A library search of counseling psychology literature yielded a journal article by Lannin et al. (2015), in which the authors investigated the usefulness of their Internalized Stigma Model. The purpose was to determine whether stigma of mental illness and/or stigma of needing psychological help affected the individual’s self-esteem, and whether either stigma was associated with the person’s decision to look for counseling. In addition, their model predicted that there was a strong interaction between external stigma and internalized stigma — the effects of external stigma were mediated by the level of internalized stigma, which predicted self-esteem and willingness to seek counseling (Lannin et al., 2015).
The first statistical concept that is important in this study is the idea of the mean and the standard deviation, along with their interrelationships. The mean and standard deviation are fundamental to the study of statistics. The mean is a measure of the central tendency of a given statistic, while the standard deviation is a measure of the variability of the statistic (MCREL, 2004). These measures should not, strictly speaking, be used with the data in this study, because it is ordinal level data. The median and the mode would be more appropriate, with the interquartile range, perhaps, as the measure of variability. However, there is a strong tradition of using mean and standard deviation with ordinal data, especially in the case of standardized scales such as the intelligence quotient (IQ). Therefore, these statistics were reported for all eight scales, separated by gender (Lannin et al., 2015).
The second statistical concept in this study is that of correlation. When two variables move together, they are said to be correlated. If they move in the same direction, they are positively correlated; if they move in opposite directions, they are negatively correlated. The value of a correlation statistic (such as Pearson’s r) ranges from -1 to +1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation. It is essential to recognize that correlation does not imply causation. One could correlate the divorce rate in Maine with per capita consumption of margarine and get a high correlation (r=0.9926), but it is silly to think that divorces cause people to eat more margarine (Vigen, n.d.).
In this study correlation coefficients were calculated for the eight measures, separated by gender. Some of the correlations were quite large; for example, the relationship between self-esteem and distress was inversely correlated for both men (-0.73) and women (-0.80). However, in some cases even a high correlation can be obtained by chance (MCREL, 2004). In order to deal with this possibility, it is crucial to understand the third concept — statistical significance.
The concept of statistical significance is based on how likely it is that a given value of a statistic occurred by chance. Determination of the probability is required to answer this question, and probability is based on the underlying distribution of values. The most commonly used distribution is the normal curve (MCREL, 2004). If a study meets the criteria, investigators can use the normal curve to determine exactly how likely it is that a given value would occur. But not all data fall on a normal curve, so some studies use the t-distribution, the Χ-square distribution, or others that have different shapes. They can be used just like the normal curve. In most studies, researchers choose an alpha level, which is a probability limit that will indicate to them that their data are statistically significant. For example, a common alpha is 0.05, which means that only 5% of the time could a person get a particular value by chance. If the probability is less than alpha, it is unlikely to be a chance result (MCREL, 2004).
The statistical concepts described here are basic ideas that are suitable for counseling research and program evaluation (with the caveat concerning ordinal data). It is imperative, of course, to select the appropriate distribution when testing a hypothesis. The Χ-square distribution is commonly used with ordinal data. When discussing correlations, it is important to remember that the type discussed here are zero-order correlations. That is, no variables are controlled, which produces a simplified and potentially spurious relationship. Using control variables can help to ensure that an appropriately diverse population is represented in the outcomes.