CONFIRMATORY FACTOR ANALYSIS ON THE TYPES OF

GOAL SCALE FOR SPORTS PERSONS

Ms. Meenakshi, Assistant Professor, IGIPESS, Delhi UniversityDr. Lalit Sharma, Associate Professor, IGIPESS, Delhi University

Abstract

Goal setting, particularly different types of goal is a topic that has been of interest

among sports psychologists, athletes and coaches. The types of goal scale (Meenakshi

and Sharma, 2013) was developed for measuring the nature and frequency of the

goals. The psychometric properties of the types of goal scale, however have not been

tested on a sample of Indian athletes, which is an important component if researchers

and applied sport psychologists have to use the scale for assessment purpose. A total

of 592 athletes were considered for the analysis. Results shown that two-factor model

of types of goal with few modifications provides an adequate fit to the data with the

internal consistency of 0.48 and 0.57 respectively for the time bound goals and

process goals subscale. The results provided the evidence for reliability and validity

of the types of goal scale for targeted population.

Key words: Measurement, Confirmatory Factor Analysis, Performance

INTRODUCTION

Researchers in sports psychology have consistently shown that goal setting is an effective

technique to enhance performance of the athletes. In fact, Singer, R, Hausenblas, H, & Janelle,

C, 2001, cited in Peak Sporting Excellence Performance in their recent meta-analysis showed

that goal-setting led to performance enhancement in 78% of sport and exercise research studies,

with moderate to strong effects.

According to McClements (1982, cited by Frankl, 2012) there are two types of goals, subjective

goals and objective goals. Subjective goals are not specific; they are typically general goals with

no real means to quantify success and therefore are not used in sport psychology quantitative

interventions. Objective goals are based on more quantifiable measures. Objective goals can also

be divided into three different categories: outcome goals, performance goals, and process goals

(Burton, Naylor, & Holliday, 2001; Hardy et al., 1996 cited by Weinberg, & Gould 2011)).

Outcome goals typically focus on achieving a certain result in a competition. Winning the

championship, to play in the starting lineup, or to beat a specific opponent are same of the

outcome goals.

Performance goals focus on improvement within an individual, such as setting a personal best

time for a race, to meet the qualifying time for a league or national meet at the next competition.

Instead of emphasizing the outcome, individuals emphasize the process by which a given

outcome is achieved. Performance goals often make the most effective type of goals because it

involves learning at the risk of making mistakes, it improves problem-solving, and it encourages

the athlete to work harder (money instructor).

Process goals focus on the skills, actions and techniques that are used to achieve a performance,

such as maintaining perfect form for a diving competition. A sprinter who has a tendency to

become overly concerned with the position of his/her competitors during the final 20m of races

might set a process goal of focusing on a point beyond the finish line to ensure focus is retained

until the line has been crossed.

These goals can vary in the time frame. Time goals have three different levels, each serving as a

means to improve performance in the general as well as smaller timeframes. These three levels

are known as short-term goals, mid-range goals, and long-term goals.

As above literature has shown that there are various types of goal in the goal setting to improve

performance. The scale was developed (Meenakshi & Sharma, 2013) which could measure types

of goal set by athletes to improve their performance. However, the psychometric properties of

the scale have not been tested on a sample of Indian athletes, which is very important if the

researchers want to use the scale with this population. Therefore the purpose of the study was to

validate the types of goal scale using confirmatory factor analysis.

METHODOLOGY

The scale was validated in three different phases.

Participants

A total of five-hundred and ninety-two sportspersons representing twenty four colleges, three

sports clubs and three institutes/colleges of physical education from Delhi/ NCR were part of the

study. The sample consisted of 312 males, 280 females, who voluntarily took part. The age of the

subjects were ranged from 17 years and above. The sportspersons’ participation level was

considered from intercollegiate level to international level. The subjects for the study who were

actively engaged in competitive sports participation in various individual and team sports were

the target population for the present study.

Administration of the Test

Subjects were informed regarding the purpose of the study and details of the subjects were

obtained on age, gender, specialized sport, types of sport and highest sport participation. Their

willingness to complete the scale was ascertained by requesting them to put their signature after

responding to the items in the scale. The subjects were informed that there is no time limit in

responding to the scale, however, completing the task doesn’t take more than 15 minutes. They

were further instructed not to brood upon any statement rather place immediately the response

that comes instantly after reading a statement. The subjects did not feel any difficulty in

responding to the scale, since the statements contained very simple terms which were invariably

used in the English language. The research scholar considered only those scales which were

completed in all respect.

Scoring

The types of goal scale were rated on 7-point Likert scale from very true of me (7) to very untrue

of me (1).

Statistical Analysis

For the present study different statistics were employed at different phases of validation.

Phase I

Confirmatory Factor Analysis: Confirmatory Factor Analysis was used to support the factor

model as defined by exploratory factor analysis (EFA). The value of x2/df ratio lower than 2.0

suggest a good fit, whereas Fulop, (2007) and few other researchers recommended x2/df ratio

values < 3.0 for good fit. The NNFI and CFI values above 0.90 considered for an acceptable fit

of the model. The GFI indices range from 0 to 1, with values close to 1 representing a perfect fit,

and the values close to 0 represent a poor fit. The values of SRMR and RMSEA close to or lower

than 0.08 and 0.09 respectively demonstrate an acceptable fit. The factor loadings of the items to

the appropriate factors should exceed the cutoff criterion of 0.30.

Reliability: Alpha coefficients to test the internal consistency were employed again after CFA.

Gliem & Gliem, (2003) suggested that, for an acceptable internal consistency, the Cronbach’s

alpha coefficient should not be less than 0.50 and the value of alpha is partially dependent upon

the number of items in the scale.

Phase II Differential reliability

To test the differences between the genders attitude towards types of goal (Sohrabi & Shajie,

2012) independent t - test was utilized to measure the scale structure reliability.

Phase III Norms

Descriptive Analysis using mean and standard deviation was conducted to construct the norm.

Keeping in mind the range of scores the norms were developed on a 3 point scale for types of

goal scale, for which total score of all items on types of goal scale were utilized (Verma &

Ghufran, 2012).

RESULTS

The date was analysed by computing various statistics. The findings of the study have been

shown in the following tables.

Phase I

Confirmatory Factor Analysis

To determine the non-normality of the data, the distributional properties of the statements of the

different subscales of types of goal were examined by using univariate skewness and univariate

kurtosis. The results described that the types of goal statements having univariate skewness were

ranged from -0.35 to 1.36 (M= 0.82) and univariate kurtosis from 0.35 to 1.74 (M= 1.02)

indicated that they are normally distributed, because they are not more than the cutoff value of 3

for skewness and 7 for kurtosis, which are set as the upper value of normality.

Table 1 Fit Indices of the Two Measurement Models of the Types of Goal Subscale

Model x2 df x2/df CFI GFI NNFI SRMR RMSEA

Model 1: two factor 35.02 8 4.38 0.87 0.96 0.75 0.07 0.11

Model 2: two factor

(revised )

7.02 3 2.34 0.98 0.99 0.92 0.03 .07

Model 3: one factor 35.77* 9 3.97 0.87 0.96 0.78 0.07 0.10

Note. x2= chi-square, df =Degree of Freedom, CFI = Comparative Fit Index, GFI= Goodness of Fitness Index, NNFI= Non-Normed Fit Index, SRMR=Standardized Root Mean Square Residual, RMSEA = Root Mean Square Error of Approximation.

As revealed from the Table 1, the two factor measurement model of types of goal subscale

demonstrated that the overall model not fit well according to fit indices. The x2 (df=8, N= 280)

value is 35.02 (p< .05), the x2 /df ratio is 4.38 the CFI 0.87, the GFI 0.96, the NNFI 0.75, the

SRMR 0.07, the RMSEA 0.11. The x2 value is not the best fit index may be due to sample size

(Tabachnick & Fidell, 1996, cited in Zervas, Stavrou, & Psychountaki, 2007). The x2/df ratio is

high which represents an unacceptable fit to the data. The NNFI and CFI values have not reached

the criteria of 0.90. The GFI value is close to 1 suggested a good fit. The SRMR value has

reached the criteria of 0.08 whereas the RMSEA has not met the criteria (0.09). The factor

loadings of types of goal’ scale ranged from 0.30 to 0.76 (mean factor loadings = 0.57).

Covariance matrix was not positive definite. Modification indices suggested to remove statement

no 16.Therefore, statement as suggested was removed and two-factor measurement model was

again tested.

In model 2, revised two-factor structure found to be fit well. The fit indices shown that the x2

(df=3, N=280) value of model fit is 7.02, the null hypothesis of a good fit is not accepted (p

>0.05). The x2 /df value is 2.34. The CFI value is 0.98 suggest a good fit, the GFI value is 0.99

suggest a perfect fit, the NNFI value is 0.92 also suggest a good fit, the SRMR and the RMSEA

values are 0.03 and 0.07 respectively suggest a very good fit. The factor loadings in the revised

two-factor model range from 0.35 to 0.65. Modification indices indicated that the statement 15

is a good indicator of time bound goals subscale as the factor loading of statement 15 is greater

(0.40) on time bound goals subscale than (0.35) process goals subscale as shown in Figure 1.

In model 3, all statements were tested on a single factor and the fit indices of the one-factor

model are as: x2 = 35.77 ((p< 0.05); x2 /df = 3.97; CFI = 0.87; GFI = 0.96; NNFI = 0.78; SRMR =

0.07; RMSEA =0.103. The single-factor measurement model of the types of goal subscale

revealed a poor fit based on the fit indices. The x2/df value is higher than the cutoff criteria of 3.

The CFI and NNFI values have not reached the desirable values of 0.90. Additionally, the

RMSEA value is high. The factor loadings for a single factor range from 0.22 to 0.63 (mean

factor loadings = 0.44).

The fit indices and significant factor loadings of the types of goal subscale in the measurement

models have shown that the second model is better than the other two models. The model

represented in Figure 1 below further indicates that the correlation between the two factors is

fairly correlated, therefore, the total of these two factors is a measure for types of goal subscale.

Figure 1: Factor loadings of the 6 statements of Types of Goal Subscale

Alpha Coefficent and Index of Reliability

To test the internal consistency reliability of the subscales, Alpha coefficient was computed after

CFA. To test the statistical validity that computes the index of reliability, was performaed for the

instrument validation. The literature confirms that if the value is more than 0.50 the test is said

to be valid.The results pertaining to Alpha Coefficient and index of reliability are presented in

Table 2 .

Table 2 Internal Consistency and Index of Reliability of Types of Goal Scales/Subscales

Scale/Subscales No of Statements α Index of Reliability

Types of Goal 5 0.58 0.76

Time goals 3 0.48 0.69

Process goals 2 0.57 0.74

Table 2 reveals the internal consistency reliability is 0.48 for the three-item time goals and for

process goals is 0.57 resulting that all coefficient are acceptable for good internal consistency

reliability in each selected subscales as well as in the total types of goal scale. The results also

reveal that in this instrument the index of reliability is 0.69 and 0.74 for subscales of the types of

goal respectively, and 0.76 for total scale which indicates that experimentally also the test is

valid to use as an instrument on the population.

Phase II - Differential Reliability

To determine subscales’ differential reliability regarding the gender, the mean scores were

compared. The related values pertaining to independent t-test for independent groups are

summarized in Table 3.

Table 3 Comparison of Subscales of the Goal Setting Scale between Genders to Determine Differential Reliability

Subscales Gender Mean SD t-test P-value

Type of Goals Male 31.11 5.910.59 .554

Female 31.35 5.26

Table 3 reveals the differential reliability regarding gender in the scale of types of goal. T-ratio

values of independent groups on types of goal is 0.59 which is not significant at 0.05 level with

df = 590, The t-test indicates that genders do not influence the types of goal.

Phase III - Development of Norms

Development of the scale is incomplete unless norms are developed to interpret the score.

Therefore, scholar has developed the norms for the instrument to interpret their score in a

meaningful manner so that the score obtained by a player could be interpreted. Descriptive

statistics using mean and standard deviation on five hundred and ninety two subjects were

computed to develop norms. The norms were developed on three grades good, average and

below average for the types of goal. The normative values along with the qualitative

interpretation of types of goal scale is presented in Table 4.

Table 4 Norms on Types of Goal

GRADES TYPES OF GOAL VALUES

Almost every time > 31

Occasionally/Sometimes 21 to 30

Never use < 20

DISCUSSION OF FINDINGS

The initial 6 items of the types of goal scale (Meenakshi & Sharma, 2013) developed by using an

exploratory factor analysis (EFA) on the 312 subjects resulted in two-factor solution was used in

the study. For further development and validation of the types of goal scale confirmatory factor

analysis (CFA) was performed on another samples consisting of 280 subjects. The confirmatory

factor analysis was performed to establish the factorial validity of the subscales of types of goal.

Confirmatory Factor Analysis (CFA) indicated that two-factor model of types of goal subscale

provides an adequate fit to the data. First factor presents that sportspersons set short-term goals -

weekly and seasonal goals as well as long term goals to increase performance at higher level as

supported by the findings of Jeff, 2000, Kyllo & Landers, 1995, Locke & Latham, 1995. The

second factor presents that sportspersons set process goals (combination of process, performance

& outcome goals) to achieve greatest improvement in the performance supported by the findings

of the Filby, Maynard, & Grayd, 1999.

Another additional measurement model provided a further examination of the factorial validity

of the scale to measure types of goal. According to the model, all statements loaded on one

factor, suggesting the uni-dimensionality of types of goal. However, the results of the

measurement model, indicating that all statements do not represent the same construct.

On the other hand, the relatively high correlation between time bound goals and process goals

suggested composite types of goal score (sum of time bound goals and process goals). Summing

up the scores of all statements on each factor produces a total types of goal score, ranging from 5

(very low types of goal) to 35 (very high types of goal). A low score could be incorporated as a

sportsperson is not receiving a favourable attitude towards using the time bound goals and

process effectively and high score indicating a favourable attitude towards using a time bound

goal and process goal effectively while setting their goals.

CONCLUSIONS

Within the limitation of the study the following conclusions were drawn:

1. Confirmatory factor analysis indicated that two-factor model of types of goal with few

modifications provides an adequate fit to the data with the internal consistency of 0.48 and

0.57 respectively for the time bound goals and process goals subscale.

Research Implications

The development of the scale will be of immense importance to the sports persons as it can serve

as an essential tool for measuring goal setting pattern of an athlete sets for his/her performance.

As the literature suggests that the combination of goals are better than setting any single type of

goal. Therefore the scale would help us to choose an appropriate goal setting intervention for an

athlete. The scale may be extremely useful to set appropriate goals depending upon the level of

the sports person performance by the coaches or trainers. Furthermore the types of goal scale

may help the sports persons not only to evaluate their own self, but also equips themselves to

understand the importance of goal setting required for excellence. The scale constructed may be

based on Indian population, especially the sports person and hence will be an important

psychological instrument in Indian context.

The scale may be used to assess the types of goal pattern among male and female athletes.

The scale may be used for the assessment of an athlete for training purpose. However, for

research purposes it is not recommended.

Reference

Field, A. P. (2005). Discovering statistics using SPSS (2nd edition). London: Sage.

Filby, W. C., Maynard , I. W., & Grayd, J. K. (1999). The Effect of Multiple-Goal Strategies on Performance Outcomes in Training and Competition. Journal of Applied Sport Psychology, 11(2), 230-246.

Frankl, D. (2012). Retrieved December 21, 2011, from http://www.kidsfirstsoccer.com/setgoalsx.htm

Gliem, J. A., & Gliem, R. R. (2003). Calculating, Interpreting, and Reporting Cronbach’s Alpha Reliability Coefficient for Likert-Type Scales. Midwest Research-to-Practice Conference in Adult (pp. 82-88). Columbus: Continuing, and Community Education.

Jeff, R. (2000, March ). The Effects of a Goal Setting Program on the Self-Confidence of Wrestlers. Research quarterly for Exercise and Sports, 71, a-86.

Kyllo, L. B., & Landers, D. M. (1995, June). Goal Setting in Sport and Exercise: A Research Synthesis to Resolve the Controversy. Journal of Sport & Exercise Psychology, 17(2), 117 – 137.

Locke, A., & Latham , G. P. (1995). The Application of Goal Setting to Sports. Journal of Sport and Exercise Psychology, 7(3).

Meenakshi & Sharma Lalit (2013),

Money Instructor. moneyinstructor.com. (n.d.). Retrieved January 27, 2012, from http://www.moneyinstructor.com/doc/setgoals.asp

Peak Sporting Excellence Performance. Peak Sporting Excellence Performance.com. (n.d.).

Retrieved May 20, 2008, from pponline.co.uk: http://www.pponline.co.uk/encyc/goal-

setting.html

Sohrabi, M., & Shajie, R. (2012, September ). Determining Validity and Reliability of Athletic

Identity Measurement Scale (AIMS-Plus) among Iranian Sample. Archives Des Sciences,

65 (9), 407-418.

Verma , J. P., & Ghufran, M. (2012). Statistics for Psychology A comprehensive Text. MC Graw

Hill.

Weinberg, R. S., & Gould, D. (2011). Foundations of Sport and Exercise Psychology (5th Ed.)

Human Kinetics, USA. 344

Zervas , Y., Stavrou , N. A., & Psychountaki , M. (2007). Development and Validation of the

Self-Talk Questionnaire (S-TQ) for Sports. Journal of Applied Sport Psychology, 19 (2),

142-159.