An a priori sample size calculation based on existing recommendations (Cohen, 2013) was carried out to identify an appropriate sample size for the study. The first step in the priori sample size analysis was the identification of inferential procedures, which are an important input into sample sizes (Cohen, 2013). The inferential procedure proposed for this study was the classic linear regression model within ordinary least squares (OLS) regression. In particular, the linear regression model chosen was a mediating model with one independent variable (X), one mediating variable (M), and one dependent variable (Y). Studies designed to measure a mediated effect have their own set of a priori sample size calculation requirements (Fritz & MacKinnon, 2007).
In psychology, one of the most highly cited studies on calculating sample size to detect the mediated effect was that of Fritz and McKinnon (2007). Fritz and McKinnon identified nine common means of calculating sample sizes for studies involving mediated effect, noting that a sample size needed for 0.8 power in such a study varied from 20,886 in Baron and Kenny’s test (Baron & Kenny, 1986) where τ′ was 0 to 462 in a bias-corrected bootstrap test. Because of the impracticability of sampling over 20,000 people, especially in a psychological study, Fritz and McKinnon suggested that the Baron and Kenny test not be used unless there was an existing reason to think that the direct path is large. One of the alternative recommendations was to use Cohen’s (2013) formula for a priori sample size computation:
n = L / f2 + k + 1,
Where sample size is n, the number of predictions in the regression is k, f is an OLS effect size measure, and L is a tabled value computed from the desired power value. In this study, Cohen’s formula was used to identify the appropriate number of participants for an examination of the mediation effect. The following values were specified:
• k = 2 (Y and M)
• L = 7.85 (resulting from a Type I error of 0.05 and a power of 0.8, which, according to Cohen, 2013, are both standard)
• f2 = 0.0196, on the assumption that f = 0.14, a parameter value that Cohen (2013) a small effect size for α
Hence, the number of participants was calculated as follows: n = (7.85 / 0.0196) + 2 + 1 ≈ 404
Therefore, 404 participants will be sought for the study. This sample size was supported by Cohen’s (2013) authoritative work on power analysis for the behavioral sciences, which was also cited by Fritz and MacKinnon (2007) as providing an appropriate a priori sample size calculation for a mediation study. It should be noted that no attempt will be made to stratify the demographic representation of the sample, for example by trying to balance the number of male and female respondents.
There are a number of available means by which the sample can be drawn. Given that the population for the study is large, consisting of those people over 18 capable of giving informed consent to the study, simple random sampling (SRS) will not be an appropriate means of drawing the sample. SRS presumes that every member of a population has an equal chance of being included in a study (Balnaves & Caputi, 2001; Creswell, 2009, 2012). However, given the practical difficulty of designing a form of study recruitment capable of reaching all members of the population equally, SRS will not be viable for this study. In purposive sampling, researchers seek to draw a representative sample by sampling from a sub-population or sub-group that is likely to represent the population (Balnaves & Caputi, 2001). Previous scholars (Ljepava, Orr, Locke, & Ross, 2013) have identified the popular social media site Facebook, which counts one of every seven people on Earth as a member, as an appropriate base from which to conduct purposive sampling, given that Facebook is representative of the global population. Given Facebook’s breadth and ease of use, it will be designated as the source from which purposive sampling activities will be conducted for the study. Facebook participants will be recruited through a paid advertising campaign in which Facebook will be asked to randomly distribute the study recruitment message to English-speaking users over 18 who give America as their location (in other words, the population of the study). This approach will ensure the appropriate use of purposive sampling as a means of recruiting at least 404 participants who are representative of the population.
The study will include four scales to measure the key variables of (a) empathy, (b) individualism/collectivism, (c) attribution styles, and (d) helping behavior. Each of these scales will be discussed below.
Empathy. Empathy will be measured through the use of the Interpersonal Reactivity Index (IRI) (Davis, 1980). The IRI is a 28-item subscale divided into four sub-scales of seven items each. The subscales are as follows: (a) fantasy, (b) perspective-taking items, (c) empathic concern items, and (d) personal distress items. Davis tested the appropriateness of the sub-scales through the use of factor analysis with oblique rotation and found that items tended to weight heavily on single sub-scales and not on others, thus validating the multidimensional approach to empathy. Davis reported Cronbach’s α for the entire scale as being 0.78, with Cronbach’s α scores for the sub-scales ranging from 0.68 to 0.79, and varying somewhat between male and female participants.
In this study, Cronbach’s α for the entire IRI and for the four sub-scales will be calculated and reported. Cronbach’s α will not be reported separately by gender. In addition, principal components analysis (PCA) with Varimax rotation will be employed to determine whether the four factors of (a) fantasy, (b) perspective-taking items, (c) empathic concern items, and (d) personal distress items can be successfully extracted from the IRI scale. The PCA will be validated with the use of both the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy and Bartlett’s test. It is anticipated that a sample of 404 individuals would ensure sampling adequacy for the PCA conducted on the IRI.
Supportive and unsupportive attributional styles. In this study, supportive and unsupportive attributional styles will be measured through the Reasons for Misfortune Questionnaire (RMQ) (Higgins & Shaw, 1999). The RMQ is a scale, but it is designed to sort test-takers into either supportive or unsupportive attributional styles. Accordingly, a subject’s results on the RMQ can be coded, for purposes of regression analysis, into a dummy variable.
The RMQ presents six negative outcomes which are then rated by subjects on one of four causal dimensions, namely (a) locus, (b) personal control, (c) external control, and (d) stability. Hence, given that 6*4 = 24, there are 24 possible Cronbach’s α values that can be reported for the RMQ. In the best-known paper presenting the RMQ, Higgins and Shaw did not report any of these Cronbach’s α; however, another paper (Higgins & Morrison, 1998) reported Cronbach’s α for the RMQ as ranging from a low of 0.51 (for cancer/locus) to a high of 0.90 (for cancer / personal control). Because of the large number of Cronbach’s α calculations possible in the RMQ, this study will not replicate these calculations.
Individualism/collectivism index. Individualism/collectivism will be measured by a scale designed by Triandis and Gelfland (Triandis & Gelfand, 1998). This 16-item scale that measures four dimensions of collectivism and individualism and departs from Hofstede’s (Hofstede, 1994, 1998) concept of individualism and collectivism. Triandis and Gelfand identified four relevant dimensions: vertical collectivism, vertical individualism, horizontal collectivism, and horizontal individualism. Vertical collectivism (VC) is seeing the self as a part of a collective and being willing to accept hierarchy and inequality within that collective. Vertical individualism (VI) is seeing the self as fully autonomous, but recognizing that inequality will exist among individuals, and accepting this inequality. Horizontal collectivism (HC) is the act of seeing the self as part of a collective but perceiving all the members of that collective as equal. Horizontal individualism (HI) is seeing the self as fully autonomous and believing that equality between individuals is the ideal. The Triandis and Gelfland (1998) measure is short and consists of 16 items ranked from 1=never or definitely no and 9= always or definitely yes. The items are arranged into the four aforementioned groups. To score this measure, each dimension’s items are summed up separately to create a VC, VI, HC, and HI score.
As such, when carrying out a mediation study, there are several ways in which Triandis and Gelfand’s (1998) can be used for coding purposes. In this study, VI and HI will be added together to create a single individualism score while VC and HC will be added to create a single collectivism score. These two scores can then be entered separately as mediators as part of the OLS regression.
Triandis and Gelfand (1998) used factor analysis to calculate loadings for items and thereby to derive the four measures. In this study, PCA with Varimax rotation will be employed to determine whether the four factors of (a) fantasy, (b) perspective-taking items, (c) empathic concern items, and (d) personal distress items can be successfully extracted from the individualism/collectivism scale. The PCA will be validated with the use of both the KMO
measure of sampling adequacy and Bartlett’s test. It is anticipated that a sample of 404 individuals would ensure sampling adequacy for the PCA conducted on the individualism/collectivism scale. Cronbach’s α for this scale, which was not presented by Triandis and Gelfand, will also be calculated.
Helping behavior. A helping behavior index was designed for this study and consists of 10 Likert-scale questions and two open-ended questions, with only the Likert-style questions used for purposes of scoring. Helping behavior is being measured using ten scenarios that presented a situation where there was a need for help. These scenarios were created to reflect real-life helping cases that can commonly be observed on streets and seen in the news every day. One example is: “You are on the phone discussing an important business matter, and you see a gentleman falling down and passing out. Would you help?” The participants will be asked to read each scenario carefully, and then indicate the extent to which they would help in the given situation using a 7-point Likert type scale ranging from definitely help (7) to not help at all (1). At the end of these scenarios, there are two open-ended questions: “How important is it to help strangers for you? Why?” and “Would you help someone that will not be able to help you later in return? Why?”
In order to determine whether this original scale measures a unidimensional construct of helping behavior, PCA with Varimax rotation will be carried out to determine whether there is more than one factor in the instrument (with Eigenvalue > 1 serving as the cutoff for a factor). Regardless of how many factors emerge from the PCA, the weightings of every item in the original scale will be calculated and reported. In addition, Cronbach’s α for the scale will be reported. The PCA will be validated with the use of both the KMO measure of sampling adequacy and Bartlett’s test. It is anticipated that a sample of 404 individuals would ensure sampling adequacy for the PCA conducted on the helping behavior scale.
Approval from the Institutional Review Board (IRB) will be sought and obtained before any data collection for the study begins. The main criterion for participants will be to give informed consent, which implies being over 18, speaking English, not knowing the researcher, and currently living in the United States.
Procedures for participants and data collection. The method of data collection will make use of a public Facebook account and a purchased Facebook recruitment advertisement to disseminate awareness of the study throughout the Facebook community. Because advertisements placed on Facebook can specify the desired demographic characteristics of participants, it will be possible to target the recruitment message to people who are (a) over 18, (b) currently located in the United States, and (c) using English-language profiles.
The recruitment message will contain a link to a Qualtrics online survey page that will have an electronic informed consent form to be read and acknowledged by all potential participants. The informed consent form will advise participants of the nature of the study, the researcher’s identity and goals, and their own rights, including the right to discontinue participation at any time, for any reason, and without penalty. The letter of informed consent will also notify participants that both their privacy and anonymity are being protected.
The Qualtrics survey page, to which access will be granted after an informed consent form is completed and submitted, will contain the four scales of the study. The items in each of the four scales will be randomized so that there is no effect of scale order on responses. Each item in each scale will first be written into Microsoft Excel; next, a random-number generator will be used to sort the items into a random order that will then be used to enter the items into Qualtrics.
Participants will be able to complete the survey in Qualtrics at their own pace. When surveys are complete, they will be downloaded from Qualtrics into SPSS for data analysis. Once the survey period has concluded, all data on Qualtrics will be deleted, with the only remaining copy of the data being the local copy stored on the researcher’s password-protected 256-bit-encrypted laptop. Because there will be no identifying information of any kind, these data will not breach participant anonymity; neither the researcher nor any other parties will know how completed any given survey.
Procedures for data analysis. Data analysis procedures will depend upon which hypothesis is being tested. Because this study is a mediation study, all analysis will ultimately depend on the choice of the mediation model. For this study, Baron and Kenny’s (1986) three-step procedure for mediation will be utilized, as also recommended by other scholars who have studied mediation (MacKinnon, Krull, & Lockwood, 2000). In this procedure, the sequential steps are as follows, bearing in mind that Y = dependent variable, X = independent variable, M = mediating variable:
1. Regress X on Y. In this step, the existence of an effect that is mediated is established.
2. Regress X on M. In this step, the link between the independent variable and the mediator is established.
3. Regress X and M on Y. In this step, X is controlled when testing the effect of M on Y.
These steps allow the calculation of mediation effect, direct effect, and total effect as depicted in Figure 1 below:
The sequential steps in Baron and Kenny’s (1986) model will be applied to each of these hypotheses of the study, and the mediation effect, or indirect effect, calculated on the basis of Baron and Kenny’s recommendations.
These regressions will allow the three-variable mediation model depicted in Figure 1 to be followed as recommended in the literature (Baron & Kenny, 1986; MacKinnon et al., 2000).
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