## Research Design and Hypothesis Testing

Identifying the Research Design

Nominal, Ordinal, Interval, and Ratio Data

Another example of ordinal data used in Audiology is the Likert scale used to assess a listener's loudness growth. Here, a stimulus is presented to the listener, who is then asked to rate perceptual loudness by providing a number associated with a descriptor (e.g., 1 = too soft, 2 = soft, 3 = comfortable, 4 = loud, 5 = too loud). The data are nominal because there are greater than/less than distinctions, with no evidence revealing by how much the distinctions differ. Findings from a loudness growth task imply that increases in amplitude cause a change in perceptual loudness for that listener. Therefore, ordinal data are coded using text values, or discrete values.

For the interval scale, however, the zero point is arbitrary. That is, the starting and ending points of the scale are not absolute values, but rather, relative values. Because the values used are relative, the responses described by the data indicate only the magnitude of the relationship between the variables. For instance, 60° F is hotter than 30° F. It is inappropriate to say, however, that 60° F is twice as hot as 30° F.

Two examples of instruments in Audiology created with an interval scale are the APHAB and the speech intelligibility rating (SIR) test (Cox & McDaniel, 1989). The APHAB is a 24-item self-assessment inventory in which patients report the amount of problems they are having with communication or aversiveness to loud sounds in various everyday listening situations. Patients who complete the APHAB rate their everyday listening experiences using a Likert scale, with each descriptor having a percentage (A = always [99%], G = never [1%]).

For the SIR test, subjects listen to a short passage of connected speech presented against noise through a hearing aid. While listening to the speech signal, the subject's task is to generate a perceptual rating of intelligibility using an interval scale ranging between 0 and 10. The 0 value on the scale indicates that connected speech was completely unintelligible and the 10 indicates that connected speech was fully intelligible. The scale assumes that each value, between 0 and 10, is equally spaced, with no true zero.

The decibel (dB) is an example of a unit measured on the ratio scale. The decibel increases in equal intervals in a logarithmic manner and the ratio is always compared with its reference point (i.e., 10−12 watts/m2, 20 μPa). With respect to ratio, an increase of 3 dB results in twice the power (in dB IL) and an increase of 6 dB results in twice the pressure (in dB SPL).

**Nominal Data.**Data classified as nominal are categorized using text values (i.e., discrete), with no implied order among the categories. For example, a survey may have two check boxes side-by-side, with male first followed by female. This order does not imply that males are better than females. In fact, by changing the order, information is neither lost nor gained. In other words, nominal data are existential—it either exists or fails to exist. Assume, for example, that the student or clinician is interested in gathering information about hearing aid use. Here, the student or clinician might have two check boxes, one for those who have previously worn hearing aids and another for those who have never worn devices. A respondent who selects the second check box indicates no experience with amplification, nullifying the first option (i.e., experience with hearing aids).**Ordinal Data.**Data classified as ordinal indicates a greater than/less than relationship, but the data does not provide information about the relative difference between each data category. Letter grades (A, B, C, D, and F) assigned to students for their academic performance is an example of ordinal data. The grade of A is better than the grade of B, B is better than a C, and so on. Now, assume that Lisa earned an A and Jill earned a B in the same course. The data indicates that Lisa performed better than Jill, but it is not known by how much (i.e., was it by 6% or 2% points?).Another example of ordinal data used in Audiology is the Likert scale used to assess a listener's loudness growth. Here, a stimulus is presented to the listener, who is then asked to rate perceptual loudness by providing a number associated with a descriptor (e.g., 1 = too soft, 2 = soft, 3 = comfortable, 4 = loud, 5 = too loud). The data are nominal because there are greater than/less than distinctions, with no evidence revealing by how much the distinctions differ. Findings from a loudness growth task imply that increases in amplitude cause a change in perceptual loudness for that listener. Therefore, ordinal data are coded using text values, or discrete values.

**Interval Data.**The interval scale provides an improvement over the nominal and ordinal scales, where values are ordered as a constant (i.e., continuous) scale, allowing for the comparison of differences between points. For example, the Fahrenheit scale of temperature has a freezing point of 32° and a boiling point of 212°. The difference is 180°, which is spaced in equal intervals. Therefore, the difference between 20° and 40° F is equal to the difference between 75° and 95° F.For the interval scale, however, the zero point is arbitrary. That is, the starting and ending points of the scale are not absolute values, but rather, relative values. Because the values used are relative, the responses described by the data indicate only the magnitude of the relationship between the variables. For instance, 60° F is hotter than 30° F. It is inappropriate to say, however, that 60° F is twice as hot as 30° F.

Two examples of instruments in Audiology created with an interval scale are the APHAB and the speech intelligibility rating (SIR) test (Cox & McDaniel, 1989). The APHAB is a 24-item self-assessment inventory in which patients report the amount of problems they are having with communication or aversiveness to loud sounds in various everyday listening situations. Patients who complete the APHAB rate their everyday listening experiences using a Likert scale, with each descriptor having a percentage (A = always [99%], G = never [1%]).

For the SIR test, subjects listen to a short passage of connected speech presented against noise through a hearing aid. While listening to the speech signal, the subject's task is to generate a perceptual rating of intelligibility using an interval scale ranging between 0 and 10. The 0 value on the scale indicates that connected speech was completely unintelligible and the 10 indicates that connected speech was fully intelligible. The scale assumes that each value, between 0 and 10, is equally spaced, with no true zero.

**Ratio Data.**The ratio scale has all the properties of the nominal, ordinal, and interval scales. In addition, the zero point of this scale has a fixed starting point. As a result, the difference between the intervals is always measured from a zero, or reference, point. As an example, consider the concept of time. The difference between 3:00 and 5:00 is the same as the difference between 8:00 and 10:00. With respect to ratio comparison, 10 hours is twice as long as 5 hours.The decibel (dB) is an example of a unit measured on the ratio scale. The decibel increases in equal intervals in a logarithmic manner and the ratio is always compared with its reference point (i.e., 10−12 watts/m2, 20 μPa). With respect to ratio, an increase of 3 dB results in twice the power (in dB IL) and an increase of 6 dB results in twice the pressure (in dB SPL).

Hypothesis Testing