Developing a physics laboratory anxiety scale

1. Findings related to the construct validity of the scale

1.1. Exploratory factor analysis (EFA)

For EFA, the KMO (Kaiser-Meyer-Olkin parameter) value must be at least 0.60 and the Bartlett Sphericity Test should be significant (Büyüköztürk, 2007). Therefore, before factor analysis, the appropriateness of the data was tested with the KMO and the Bartlett Sphericity Test. The results showed that the data were suitable for factor analysis.

**Table 1. Appropriateness of the data for factor analysis**
Kaiser-Mayer-Olkin (KMO) parameter		0.892
Bartlett	Chi Square	1643.066
	Sd	171
	Significance	0.000

EFA is a statistical technique which aims at explaining the measurement with few factors by gathering the variables that measure the same structure or quality (Büyüköztürk, 2007). With regard to EFA, four factors with Eigenvalues greater than one were found which explained 57.7% of the total variance. These four factors include 19 items.

**Table 2. Eigenvalues of the scale’s sub-dimensions and percentage of variance**
Component	Initial Eigenvalues			Rotation Sums of Squared Loadings
Component	Total	% of Variance	Cumulative %	Total	% of Variance	Cumulative %
1	6.731	35.428	35.428	3.767	19.828	19.828
2	1.774	9.337	44.765	3.013	15.860	35.687
3	1.276	6.715	51.480	2.197	11.561	47.248
4	1.185	6.239	57.719	1.989	10.471	57.719

The given values related to the factor structure were found for rotations that were undertaken with the varimax method. The factor loading values of the scale range from 0.421 to 0.832.

**Table 3. Rotated factor loading value**
	Component
	1	2	3	4
item30	.763
item31	.736
item35	.704
item24	.639
item32	.623
item21	.494
item29	.491
item11		.753
item18		.732
item13		.625
item20		.509
item16		.499
item3			.832
item2			.791
item15			.578
item27			.421
item19				.770
item7				.689
item33				.647

1.2. Confirmatory factor analysis (CFA)

In CFA, testing a previously established hypothesis or theory concerning the relationship between the variables is the objective (Büyüköztürk 2007). After EFA testing, four sub-dimensions of the scale were tested through CFA.

Finally, CFA was conducted in order to test whether the model was four-dimensional. For this purpose, the data were prepared in Microsoft Excel, WordPad and Statistica programmes and transferred to LISREL software. Path analysis (Figure 1) and consistency indices were calculated with the LISREL programme. The consistency of the model, which includes the structures of four relevant sub-scales, was examined by computing the consistency indices and comparative consistency indices.

Figure 1.Four-factor model showing the relationship between the dimensions of the scale

Consistency index values according to the results of the CFA given in Figure 1 are as follows: Chi-Square (χ2 ) is % = 375.75; Degrees of Freedom (df) are 146 (P = 0.00) and accordingly %/ df is 2.57. If this latter value is less than one, it means that there is weak consistency; if the value is greater than five, it means that development within the model is required. The scale is consistent if this value is three (Schumacker & Lomax, 2004). Kelloway (1998) believes that a %/sd ratio of less than five is the indicator of good consistency. Goodness of Fit Index (GFI) is 0.862. The GFI value is between zero and one, which suggests better consistency as it is closer to one (Schumacker & Lomax, 2004). Normed Fit Index (NFI) is 0.80 and Root Mean Square Error of Approximation (RMSEA) is 0.080. Hooper et al. (2008) state that an RMSEA value between zero and 0.080 is the indicator of a good consistency and an RMSEA value between 0.05 and 0.10 is adequate for the consistency of the scale. Also, if the NFI value is 0.85 or above, this means that the scale is consistent (Cheng, 2001; Kelloway, 1998; Pang 1996).

In general, the consistency index values are appropriate for the evaluation criteria. Thus, it is fair to say that the results of EFA and CFA are consistent with each other.

1.3. Naming the factors

When the four-factor scale with 19-item, which emerged as a consequence of EFA and CFA, was examined, it was seen that six of the seven items in factor 1 represented 'anxiety about finishing the experiment'. It was also determined that four of the five items in factor 2 represented 'anxiety about doing the experiment as intended'. Three of the four items in factor 3 indicated 'constant anxiety towards the physics laboratory'.

Anxiety emerges when an individual feels that their self-esteem is under threat or feels that the current situation is stressful. This is called 'Constant Anxiety' (Öner & Le Compte, 1985). Constant anxiety is stable and is recognised as a personal characteristic. It was observed that three items in factor 4 were related to 'anxiety related to the use of materials in the laboratory'. By the end of this examination, three of the 19 items presented by the analyses were eliminated. The remaining 16-item scale was re-examined through CFA. The replicated CFA results of the 16-item, four-factor scale are displayed in the Figure 2 below.

Figure 2. Second CFA results

According to the results of the first-level factor analysis given in Figure 2, the consistency index values are as follows: Chi-Square is {% = 267.27) and Degrees of Freedom (df) is 98 (P=0.00). Accordingly, %/ df is 2.72. Goodness of Fit Index (GFI) is 0.88, Normed Fit Index (NFI) is 0.82, and Root Mean Square Error of Approximation (RMSEA) is 0.084. When all of the index values were evaluated altogether, it was concluded that the scale is valid.

2. Findings related to the validity of the scale

Cronbach α reliability

If there are three or more answers for the test items, the Cronbach α reliability coefficient is applied. Where the Cronbach α reliability coefficient is 0.70 or above, the reliability of the test points is accepted as adequate (Büyüköztürk, 2007). In consequence of analyses, a scale including 16 items was finally obtained. The Cronbach α reliability values of the scale are given in Table 3.

**Table 3. Reliability values related to the final form of the scale**
Sub-dimensions	Cronbach α
Factor 1: Anxiety about finishing the experiment	.81
Factor 2: Anxiety about doing the experiment as intended	.73
Factor 3: Constant anxiety towards the physics laboratory	.72
Factor 4: Anxiety related to the use of materials in the laboratory	.61
Scale	.87

The Cronbach α value was computed as 0.87. This value means that the scale has a high internal consistency.

Difference reliability between the bottom 27% and the top 27% groups
The total average scores of participants in the bottom 27% and the participants in the top 27% group were compared for each item through t-tests. The t-test results are given in Table 4.

**Table 4. T-test results for the bottom 27% and the top 27% groups**
Sub-dimensions	t	p
Factor 1 : Anxiety about finishing the experiment	-29.77	.000
Factor 2: Anxiety about doing the experiment as intended	-28.34	.000
Factor 3: Constant anxiety towards the physics laboratory	-29.32	.000
Factor 4: Anxiety related to the use of materials in the laboratory	-26.76	.000
Scale	-25.61	.000

Table 4 shows that all of the items are significant at the level of p <0.001. This means that the scale can discriminate participants with low scores from participants with high scores.

Split halves test reliability

By splitting the items of the test into two equal halves as odd-even, the first half-remaining half or neutral, the correlation coefficient is computed for the whole test through the Spearman Brown formula. The correlation coefficient is explained with split halves test reliability, which is based on the relationship between two halves of the test. Split halves test reliability shows the consistency between the collected test scores (Büyüköztürk, 2007).

The split-halves test reliability provided by the Spearman Brown formula is 0.78 and the split-halves test reliability calculated via the Guttman Split-Half technique is 0.77. These values indicate that internal consistency and split halves test reliability of the scale are high.

3. Item Analyses

**Table 5. Mean, standard deviation and item-total correlation values of scale items**
Item no	Mean	Std. Deviation (S)	Corrected Item-Total Correlation (r)
Item 21	2.69	1.345	.41
Item 24	2.79	1.225	.54
Item 30	3.00	1.288	.67
Item 31	3.00	1.273	.62
Item 32	3.45	1.240	.54
Item 35	2.62	1.232	.56
Item 11	2.84	1.251	.40
Item 16	2.97	1.238	.64
Item 18	2.84	1.221	.55
Item 20	3.00	1.141	.56
Item 2	3.40	1.164	.46
Item 3	3.60	1.282	.31
Item 15	3.48	1.201	.60
Item 7	4.07	1.021	.39
Item 19	3.78	1.012	.39
Item 33	3.80	1.012	.30

As seen in Table 5, corrected item-total correlations range between 0.30 and 0.67. As stated by Büyüköztürk (2007), these results indicate that the items are distinctive because they score 0.30 and above.