Importance of Normal Distribution Curve and Its Applications in Psychology - Essay Example

Importance of Normal Distribution Curve and Its Applications in Psychology In making statistical inferences on a population using a sample, statisticians make reasonable assumptions on how data or variable values may be distributed in a population. There are several possibilities or assumptions that a statistician can make on how variable values or data may be distributed in a population. One such possible distribution or distribution pattern is the normal distribution. A normal distribution of variable values or data is a reasonable assumption on how data or variable values may be distributed in a population.

In the normal distribution, the frequency count is distributed symmetrically to the left and right sides of the mean. In addition, the mean, median and mode coincide such that what we have when the variable values are distributed along the x-axis and the frequency count is along the y-axis in a graph is a bell-shaped curve known as the normal distribution. Such a bell-shaped curve is illustrated in Gravetter and Wallnau (47), particularly in Figure 2.8. Z-scores were devised to standardize a normal distribution (Gravetter and Wallnau, 74).

To convert a variable value into a z-score, its distance from the mean has to be computed and divided by the standard deviation. This is described in Gravetter and Walnau (128). From Gravetter and Walnau (128), to get the z-score of a variable value, one must use the following operation: Z = (X - µ)/. This is a transformation process in which “the original population mean is transformed into a value of zero in the z-score distribution.” Thus, the mean or µ of z-scores is zero (Gravetter and Walnau, 129).

In addition, “the distribution of z-scores will always have a standard deviation of 1” (Gravetter and Walnau, 129). The z-scores combined with the standard normal curve are associated with probabilities. For example, based on Gravetter and Walnau (152), the area under the standard normal curve from z = 0 to z = +1 has an area of 0.3413 and is associated with a probability of 34.13%. Based also on Gravetter and Walnau (152), the area under the standard normal curve from z=0 to z=2 is 0.3413 plus 0.

1359 or equal to 0.4772. In turn, the area 0.4772 under the normal curve from z=0 to z=2 is associated with a probability of 47.72%. Consistent with the foregoing, the probability associated from z = -1 up to z = +1 is 34.13% plus 34.13% or 68.26%. Further, the probability associated with z = -2 up to z = +2 is 47.72% plus 47.72% or 95.44%. Some of the z-scores that are very important for inferential statistics are z = 1.96 and z = 2.57. Based on the statistical table for the standard normal distribution in Gravetter and Walnau (586-587), the probability associated with z < 1.96 is 97.5%.

The probability associated with z > 1.96 is 2.5%. The probability associated with z < -1.96 is also 2.5%. Based also on the statistical table in Gravetter and Walnau (586-587), the probability associated with z > 2.58 is less than 0.5%. The probability associated with z < -2.58 is also less than 0.5%. Based also on the statistical table in Gravetter and Walanu (586-587), the probability associated with z > +2.33 is less than 1%. This is also the probability associated with z < -2.33. In inferential statistics, 2 sets of hypothesis are formulated: the null and alternative hypothesis.

Conventionally, for the null hypothesis to be rejected, the probability for the null hypothesis must be adequately low. Otherwise, one will have no statistical basis to reject the null hypothesis that will give him or her conventionally acceptable justification to accept the alternative hypothesis. If one is not conventionally justified to reject the null hypothesis, one has to conventionally accept that he or she is unable to reject the null hypothesis; alternatively, he or she may accept the null hypothesis as true.

If he or she is not inclined to declare that the null hypothesis can be accepted as true, he or she can simply state that he or she is unable to reject the null hypothesis. In a psychology study, one application of the normal distribution for inferential statistics is in the study of Walker and others. In studying the effect of asthma management beliefs and behaviors, the study of Walker and colleagues found that the relationship between asthma management beliefs and behaviors is statistically significant at the .

05 level based on the z-statistics (385). The study of Chen and colleagues, on the other hand, found via z-statistics that there is a role between the social environment and children/adolescents asthma symptoms based on the z-statistics (644). According to Chen and colleagues, the z-statistics are significant at the 0.05 level (644). In studying depression anxiety, the study of Henry and colleagues also used z-statistics (231). The studies cited are studies in psychology or studies in medicine in which psychology was useful in understanding deeper a medical problem.

Based on the foregoing, we have adequate basis to say that the normal distribution is widely used in psychology studies. Work Cited Chen, Edith, Louise Chim, Robert Strunk, and Gregory Miller. “The role of social environment in children and adolescents with asthma.” American Journal of Respiratory and Critical Care 176 (2007): 644-649. Web. 7 September 2011. < http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1994239/>. Gravetter, Frederick and Wallnau, Larry. Essentials of Statistics for the Behavioral Sciences. 7th ed. Australia and the United States: Wadsworth Cengage Learning, 2011.

Henry, Juliet and John Crawford. “The short-form version of the Depression Anxiety Stress Anxiety Scales (DASS-21): Construct validity and normative data in a large non-clinical sample.” British Journal of Clinical Psychology 44 (2005): 227-239. Web. 7 September 2011. . Walker, Hope, Louise Chim and Edith Chen. “The role of asthma management beliefs and asthma immune and clinical outcomes.” Journal of Psychiatric Psychology 34.4 (2009): 379-388. Web. 7 September 2011. .