9.6.4: Satisfaction with Sport Participation
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- 64650
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Earlier we considered a study that investigated how success, personality, emotional competence, and sport type (team or individual) are associated with sports satisfaction (Lepir and Lakić 2025). For the study athletes were surveyed through various organizations. The survey was designed to measure various personality traits as well as satisfaction with sport participation. The researchers report summary statistics for several of the measurements. See Table 9.12.
Table 9.12. Summary statistics for several of the measures used in the study of sports satisfaction (Lepir and Lakić 2025).
|
Measure |
Mean |
Median |
Standard Deviation |
|
Athletic Satisfaction |
0.00 |
0.18 |
1.00 |
|
Extraversion |
3.78 |
3.88 |
0.62 |
|
Agreeableness |
3.65 |
3.67 |
0.54 |
|
Conscientiousness |
3.82 |
3.89 |
0.59 |
|
Neuroticism |
2.73 |
2.75 |
0.59 |
|
Openness |
3.40 |
3.44 |
0.63 |
The first measure that we will consider is athletic satisfaction. We can observe from Table 9.12 that the mean level of satisfaction is 0 and the standard deviation is 1.00. It might seem a little strange that the data have this exact type of structure, but there is a very good reason for this. This measure has been specifically designed so that the mean is 0 and the standard deviation is 1, through a process called standardization. This makes individual satisfaction measurements very easy to interpret. For example, if an individual has a satisfaction measurement equal to 2.3, then we know that their level of satisfaction is above the mean satisfaction level because it is positive. The empirical rule will give us even more relevant information. We know from the empirical rule that approximately 95% of the data is within two standard deviations of the mean. Because the standard deviation is 1.0 in this case, the measurement of 2.3 is more than two standard deviations above the mean. This means that this rate of satisfaction is unusually high as it is beyond the range around the mean that contains 95% of the data. We can also gain more information by noting that the median is 0.18. This means that 50% of the data is above 0.18 while 50% of the data is below 0.18. This indicates that more than half of the respondents had a positive satisfaction level.
The next measurement is that of extraversion, which refers to whether an individual is focused externally, such as on social interaction rather than being more focused internally on their own thoughts and feelings. The measure is somewhat difficult to interpret so we will simply consider the summaries of the characteristics of the data. The mean value of extraversion is 3.78 and the median is 3.88. Once again, we can observe that the median is larger than the mean, which indicates that more than half of the values are larger than the mean. The standard deviation is 0.62. This indicates that almost all the measures of extraversion will be between \(3.78-3\times 0.62=3.78-1.86=1.92\) and \(3.78+3\times 0.62=3.78+1.86=5.64\). The summaries for the remaining measures can be interpreted in a similar way.