Ingleton Violations in More General 2-Transitive Groups

119

seeing that the result in the pooled regression model is statistically significant (p-value which is .000 is less than 0.05).

Using the formular below, the result of the Chow test is given as:

(RSSp – (RSS1 + RSS2)) / k (RSS1 + RSS2) / (N1 + N2 – 2k)

F-critical value = 2.128

Looking up 91 under 8 in the F-table distribution (5% significance level), the outcome reveals that the F-table value obtained is 2.02. Thus, when F-critical value (2.128) is greater than the F-table value (2.02), the null hypothesis which states that ―there is no break point (different data set can be represented as one single linear regression)‖ is rejected and the alternate hypothesis accepted.

120

Table 4.16: ANOVA^a for Pre IFRS Period

Model Sum of

Squares

df Mean Square F Sig.

1 Regression 2526.907 8 315.863 5.140 .005^b

Residual 655.496 41 15.987

Total 3182.403 49

a. Dependent Variable: Financial Data Digit Deviation Score (FDDDS)

b. Predictors: (Constant), Digit 9 (t9), Digit 7 (t7), Digit 2 (t2), Digit 1 (t1), Digit 6 (t6), Digit 3 (t3), Digit 5 (t5), Digit 8 (t8), Digit 4 (t4)

Table 4.18: Model Summary for Post IFRS Period

Model R R Square Adjusted R Square Std. Error of the Estimate

1 .760^a .577 .260 5.902399

a. Predictors: (Constant), Digit 9 (s9), Digit 4 (s4), Digit 3 (s3), Digit 1 (s1), Digit 2 (s2), Digit 7 (s7), Digit 6 (s6), Digit 8 (s8), Digit 5 (s5)

Table 4.19: ANOVA^a for Post IFRS Period

Model Sum of

Squares

df Mean Square F Sig.

1 Regression 570.786 8 71.348 4.820 .016^b

Residual 418.060 41 10.1965

Total 988.845 49

a. Dependent Variable: Financial Data Digit Deviation Score (FDDDS)

b. Predictors: (Constant), Digit 9 (g9), Digit 4 (g4), Digit 3 (g3), Digit 1 (g1), Digit 2 (g2), Digit 7 (g7), Digit 6 (g6), Digit 8 (g8), Digit 5 (g5)

Results from tables 4.15 and 4.18- Model summaries for Pre IFRS and Pre IFRS periods show that the R² which measured the overall goodness fit of the regression model for both financial reporting regimes, recorded values of .794 and .577.

Outcome of both periods relevant ANOVA tables equally show that the equations in both situation are statistically significant (p-value of .005 and 0.016 in Pre IFRS and Post IFRS periods are less than 0.05).

Pooled result for Pre IFRS and Post IFRS financial reporting period is given below:

Table 4.21: Model Summary for Pre and Post IFRS Period

Model R R Square Adjusted R Square Std. Error of the Estimate

1 .735^a .540 .419 7.597946

a. Predictors: (Constant), Digit 9 (t9,g9), Digit 6 (t6,g6), Digit 7 (t7,g7), Digit 5 (t5,g5), Digit 8 (t8,g8), Digit 3 (t3,g3), Digit 4 (t4,g4), Digit 2 (t2,g2), Digit 1 (t1,g1)

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Table 4.22: ANOVA^a for Pre IFRS and Post IFRS Periods

Model Sum of

Squares

df Mean Square F Sig.

1 Regression 2308.261 8 288.532 4.443 .001^b

Residual 1962.778 91 21.563

Total 4271.039 99

a. Dependent Variable: Financial Data Digit Deviation Score (FDDDS)

b. Predictors: (Constant), Digit 9 (t9,g9), Digit 6 (t6,g6), Digit 7 (t7,g7), Digit 5 (t5,g5), Digit 8 (t8,g8), Digit 3 (t3,g3), Digit 4 (t4,g4), Digit 2 (t2,g2), Digit 1 (t1,g1)

Pooled results from tables 4.21 and 4.22- pooled Model summary of Pre IFRS period and the Post IFRS period as a single linear regression show that the R² .recorded values of .540. Outcome of their relevant ANOVA table equally shows that the equations in both country situations are statistically significant (p-value of .001 in both countries is less than 0.05).

However, a Chow test was further conducted to help substantiate if the two separate linear regressions for Pre IFRS period and the Post IFRS period can truly be represented as one single linear regression as depicted above seeing that the result in the pooled regression model is statistically significant (p-value which is .001 is less than 0.05).

Using the formular below, the result of the Chow test is given will be:

(RSS_p – (RSS₁ + RSS₂)) / k (RSS1 + RSS2) / (N1 + N2 – 2k)

F-critical value = 215.356926

Looking up 91 under 8 in the F-table distribution (5% significance level), the outcome reveals that the F-table value obtained is 2.02. Thus, when F-critical value is greater than the F-table value, the null hypothesis which states that ―there is no break point (different data set can be represented as one single linear regression)‖ is rejected and the alternate hypothesis accepted. Given the above result (215.35 > 2.02), we conclude that both separate models for the Pre IFRS period and the Post IFRS period cannot be represented as one single linear regression model, thus due consideration being given to them separately for the purpose of this hypothesis

122 4.2.5 Test of Hypothesis Four

Using the Mann Whitney U Test statistical tool, the hypothesis evaluated the Pre IFRS and Post IFRS financial data disclosures‘ indicators of the 8 Bemeish Predictive ratios towards understanding whether such ratios outcome differed significantly across the two reporting regime.

H₁: Ratios outcome of the test of financial data faithful representation using the Beneish Predictive model differ significantly in the pre and post IFRS financial reporting regimes of selected public listed manufacturing companies in Nigeria

Below is the result obtained from the analysis carried out:

The above chart and figure to hypothesis four clearly shows that the probability value (.105) is greater than 0.05 (p>0.05) indicating a state of significant difference.

Moreso, the Mean Rank to both financial reporting regime differed. While the Pre IFRS indicators ranked 55.20, the Post IFRS Mean Rank stood at 45.80.

Figure 4.1: Mann Whitney U test outcome to hypothesis four

123 4.2.6 Test of Hypothesis Five

Using the Mann Whitney U Test statistical tool, the hypothesis comparatively evaluated the Implications of the Benford‘s law digital analyses of the pre and post IFRS financial reporting practices of selected Nigerian manufacturing companies

H₁: Implications of the Benford‘s law digital analyses of the pre and post IFRS financial reporting practices of selected Nigerian manufacturing companies differ significantly.

Below is the outcome of the relevant analysis carried out:

The above chart and figure 4.2 to hypothesis five clearly shows that the probability value (p-value) = .111 is greater than 0.05. Besides, the Mean Rank for both reporting regimes does not differ significantly. Analysis Mean outcome from the Pre IFRS financial reporting regimes ranked 45.88 while that of the Post IFRS regime ranked 55.12.

Figure 4.2: Mann Whitney U test outcome to hypothesis five

124 4.2.7 Test of Hypothesis Six

The Mann Whitney U Test statistical tool was also used to test hypothesis seven towards understanding whether the outcome (integrity scores) of Beneish model analysis executed on the financial data of pre-IFRS and post-IFRS Financial Statements of selected Nigerian manufacturing companies differed.

Below is a detailed outcome of the extensive analysis executed using Mann Whitney U Test statistical tool:

Screening through chart and figure 4.4, evidence shows that the probability value (p-value) = .124 is greater than 0.05. Besides, the Mean Rank for both periods does not differ significantly. The Mean score of Nigeria‘s post-IFRS financial reporting practices (2012 – 2016) ranked 46.04 while those of her pre-IFRS financial reporting periods (2007 – 2011) ranked 54.96.

Figure 4.3: Mann Whitney U test result to hypothesis six

125 4.3 DISCUSSION OF ANALYSES RESULTS

This section makes extensive effort at interpreting and discussing the relevant findings made by this study which is based on relevant analyses earlier carried out in section 4.2.

4.3.1 Benford’s Law is significantly effective in evaluating the faithful