Asia-Pacific Forum on Science Learning and Teaching, Volume 9, Issue 1, Article 12 (Jun., 2008)
Nelson Cheng-Chih CHEN, Ching-Hao CHEN and Ming-chun LIN
An analysis of applied mechanics Contest for senior high school students in Taiwan

Statistical Analysis

Since 2004, the NSTM has been conducting the projects. At first, both the primary test and the final test were written tests. In 2005, the test mode was changed; the primary test kept the same written test pattern, and the final test was changed to merge theory and practical hands-on activities. The descriptive statistics about the final contestants and their primary and final scores are shown in Table 1. In 2005, there was a huge gap between the primary and the final test scores. The difference for the two average test scores almost reached 36(=94.20-58.24), and the reason may be because the testers were not accustomed to the newly changed test pattern.

Table 1: The descriptive statistics of the primary test and final test

 Year Primary test Final test Number of contestants Average score Standard deviation Number of contestants Average score Standard deviation 2004 226 73.47 8.88 209 60.27 13.96 2005 210 94.20 4.07 210 58.24 11.10 2006 201 77.46 6.94 198 62.75 11.02 2007 203 77.59 8.58 200 57.97 14.05 2004-2007 840 80.60 10.91 817 59.78 12.74

Note 1: The number of primary test contestants is not the original competition attendance number; the number shown is representative of those permitted to join the final test after the primary test was held.

Note 2: Full score is 100.

Table 2: The correlation analysis of various tests between 2004 -2007

 Year Test method Pearson correlation coefficient (r) for primary and final test scores p value Primary Final 2004 Written Written 0.36 0.00* 2005 Written Hands-on 0.09 0.19 2006 Written Hands-on 0.26 0.00* 2007 Written Hands-on 0.51 0.00*

* Means p value < 0.05

The correlation analysis between the primary and the final test scores for each year is shown in Table 2. In 2004, the Pearson correlation coefficient between the primary test and the final test is 0.36. Statistical test results showed that there was significant correlation between the two tests. When the test method for the final test was changed to a hands-on approach in 2005, the correlation coefficient among the two tests dropped to 0.09.  It appears that the primary test was not significantly linearly correlated with the final test. The reason might be that the testers were not familiar with the newly created tests. Nevertheless, the correlation gradually increases during 2006 and 2007, and the testers may be getting used to the changes.

The one factor ANOVA test about the final scores for different areas where contestants are from is shown in Table 3. The testing results show that from 2004 to 2007, there is no significant difference among the final scores for the different areas; the contestants from different areas seem to have equal ability in such applied mechanics contests.

Table 3: Final score analysis from different regions from 2004 to 2007

 Area Final test F test Testersâ€™ number Average score Standard deviation F value p value Northern 186 59.56 12.72 0.33 0.80 Taoyuan Hsinchu 115 60.77 13.41 Middle 157 59.29 12.37 Southern 359 59.80 12.73 Total 817 59.78 12.74

The frequency distributions from 2004 to 2007 for various medals and areas where contestants from are shown in Table 4 to Table 7, respectively. Table 8 shows the correlation analysis among the medal types and the areas during the four years. Testing results suggested there was no significant correlation among the medal types and the areas where the contestant was from; the mechanics contest contestants seemed to have an equal ability in obtaining medals no matter where he/she came from.

Table 4: The cross table about medals and areas in year 2004

 Area Counts for medal rank gold silver bronze excellent total Northern 1 0 15 33 49 Touyuan Hsin-Chou 3 1 9 10 23 Middle 1 4 10 28 43 Southern 5 14 15 60 94 Total 10 19 49 131 209

Table 5: The cross table about medals and areas in year 2005

 Area Counts for medal rank gold silver bronze excellent total Northern 2 4 10 30 46 Touyuan & Hsin-Chou 4 4 12 26 46 Middle 1 1 10 18 30 Southern 3 11 18 56 88 Total 10 20 50 130 210

Table 6: The cross table about medals and areas in year 2006

 Area Counts for medal rank gold silver bronze excellent total Northern 3 9 16 29 57 Taoyuan & Hsinchu 3 2 4 12 21 Middle 1 2 10 25 38 Southern 3 7 20 52 82 Total 10 20 50 118 198

Table 7: The cross table about medals and areas in year 2007

 Area Counts for medal rank gold silver bronze excellent total Northern 1 3 11 19 34 Taoyuan & Hsinchu 0 3 5 17 25 Middle 4 3 16 23 46 Southern 5 11 18 61 95 Total 10 20 50 120 200

Table 8: The correlation analysis about medals and areas from year 2004~2007

 Area Counts for medal rank Chi-Square test gold silver bronze excellent total Chi-Square value p value Northern 7 16 52 111 186 14.88 0.09 Taoyuan & Hsinchu 10 10 30 65 115 Middle 7 10 46 94 157 Southern 16 43 71 229 359 Total 40 79 199 359 817