Chapter Twenty-Four - Additional Resources

EXAMPLES OF REPORTING STATISTICS USED

Reporting frequencies

Set out the table/chart/graph and then provide a commentary.

Report raw scores and percentages.

Report the modal/bi-modal scores for each item.

Consider which items score highly, which score low (refer to the different points on a rating scale)

Look for skewness (do some items lean towards one end of a rating scale).

Aggregate scores – the highest two categories, the lowest two categories

Reporting Correlations

A correlation matrix was constructed in order to discover important relationships which tests had with other factors, using Spearman’s rho (or the Pearson coefficient). Table XXX presents only those correlations where r £ 0.05. A statistically significant correlation was found between muscular strength and weight (r = .96, r <0.05). Those with the greatest muscular strength also tended to be heavier.

There was a statistically significant negative correlation between musical ability and mathematical ability (r = –.89, r <0.001). Those with the highest musical ability tended to be those with the lowest mathematical ability and vice versa.

There was a statistically significant correlation between spatial awareness and mathematical ability (r = .96, r <0.05). Those with the greatest spatial ability tend to be those with the highest mathematical ability.

There was no statistically significant correlation found between height and intelligence (r= .46, r =.064).

The alpha reliability index for the whole of the final version of the pilot was a =.9774; for the leadership and management factor the alpha coefficient was a =.9780; for the teaching and learning factor the alpha coefficient was a =.8929; for the staff participation factor the alpha coefficient was a =.9132. For all the calculations N=125. These are extremely high reliability coefficients.

Crosstabs

Crosstabs

Reporting chi-square

The chi-square statistic was calculated for the distributions of males and females on the kinds of television programmes watched. There was a statistically significant difference between the males and females ( c 2 = 13.76, d.f.=2, r =0.01) in their preferences for different preferred types of television viewing.

There was a statistically significant association between sex and preferred types of television programme ( c 2 = 13.76, d.f.=2, r =0.01).

Girls were more likely than boys to prefer crime programmes and less likely to prefer soap operas or both programmes.

Reporting the Mann-Whitney and Kruskal-Wallis tests

When the Mann-Whitney statistic was calculated to determine whether any of the distributions varied statistically significantly according to the nominal characteristics of the sample (U= 23.5, r =.032), a statistically significant difference was found between boys and girls on the variable . . . . A crosstabulation indicated that the differences were: the boys watched far more films than girls and girls watched far more domestic situation dramas than boys.

When the Mann-Whitney statistic was calculated to determine whether the distribution of the responses to the rating scale item XXX varied statistically significantly according to the nominal characteristic of the sample ‘sex’, a statistically significant difference (U= 23.5, r =.032) was found between boys and girls on the variable . . . . A cross-tabulation found that boys preferred comic books more than girls, and girls preferred novels more than boys.

When the Kruskal-Wallis statistic was calculated to determine whether any of the distributions varied statistically significantly according to the nominal characteristics of the sample ( c 2 = 6.955, r =.031), a statistically significant difference was found between boys, girls, adult males and adult females on the variable . . . . A cross-tabulation found that adult males and boys preferred comic books more than girls and adult females, and adult females and girls preferred novels more than boys and adult males.

When the Kruskal-Wallis statistic was calculated to determine whether the distribution of the responses to the rating scale item XXX varied statistically significantly according to the nominal characteristic of the sample ‘ethnicity, a statistically significant difference (U= 23.5, r =.032) was found between Chinese, Portuguese and Macanese respondents on the variable . . . . A cross-tabulation found that Chinese worked later into the evening much more frequently than Portuguese and Macanese.

When Mann-Whitney and Kruskal-Wallis statistics were calculated to determine whether any of the distributions varied statistically significantly according to the nominal characteristics of the sample (i.e. r £ .05), in only 5.5% of cases were the distributions statistically significant, suggesting that the data hold true, regardless of the nominal characteristics of the sample.

Reporting t-tests

The mean number of marks scored by student in the mathematics test (M=54.43, SD=6.87) is statistically significantly higher (t=5.64, df=16, two-tailed r =.003) than those of students in the English language test (M=43.54, SD=12.43).

The mean number of marks scored by students in the test of English reading (M=71.56, SD=4.32) and in the test of English listening (M=73.12, SD=2.34) did not differ statistically significantly (t=1.76, df=6, two-tailed r =.065).

The mean number of attendances by females from October to December (M=98.12, SD=3.65) and males (M=96.89, SD=4.12) did not differ statistically significantly (t=2.34, df=3, two-tailed r =.087). or r >.05 or r =n.s.

The t-test revealed that University graduates had statistically significantly higher IQ scores than college graduates (t=6.34, df=8, two-tailed r =.016). 

ANOVA revealed a statistically significant main effect of type of reader and the number of books read (F­ 1, 4 = 10.6, r =.004).

The effect of the reading programme on the types of reader was statistically significant overall (F­ 2, 6 = 13.56, r =.012). The mean for adult males (M=7.56, SD=2.34) was statistically significantly greater than that for adult females (M=4.54, SD=2.65). There was no statistically significant difference between the mean of adult females and teenage females.

Regression results suggest that the unemployment rate (independent variable) affects the duration of unemployment (dependent variable), F (1, 33) = 10.91, p < 0.01.

A linear regression indicated that the increase in one percentage point on the final university examination was associated with an additional .763 percentage point on the university entrance examination result (p=.000).

For this sample, an increase of one percentage point in the unemployment rate was associated with an additional 0.97 weeks in duration of unemployment. There was a weak positive association between the natural rate of unemployment and duration of unemployment (r = 0.35). The regression as a whole fit reasonably well (R 2 = 0.63, adjusted R 2 = 0.57) and was statistically significant at the 1 percent level (F = 10.91, p = 0.0017).”

Multiple regression was used for data analysis, and the results of this, which include the standardized b coefficients of each component variable of customer satisfaction, are presented below. The multiple regression for weightings of variables for the whole sample were:

The formula used for calculating the school conditions for effectiveness index was:

Using this formula, the overall school effectiveness conditions index is: {(0.392941 ¸ 0.49267)x100=79.75%. The schools concerned are 79.75% effective in their internal conditions.

Factor Analysis (principal components analysis)

In order to obtain conceptually similar and significant clusters of issues from Tables V, VI, and VII, principal component analyses with varimax rotation and Kaiser Normalization were conducted. The scree test was used to determine the number of factors, and Eigenvalues equal to or greater than 1.00 were extracted. With regard to the 11 variables in Table V, the scree test and orthogonal rotation of the factors yielded two factors, accounting for 35.7 per cent and 22.4 per cent of the total variance respectively. The factor loadings are presented in Table IX . . . . To enhance the interpretability of the factors, only items with factor loadings of >0.55 for factor one and >0.82 for factor two were selected for inclusion in their respective factors. Factor one is named declining motivation because of the domination of tests and examinations, and factor two is named insufficient opportunity for self-assessment.

With regard to the 15 variables in Table VII, the scree test and orthogonal rotation of the factors yielded three factors, accounting for 25.4 per cent, 22.7 per cent and 15.6 per cent of the total variance respectively. The factor loadings are presented in Table XI . . . . To enhance the interpretability of the factors, only items with factor loadings of >0.61 for factor one, >0.67 for factor two and >0.77 were selected for inclusion in their respective factors. Factor one is named the superficiality and inbuilt failure of tests and examinations, factor two is named students learn only for the sake of the test and examinations, and factor three is named tests and examinations put undue pressure on all parties.

A principal components analysis was conducted on the correlations of the six variables. Two factors were initially extracted with eigenvalues equal to, or greater than, 1.00. Orthogonal rotation of the factors yielded the factor structure give in Table XX. The first factors accounted for 47% of the variance and the second factor 42%. The first factor seems to be hand-eye coordination and the second factor seems to be verbal flexibility.