Descriptive and inferential statistics are reported in the results section of a scientific article. This section is usually shorter than the other sections but is filled with Greek symbols, initials, tables, and graphs that can be confusing to the reader. Generally, the characteristics of the participants, such as age, weight, or activity level, are reported first using means (M) and SDs (s or SD). This is important information to have when considering to which type of patient (age, activity level, medical history, etc) the results can be applied. The M and SDs for the dependent variables are usually reported after the participant characteristics. Next, the researchers state the results of the inferential tests. Each test has been assigned a letter of the Greek alphabet (Table 3-2). If a test has a statistically significant result, the author will report the value for that test and the p-value (similar to a). For example, the ANOVA finds the value forf A typical significant result would be written as f(1,34) = 2.21, p = .03. The numbers in parentheses are the degrees of freedom. The first is the number of groups minus 1. The second is the number of participants minus 1. The value off was 2.21, which is significant because the p-value is less than .05. Prior to the study, the probability that a result is by chance is symbolized by a. After the study, an actual risk that the result is by chance is calculated, and p is its symbol. If the p-value is less than or equal to a, then the result is statistically significant. The term interaction is also used when discussing a study that has more than one treatment group. For example, if researchers were comparing the effect of static stretching to proprioceptive neuromuscular facilitation stretching, they would expect that ROM would increase in both groups and the posttreatment scores show some difference, but it is not clear if one treatment was really better. The interaction between the treatment group and the change in the dependent variable, in this case ROM from pre- to posttreatment, tells you if the treatment was the cause of the change. The ANOVA test is used to determine if there is a significant group x time interaction. When there is a significant change in the dependent variable and a significant
Without a significant group x time interaction, the researcher cannot say that the treatment worked, even if there are significant improvements in the dependent variable.
Researchers also use tables and graphs to illustrate their data. Result tables contain the means and SDs for the outcome variables within the treatment groups. If the result has an asterisk (*) after it, that means the number is significantly different from another in the table. A key at the bottom of the table will provide the p-value and explain whether the difference was between the groups or a change from pre to post in a dependent variable (Table 3-3).
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Graphs are another way to show relationships between the variables. They help illustrate differences between groups, changes in the dependent variable, and the direction of correlations between variables. Bar graphs are used for comparisons between groups and may contain multiple data points (pre, mid, and post) to show changes over time. The height of the bar represents the mean or the frequency of the measured variable. Some bar graphs include an estimate of the range of the data by adding a symbol that looks like a capital letter I to show the upper and lower limits of the data (Figure 3-8). When reading bar graphs, it is important to note the scale on the vertical (Y) axis. Differences between groups can be made to look larger than they are by decreasing the size of the scale. For example, if pain was the dependent variable and the scale was from 0 to 10, an author could exaggerate the difference between groups by narrowing the scale on the graph to 0 to 7. All statistically significant differences between groups are noted with an asterisk (*). Bar graphs that contain multiple levels of a treatment on the horizontal axis can illustrate dose-gradient and dose-response relationships. A dose-gradient graph shows increasing effects with greater exposures, or doses, of the treatment. For example, more intense exercise is related to greater improvements in oxygen uptake (Figure 3-9). The concept of dose-response is that there is a certain amount of a treatment that is needed to see a change in the dependent variable. This graph will show a step up or down at a particular level of the independent variable. Figure 3-10 illustrates the relationship between different volumes of physical activity and weight loss. While lower levels of physical activity are related to weight loss, there is a clear jump in the effect of physical activity on weight loss at 225 minutes/week.
The line graph is especially useful for showing relationships between 2 variables. These are common in nonexperimental research in which researchers are predicting the impact of risk factors on injury or disease. The direction and shape of the line defines the type of relationship. There are 3 general types of relationships between variables, including positive, negative, and curvilinear. Figure 3-11 shows a positive correlation between hours spent studying and grade point average; as study time increases, so does grade point average. This is also called a linear relationship. In a negative relationship, one variable increases as the other variable decreases. Another term for negative relationship is an inverse relationship, and the line slopes down to the right (Figure 3-12). The last type of relationship seen in line graphs is called curvilinear. Here, the relationship between the variables is more complex. At some points, the data are more strongly related than they are at other points (Figure 3-13). A curvilinear line is another way to illustrate a dose-response.