Statistical Techniques

While all statistical analyses in this study were computed using the SPSS software, the basis for these calculations are discussed in more details below. Specifically, each research question was analyzed based on the described statistical techniques.

Research question 1: What are the demographics of student respondents studying at institutions

in Australia, the UK, and the US?

For research question 1, descriptive statistics will be used to display frequency distributions and cross tabulations of student respondents in the 2016 International Student Barometer survey from institutions in Australia, the UK, and the US. A frequency distribution is

“an organized tabulation of the number of individuals located in each category on the scale of measurement” (Gravetter & Wallnau, 2013, p. 39). In other words, it groups all individuals with the same scores together and rearranges the set of unorganized scores in order of higher scores to lower scores. Frequency distributions are usually displayed in tables or graphs. Cross tabulation is a statistical tool that the researcher uses in SPSS for this study to quantitatively analyze

categorical data and jointly show their frequency distributions. The demographic variables in this study are listed as age, gender, nationality, field of study, year of study, and source of funding.

Percentages were used to answer research question 1, where f stands for frequency and n is the number of scores (Gravetter & Wallnau, 2013, p. 41).

𝑃𝑃��𝑐𝑐���𝑎𝑎�� = �(100)

=

�

� (100)

Research question 2: To what extent are international students satisfied with their campus

arrival, learning, living, and support services environments?

Frequencies, means, and standard deviation were used to provide a general sense of students’ overall level of satisfaction with their respective institution, as well as with their

arrival, learning, living, and general support services settings. The independent–sample t test was also used to compare means across the three institution countries.

an arithmetic average or calculated central value of a set of numbers. It is “the point in a

∑

distribution about which the sum of the squared deviations is at a minimum” (Punch, 1998, p.

113). The mean is determined by adding all the data points in a population and then dividing the total by the number of points.

𝑀𝑀�𝑎𝑎� (�̅) =

𝑛𝑛 𝑖𝑖=1

𝑛𝑛 𝑥𝑥_𝑖𝑖

For research question 2, the average level of satisfaction is calculated using the above formula, where n is the number of respondents in the survey and x is the response scale, which can hold the value of 1, 2, 3, or 4.

The standard deviation, one of the two most popular measures of variability, is the square root of the variance, which is a measure of the average deviation from the mean in squared units (Johnson & Christensen, 2008). In other words, the standard deviation is an index of the amount of variability in a set of data, which is how far a number tends to vary from the mean (Babbie, 2001). A high standard deviation is an indication that the data is more dispersed, hence a wider range of values. The lower the standard deviation, the more compact the data points tend to be to the mean.

Standard deviation (s) = √

∑(� −

�̅)²

� − 1

The standard deviation of the satisfaction variables is calculated using the above formula, where n is the number of respondents in the survey, x is the response scale, and �̅ is the mean.

To determine whether any of the differences between the means are statistically significant, ANOVA, which is “a hypothesis-testing procedure that is used to evaluate mean differences between two or more treatments or populations” (Gravetter & Wallnau, 2013, p.

387), was used to compare the p-value to the significance level to assess the null hypothesis.

Since the null hypothesis states that the population means are all equal, a significance level of

0.05 would indicate a 5% risk of concluding that a difference exists when there is no actual difference (Minitab, n.d.).

Research question 3: Are there any apparent associations or correlations between international

students’ overall level of satisfaction with their institution and their experience with their arrival, learning, living, and support services environments?

Regression analysis was used to test for associations and answer research question 3.

Regression analysis “is a set of statistical procedures used to explain or predict the values of a dependent variable based on the values of one or more independent variables” (Johnson &

Christensen, 2008, p. 486). There are two main types of regression: simple regression, in which there is only one independent variable, and multiple regression, in which “a given dependent variable is affected simultaneously by several independent variables” (Babbie, 2001, p. 444).

Multiple regression analysis, also known as an extension of a simple linear regression, can be calculated as follows:

� = 𝛽𝛽0 + 𝛽𝛽1�₁ + 𝛽𝛽2�₂ + 𝛽𝛽3�₃ + �

where � is the value of the DV that is being predicted or explained; 𝛽𝛽0 is the constant or intercept; 𝛽𝛽1 is the beta coefficient for �₁; �₁is the first independent variable that is explaining the variance in �; and u is the error term, which captures the combined effect of omitted variables.

For instance, in research question 3, multiple regression takes the form of:

����𝑎𝑎��_�𝑎𝑎� = 𝛽𝛽0 + 𝛽𝛽1����𝑎𝑎��_𝑎𝑎��𝑖𝑖�𝑎𝑎� + 𝛽𝛽2����𝑎𝑎��_��𝑎𝑎��𝑖𝑖�� + 𝛽𝛽3����𝑎𝑎��_�𝑖𝑖�𝑖𝑖��

+ 𝛽𝛽4����𝑎𝑎��_����𝑖𝑖𝑐𝑐�� + ����� ����

Correlational analyses were performed to assess the relationship between the variables of satisfaction and overall institutional experience. Correlation is a statistical technique that is used to measure and describe the strength of a linear relationship between two variables, although its

value generally does not necessarily characterize their relationship (Gravetter & Wallnau, 2013).

A perfect correlation is identified by a value of 1.00 (perfect positive correlation) or -1.00 (perfect negative correlation). A value of 0 indicates no relationship of consistency between the variables.

Research question 4: How do the demographic variables of respondents (age, gender,

nationality, field of study, study stage, and funding) impact their level of satisfaction with their institution?

To answer this research question, a combination of descriptive and inferential analyses were used. A two-way logistical analysis was performed to understand how the overall

satisfaction scores of international students were distributed by demographics groups. A multivariate regression analysis, with demographic variables as covariates, was conducted to look at the impact of demographic variable in associations between each dimension of

experience (arrival, learning, living, and support services) and overall satisfaction. For instance, the regression equation for Chinese student respondents as a covariate looks as follows:

����𝑎𝑎��_{�𝑎𝑎�} = 𝛽𝛽0 + 𝛽𝛽1����𝑎𝑎��𝑎𝑎��𝑖𝑖𝑣𝑣𝑎𝑎𝑙𝑙 + 𝛽𝛽2����𝑎𝑎��𝑙𝑙𝑒𝑒𝑎𝑎�𝑛𝑛𝑖𝑖𝑛𝑛𝑔𝑔 + 𝛽𝛽3����𝑎𝑎��𝑙𝑙𝑖𝑖𝑣𝑣𝑖𝑖𝑛𝑛𝑔𝑔

+ 𝛽𝛽4����𝑎𝑎���𝑒𝑒�𝑣𝑣𝑖𝑖𝑐𝑐𝑒𝑒� + 𝛽𝛽5�𝑎𝑎�𝑖𝑖��𝑎𝑎�𝑖𝑖��𝐶𝐶ℎ𝑖𝑖𝑛𝑛𝑎𝑎 + ����� ����

Research question 5: How likely are international students to recommend their current

institution to prospective applicants based on their satisfaction and experience with that institution?

Multiple regression analysis, as described above, will be used to look for associations between the dependent variable (institution recommendation) and the independent variables (satisfaction with arrival, learning, living, support services, and overall satisfaction) to answer research question 5. In each analysis, the dependent variable will take the form of a demographic

variable and the independent variables with be the satisfaction variables in the study. The multiple regression equation will look as follows:

𝑖𝑖���𝑖𝑖���𝑖𝑖���𝑒𝑒𝑐𝑐 = 𝛽𝛽0 + 𝛽𝛽1����𝑎𝑎��𝑎𝑎��𝑖𝑖𝑣𝑣𝑎𝑎𝑙𝑙 + 𝛽𝛽2����𝑎𝑎��𝑙𝑙𝑒𝑒𝑎𝑎�𝑛𝑛𝑖𝑖𝑛𝑛𝑔𝑔 + 𝛽𝛽3����𝑎𝑎��𝑙𝑙𝑖𝑖𝑣𝑣𝑖𝑖𝑛𝑛𝑔𝑔

+𝛽𝛽4����𝑎𝑎��_����𝑖𝑖𝑐𝑐�� + 𝛽𝛽5����𝑎𝑎��_�𝑎𝑎 + ����� ����

Correlational analyses were performed to assess the relationship between the variables of satisfaction and institutional recommendation.