Setting valid cut-off scores for competency

Reliability and validity are two important considerations that must be made with any type of data collection. Reliability refers to the ability to consistently produce a given result. In the context of psychological research, this would mean that any instruments or tools used to collect data do so in consistent, reproducible ways.

The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height of...

A z score (or standardized value) is measured in units of the standard deviation. It indicates how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
z scores help...

A percentile indicates the relative standing of a data value when data are sorted into numerical order from smallest to largest. It represents the percentages of data values that are less than or equal to the pth percentile. For example, 15% of data values are less than or equal to the 15th percentile. Low percentiles always correspond to lower data values. High percentiles always correspond to higher data values.Percentiles divide ordered data into hundredths. To score in the...

In general, the sign test serves as a nonparametric method to test hypotheses about the median of a single population when the data does not follow a known distribution. This simplicity makes it particularly useful for small sample sizes or when the assumptions of parametric tests cannot be met. The process begins with identifying a null hypothesis, typically stating that the population median equals a specific value. The alternative hypothesis could be that the median is either not equal to,...