# SID Data Analysis Science

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## Introduction

The data collected to determine optimal SID and mouth opening value was analysed using various statistical measures for ordinal data. Three different radiologists were asked to rate seventy-five X-ray images with patients positioned at five different SID(cm) measures. The rating scale established produces completely ordinal data. To ensure an appropriate analysis that produces meaningful results, the data were first tested for central tendency using median and mode. A Mann-Whitney U test was then conducted because it is a non-parametric test often used to assess for significant differences in an ordinal dependent variable using a significant level of P ≤ 0 .5. Pinedo et al. (2010) argue that Mann-Whitney U is the non-parametric equivalent of the independent samples t-test. Therefore, the test doesn’t assume any properties regarding the distribution of the dependent variable in the analysis. Median scores of each of the category scores were used to produce the results. Lastly, the inter-and intra-observer analysis was conducted using the intra-class correlation coefficient using the confidence interval of 68% (Pinedo et al., 2010).

## Central Tendency Analysis

Since the data acquired from the research is ordinal, the best measures for central tendency are median and mode. Using SPSS results for central tendency were produced, grouping the results based on mouth opening and SID. Table 1 provides insight into the median and modes of radiologist responses for each category of assessment. When analysing image quality scores for a centring point of A0, the optimal SID established based on the raters’ responses was at SID 60.00cm, 120.00cm, and 140.00cm. This is concluded because, within the group, both SID 60.00cm, 120.00cm, and 140.00cm received a median score of 5, which is higher than the others. At a centring point of A1, the image quality scores produced all had high scores from raters at a median of 5. At a centring point of A2 image quality scores from raters suggest that quality images were produced all SID points with a median score of 5. At A3 optimal SIDs were at 60.00cm, 80.00cm, and 100.00cm with median scores of 5. At A4 centring point all SID values from 60.00cm to 140.00cm had rated at 4 score medians.

Table 1- Results of Central Tendency for Various Centering Point and SIDs

 Statistics Centering Points SID (cm) Median Image Quality Score Median Acceptability Score Median Total Image Quality Score A0 60.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 5.00 3.00 6.00a 80.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 3.0000 8.0000 Mode 4.00 3.00 7.00a 100.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 5.00 3.00 8.00 120.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 5.00 3.00 8.00 140.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 3.0000 7.0000 Mode 4.00 2.00a 6.00a A1 60.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 3.00a 3.00 6.00a 80.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 9.0000 Mode 5.00 3.00 9.00 100.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 4.0000 8.0000 Mode 3.00a 4.00 6.00a 120.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 2.00a 3.00 5.00a 140.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 3.00a 3.00 5.00a A2 60.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 4.0000 8.0000 Mode 4.00a 4.00 8.00 80.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 9.0000 Mode 5.00 3.00 9.00 100.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 5.00 3.00 6.00a 120.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 5.00 3.00 8.00 140.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 2.0000 7.0000 Mode 4.00 2.00 6.00a A3 60.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 5.00 3.00 8.00 80.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 8.0000 Mode 4.00a 3.00 8.00 100.00 N Valid 3 3 3 Missing 0 0 0 Median 5.0000 3.0000 9.0000 Mode 5.00 3.00 9.00 120.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 3.0000 7.0000 Mode 4.00 3.00 7.00 140.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 3.0000 8.0000 Mode 4.00 3.00 8.00 A4 60.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 4.0000 8.0000 Mode 4.00 4.00 8.00 80.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 3.0000 8.0000 Mode 4.00 3.00 8.00 100.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 3.0000 8.0000 Mode 4.00 3.00 8.00 120.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 3.0000 7.0000 Mode 2.00a 3.00 7.00 140.00 N Valid 3 3 3 Missing 0 0 0 Median 4.0000 3.0000 7.0000 Mode 4.00 3.00 6.00a a. Multiple modes exist. The smallest value is shown

When testing these scores for acceptability, it is found that at centring A0 all SID measures had received an equal median score of 3 from all raters. This pattern repeats centring points A3. All SIDs received a median value of 3 from all three raters. At centring point A2, the optimal SID is viewed as 60.00cm because the median value is 4 while remaining SIDs had a median value of 3 and SID 140.00cm had a value rated at 2. Lastly, at centring point, A4 SID value of 60.00cm produced the best acceptability score with a median of 4.

The last measure of central tendency tested median scores for total image quality scores based on varying centring points and SID. At centering point A0, maximum median value produced was 8 at SID 60.00cm, 80.00cm, 100.00cm, and 120.00cm. At centring point, A1, the optimal SID based on rater’s observance of total image quality was at SID 80.00cm with a median score of 9. Lastly, at a centring point of A2 the median score given by raters for optimal SID 80.00cm with a score of 9.

Based solely on central tendency results, the optimal SID and centring points for image quality is 60.00cm and 80.00cm. Optimal SID and mouth opening based on acceptability scores is A3 and 80.00cm SID. Lastly, based on the total image quality score, the best SID and centring point is0.00cm SID.

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## Mann-Whitney U Analysis

Mann-Whitney U is commonly used for assessing two independent variables. However, SID (cm) values for the current study researched five values, 60.00cm, 80.00cm, 100.00cm, 120.00cm, and 140.00cm. For this reason, when conducting the Mann-Whitney U test, the independent variables were taken in combinations to compare SID groups. Using SPSS, rank tables were produced which have been consolidated in tables 2- 10 below. Mean ranks allow comparison between variables to identify which one is the most optimal, which is the two’s highest rank. The mean rank tables allow a comparison to be conducted of the two independent variables analysed to determine which of the independent SID variables are optimal for image quality, acceptability, and total overall image scores. To determine if the independent SID variable produced optimal results, it was essential to check for statistical significance based on the asymptotic 2-tailed p-value. The results of the Mann-Whitney U analyses are provided below.

Table 2- Mean Rank Values of Image Quality Scores

 Mean Rank- Image Quality Scores SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 14.17 14.83 17.60 17.17 80.00 16.83 – 16.3 18.73 18.30 100.00 16.17 14.70 – 18.07 17.73 120.00 13.40 12.27 12.93 – 14.90 140.00 13.83 12.70 13.27 16.10 –

When analysing image quality scores (see table 2) mean ranks helped determine which group can be considered as having the higher image quality score based on SID. Compared to each SID, 80.00cm SID always had a higher mean rank compared to SIDs it was compared against. For example, SID 80.00 produced a mean rank of 16.83 compared to 60.00cm SID having a mean rank of 14.17. This trend continues with all other SID values.

Table 3- U values for Image Quality Scores

 Mann-Whitney U – Image Quality Scores SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 92.500 102.500 81.000 87.500 80.00 – 100.500 64.000 70.500 100.00 – 74.000 79.000 120.00 – 103.500 140.00 –

Table 4- Asymptotic Significance p-values Image Quality Scores

 Mann-Whitney U Statistical Sig – Image Quality Scores SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 0.400 0.671 0.185 0.295 80.00 – 0.610 0.042 0.079 100.00 – 0.103 0.160 120.00 – 0.705 140.00 –

Tables 3 provides U values for image quality scores for each SID (cm) and table 4 provides p-values to determine statistical significance. Based on these tables, only a single value of U and were statistically significant. From the data, it can be concluded that image quality scores with a SID of 80.00cm were statistically significantly higher than the SID 120.00cm at U= 64.00, p= 0.042. Various other groups had a higher U value, for example, SID of 60.00cm was statistically higher than 100.00cm at U= 102.500. However, its p values were greater than 0.05, making the greater difference statistically insignificant.

Based on analysis of image quality scores, optimal image quality is gained at SID 80.00cm because it produced the highest mean rank of 18.73, at U= 64.00, p= 0.042. The remaining SIDs were unable to produce statistically significant values.

Acceptability scores were also measured using the same techniques detailed. Based on table 5, SID at 60.00cm had greater mean rank values for all other comparable rates of SID. For example, SID at 60.00cm produced a mean rank of 19.73 compared to SID at 140.00cm with a mean rank of 11.27. Another notable value is SID at 80.00cm, which produced a mean rank of 19.03 compared to 140.00cm SID with a mean rank of 11.97. These mean ranks indicate that acceptability scores had a greater value at 60.00cm and 80.00cm.

Table 5- Mean rank values for Acceptability Scores

 Mean Rank- Acceptability Scores SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 16.37 16.4 17.30 19.73 80.00 14.63 – 15.67 18.73 19.03 100.00 14.60 15.33 – 16.23 18.43 120.00 13.70 12.27 14.77 – 17.73 140.00 11.27 11.97 12.57 13.27 –

Table 6 below presents the results of the U values for acceptability scores. U’s greater values are found when comparing SID at 80.00cm to 100.00cm, which produced a U value of 110.000, which suggests that the null hypothesis of the research is supported. However, keeping with the previous table results, SID at 60.00cm compared to 140.00cm produced a value of 49.000 and SID at 80.00cm compared to 140.00cm produced a U value of 59.500. According to Giraudeau (1996), a lower U supports the research hypothesis, while larger values support the null hypothesis. The significance of these scores was determined using data from table 7, which reports asymptotic p-values.

Table 6- Mann-Whitney U values for Acceptability Scores

 Mann-Whitney U – Acceptability Scores SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 99.500 99.000 85.500 49.000 80.00 – 110.000 95.500 59.500 100.00 – 101.500 68.500 120.00 – 79.000 140.00 –

Table 7- Asymptotic Significance p-values Acceptability Scores

 Mann-Whitney U Statistical Sig – Acceptability Scores SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 0.554 0.547 0.267 0.006 80.00 – 0.913 0.462 0.022 100.00 – 0.639 0.061 120.00 – 0.152 140.00 –

The only statistically significant values produced from the test (see table 7) are SID at 60.00cm compared to 140.00cm and SID at 80.00cm compared to 140.00. Both SIDs are statistically significant because their p-values are less than 0.05. For this data, it can be concluded that the SID value of 60.00cm is statistically significantly higher than the 140.00cm SID group at U= 49.000, p= 0.006. Also, SID value of 80.00cm is statistically significantly higher than 140.00cm SID group at U– 59.500, p= 0.022. Therefore, images produced at 60.00cm and 80.00cm SIDs are considered more acceptable than those produced at the other values.

The final component analysed was total overall image score. As observed in table 8, SID at 80.00cm had produced greater mean ranks against other comparable SID values. The highest mean rank produced by 80.00cm SID is 18.43 compared to 12.57 mean rank at SID 120.00cm. However, the highest mean rank produced from the data is SID 100.00cm which had a mean rank of 18.63 against SID 140.00cm. At 80.00cm, the mean rank produced when comparing to 140.00cm was 18.09.

Table 8- Mean rank values of Total Overall Image Score

 Mean Rank- Total Image Score SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 14.50 15.23 17.67 18.33 80.00 16.50 – 16.50 18.43 18.09 100.00 15.77 14.50 – 17.87 18.63 120.00 13.33 12.57 13.13 – 15.83 140.00 12.67 12.1 12.37 15.17 –

The lowest U values produced for SID were at 80.00cm at 61.500 and 100.00cm with 65.500. These values indicate that the research hypothesis is true. The significance of these values is corroborated with data from table 10. According to table 10, that SID value of 80.00cm is statistically significantly higher than the 140.00cm SID group at U= 61.500, p= 0.034. Also, SID value of 100.00cm is statistically significantly higher than 140.00cm SID group at U– 65.500, p= 0.050. Therefore, images produced at 80.00cm and 100.00cm SIDs have more acceptable total overall image scores than those produced at the other values.

Table 9- Mann-Whitney U values for Total Overall Image Score

 Mann-Whitney U- Total Image Score SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 97.500 108.500 80.000 70.000 80.00 – 97.500 68.500 61.500 100.00 – 77.000 65.500 120.00 – 107.500 140.00 –

Table 10- Significance p-values Total Overall Image Scores

 Mann-Whitney U Statistical Sig – Total Image Score SID(cm) 60.00 80.00 100.00 120.00 140.00 60.00 – 0.531 0.867 0.175 0.076 80.00 – 0.527 0.066 0.034 100.00 – 0.138 0.050 120.00 – 0.835 140.00 –

The analysis concludes that optimal images are produced at SID 60.00cm, 80.00cm, and 100.00cm. This conclusion is based on the Mann-Whitney U results for image quality, acceptability, and total overall image scores. SID values of 80.00cm had high mean ranks than all other SIDs for all three categories of assessment. Furthermore, U values produced for SID 80.00cm were statistically significantly higher than those produced for other values of SID.

## Inter- and Intra-Observer Analysis

Inter-observer/rater reliability was analysed using the interclass correlation coefficient (ICC) for each assessment category. According to Giraudeau (1996), inter-rater reliability is the degree of agreement between observers. The purpose of the test is to provide a score of homogeneity between the ratings given by the observers. ICC provides a quantification of the proportion of variance within observations caused by between-subject variability in true scores.

Table 11- Image Quality Score Inter-Overserved Analysis

 Image Quality Score Inter-Observer Analysis SID(cm) Std.Dev ICC Score SEM 60.00 2.60403 -0.10 2.731 80.00 2.43389 -0.25 2.721 100.00 1.68466 -0.11 1.775 120.00 2.57645 0.083 2.467 140.00 2.48424 -0.046 2.541

Table 11 provides the inter-observer analysis results for each SID(cm) values for image quality. According to Cicchetti (1994), values of ICC inter-observer agreement measures that are less than 0.40 should be considered poor. The values produced for image quality score are either negative or less than 0.40, concluding that there is poor consistency among the observers when scoring the quality of images based on SID.

Table 12- Acceptability Score Inter-Overserved Analysis

 Acceptability Score Inter-Observer Analysis SID(cm) Std.Dev ICC Score SEM 60.00 0.82808 -0.157 0.891 80.00 0.98561 0.020 0.976 100.00 1.39728 0.282 1.184 120.00 1.30201 0.127 1.217 140.00 1.34519 0.090 1.283

Table 13- Total Overall Image Score Inter-Overserved Analysis

 Total Overall Image Score Inter-Observer Analysis SID(cm) Std.Dev ICC Score SEM 60.00 2.79455 -0.134 2.976 80.00 2.89499 -0.075 3.002 100.00 2.80815 0.124 2.628 120.00 3.44065 0.064 3.329 140.00 3.27036 0.009 3.256

Similarly, table 12 and 13 also produced ICC scores that were negative or less than 0.40 indicating poor consistency among the observers when rating for acceptability of images and total overall images. ICC is negative whenever mean squared between groups (MSB) < mean squared within (MSW). Basically, in this case, ICC is negative because variability within the SID groups exceeds variability across them. This shows that there is divergence within SID groups based on observer responses, causing the ICC to be negative.

Intra-observer reliability was also conducted using ICC to assess each of the three radiologists’ ratings for SID values. However, this analysis was conducted on duplicate images to examine the consistency of the observer’s ratings.  According to table 14, radiologist 1 kept good to excellent consistency when rating images in SIDs 60.00cm, 100.00cm, and 140.00cm. This assessment is based on guidelines quoted by Cicchetti (1994), who stated that ICC measures between 0.60 and 0.74 are good while between 0.75 and 1.00 are excellent. Hence, radiologist 1 is maintaining consistency when scoring the x-ray images even though they are duplicates.

Table 14- Radiologist 1 Intra-Observer Analysis

 RAD 1 Intra-Observer Analysis SID(cm) Std.Dev ICC Score SEM 60.00 3.99106 0.817 1.707 100.00 3.00000 0.861 1.118 140.00 7.11805 0.893 2.328

Table 15- Radiologist 2 Intra-Observer Analysis

 RAD 2 Intra-Observer Analysis SID(cm) Std.Dev ICC Score SEM 60.00 2.81842 0.650 1.667 100.00 1.91485 0.614 1.190 140.00 2.58199 0.750 1.291

Radiologists 2’s ICC scores range from fair to good showing that consistency among the scoring of images exists (see table 15). Lastly, radiologist 3 obtained ICC scores within the good range based on the scores observed in table 16. This affirms that all three radiologists maintained consistency in their x-ray images’ ratings and had limited variability when ranking these images, although they were duplicates.

Table 16- Radiologist 3 Intra-Observer Analysis

 RAD 3 Intra-Observer Analysis SID(cm) Std.Dev ICC Score SEM 60.00 2.12132 0.869 0.768 100.00 2.58199 0.863 0.956 140.00 3.41565 0.879 1.188

## References

Cicchetti, D. V., 1994. Guidelines, criteria, and rules of thumb for evaluating normed and standardized assessment instruments in psychology. Psychological Assessment, 6(4), 284-290.

Giraudeau, B., 1996. Negative values of the interclass correlation coefficient are not theoretically possible. Journal of Clinical Epidemiology, 49(10), 1205-1206.

Pinedo, M., Villacorta, E., Tapia, C., Arnold, R., Lopez, J., Revilla, A., Gomez, I., Fulguet, E., & San Roman, J.A. 2010. Inter- and intra-observer variability in the echocardiographic evaluation of right ventricular function. Revista Espanola de Cardiologia, 63(7), 802-809.

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