant. You will also be provided with a scatterplot with a line of best fit. As the values in x (Data 1) increased, so did the values in y (Data 2).

NOTE: All content is licensed CC-BY-NC unless otherwise noted. This courseware includes resources from multiple individuals and organizations. See the “References” section at the bottom of each page for copyright and licensing information specific to the material on that page. If you believe that this courseware violates your copyright, please contact us.

References

Embury, J., Tsou, M.-H., Nara, A., & Oren, E. (2022). A Spatio-Demographic Perspective on the Role of Social Determinants of Health and Chronic Disease in Determining a Population’s Vulnerability to COVID-19. https://www.cdc.gov/pcd/issues/2022/21_0414.htm

            License: CC-Public Domain

Price, P. C., Jhangiani, R., Chiang, I.-C. A., Leighton, D. C., & Cuttler, C. (2017). Research Methods in Psychology. Pressbooks. https://opentext.wsu.edu/carriecuttler/chapter/11-2-writing-a-research-report-in-american-psychological-association-apa-style/

            License: CC-BY-NC-SA