Descriptive statistics provide general information about the study participants, but they do not test differences between groups or predict outcomes. Inferential statistics are tests that determine if there is a relationship between the independent and the dependent variables. Recall the difference between experimental and nonexperimental studies? Experiments show cause and effect, meaning that a change in the dependent variable was due to the independent variable. Cross-sectional and longitudinal cohort studies demonstrate how related the 2 variables are to each other. Each relationship has its own set of statistical tests. For example, the difference between pre- and posttreatment ROM in physical therapy patients can be evaluated by a t-test or analysis of variance (ANOVA). The relationship between patient pain and the number of treatments they have received can be tested by a Pearson correlation.
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The term statistically significant is used when a relationship is unique or different from expected. In normally distributed data, you know that 68% of the data will fall within one SD of the mean. Ninety-six percent will be found between 2 SDs and 99% within 3 SDs. When the result of a statistical test is found at either end of the normal distribution, it is said to be significant because it is different than what would be found in the middle of the curve. Researchers set a threshold for significance prior to collecting data, called alpha (a). This is the probability that the result was not by chance. The lower the a, the farther away from the mean the result has to be to be significant. An a = 0.01 means that there is a 99% probability that the results are not by chance. If the a = 0.05, there is a 95% probability that the results are not a random accident. The a levels of some Figure 3-7. Two-tailed test allows for chance of significance on each end of the curve. epidemiology studies can be very small (0.001 to 0.00001) because as the number of participants in the study increases, so does the likelihood of finding a significant relationship.
An inferential test can look for significance at one or both ends of the normal curve. These ends are called tails. A 2-tailed test means that half of the a value is placed on each end of the curve (Figure 3-7). A one-tail test takes all of the a and puts it on one side of the curve, giving it a better chance of finding a significant relationship on that particular side. One-tail tests are used when the researcher knows the direction of the relationship between the independent variable and the dependent variable. If you set up an experiment to examine the effect of a single ultrasound treatment on tendon extensibility, it seems obvious that any change in extensibility is going to be positive. You would use a one-tail test in this case. If you had no hypothesis about what would happen, a 2-tailed test would be appropriate.