1. MANG6322 FOUNDATIONS OF RESEARCH IN ACCOUNTING AND FINANCE 2017/18
Week 6 – 07, 08 Mar 2018:
Quantitative research methods 2
Student learning activities [Weeks 5 & 6]:
Exercise 1 – with suggested solution.
Exercise 2 – with suggested solution.

2. Weeks 5 & 6: Student learning activities
Exercise 1: Based on real data from an anonymous research project
Purpose of exercise 1 – opportunity to exercise:
Importing data into SPSS.
The use of SPSS to calculate descriptive statistics, test hypothesised similarities/differences, and associations/correlations between variables, and perform an ordinary least squire (OLS) regression analysis to test hypotheses.
Interpreting the results of quantitative analysis using SPSS outputs in (2).

3. Exercise 1: Task to perform
Import the data set Exercise 1 MANG_6322_Excel_Datafile.xls into SPSS.
Calculate the basic descriptive statistics
(i) For each variable, and
(ii) What do the statistics tell you? – statistical interpretation
Test the no difference and no association hypotheses
(i) The differences in the variables of interest (IVs) between December year-end and ‘other’ companies.
(ii) Examine potential relations between variable
(ii) Statistical interpretation of (i) and (ii)
OLS regression analysis
(i) to test the relationship between the assumed DV (Market value of equity) and other variables
(ii) statistical interpretation and conclusions:
On the hypotheses
suitability of using OLS to test them?

4. Import data set into SPSS
SPSS has 3 windows:
Data Editor
Viewer or Draft Viewer which displays the output files
Syntax Editor, which displays syntax files
The Data Editor has two parts:
Data View window
Displays data from the active file in spreadsheet format
Variable View window
Displays metadata or information about the data in the active file,
e.g. variable names/labels, value labels, formats, and missing value indicators.
Data Entry into SPSS – Two ways
Directly enter in to SPSS by typing in Data View
Enter into other database software such as Excel then import into SPSS

5. (a) Import data set into SPSS
In SPSS, go to:
File  Open  Data
Select Type of file (e.g. Excel) you want to open
Select File name you want to open
(a) Import data set into SPSS

6. (b) Descriptive statistics and examination of potential relationships
Key questions.
NOTE – PAT = Profit after Tax = EAT = Earnings after Tax
What are the main features of the data?
Can sample statistics (e.g. mean/SD) be representative of the population?
Check Indicators of data normality and choice of data analysis methods
Do the data indicate the hypothesised relationships?
1. Minimum, Maximum, and Std. Deviation
indicates normality issues
Larger ranges/SDs are signals of normality problems in the variable

7. (b) Descriptive statistics – exploring normality of data distribution
Kurtosis is a more peaked distribution than ‘normal’
positively skewed (most observations are at lower end of the range)

8. (b) Descriptive statistics: testing normality of data distribution
2. Skewness and kurtosis statistics
Testing the significance of H0 of No skewness/Kurtosis (S/K)
Compute Z-score of the stat. = stat./SE, if > 1.96, the effect of S/K is statistically significant (at p-value of 0.05), hence reject H0
e.g. SALES = /0.152 = , hence reject H0 – Therefore SKEWED!!

9. (b) Descriptive statistics – Testing for normality
3. Statistical tests of normality
Test H0 = sample is normally distributed
Kolmogorov-Smirnov
Shapiro-Wilk
If p-value for the test is significant (i.e. Sig. ≤ 0.05), then
reject H0 – i.e. the distribution of the variable deviates from normality.
Confirms the statistical significance of the skewness/Kurtosis

10. (b) Descriptive statistics – Testing for normality
In SPSS, go to:
Analysis  Descriptive Statistics , Explore, and
Move SALES & MV into Dependent List
Under Statistics: Select Descriptive with 95% CI for mean (-continue)
Under Plots: Select Normality plots with tests & Histograms (-continue)
Click OK for the output
Testing: H0 of No skewness/Kurtosis
Caution:
Very sensitive to sample size
At this level, sample size of n=, > 30 – can assume normality

11. (c) Inferential statistics – similarities and differences
Key question:
Is there a difference in the variable of interest between two groups?
H0 = there is no difference between the two groups
t-test (parametric data), Mann-Whitney test (non-parametric)
In SPSS, go to:
Analysis  Compare Means  Independent-Samples T-Test (Paired-Sample T-Test), and
Move All variables of interest into Test variable(s) and Grouping Variable boxes, then
Click the Define Groups to identify the two groups.
1 = December year-end companies
0 = other companies
Click OK for the output

12. (c) Inferential statistics – similarities and differences
Required:
Test the difference in means between DEC-DUM and other companies
H0 = there is no difference between the two groups

13. (c) Inferential statistics – independent samples t-test
Look First: the Levene’s Test for Equality of Variance
Levenes’s test
Tests homogeneity of variance assumption
A required t-test assumption
H0 = sample variances (SD) are the same (stat. sig.)

14. (c) Inferential statistics – independent samples t-test
Levenes’s test – Sales?
F-value = 1.390, Sig. = 0.240
F-value (small), Sig. > .05 (i.e. not stat. sig)
Do not reject H0, SD are the same!
Continue interpreting t-test
If Sig. <, = 0.05, Reject H0, SDs are not the same (sampled from different populations?)
Problem in interpreting the t-test
Use equal variances not assumed

15. (c) Inferential statistics – independent samples t-test
t-test for equality of Means – SALES?
t-value = 0.704, df = 256, Sig. = 0.482
Sig. > .05 (not stat. sig), Not able to reject the H0 that means are the same
Results are the same even when equal variances are not assumed (because SD are the same!)
If Sig. <,= 0.05, Reject H0 of No differences between the means
Differences in means between Dec-year-end and others are not by chance (95% confidence)

16. (c) Inferential statistics – independent samples t-test
Other statistics
Mean difference between groups
SE associated with mean difference
Confidence interval of the difference
NOT COMMONLY REPORTED IN RESULTS

17. (c) Testing for differences – Non-parametric

18. (c) Examination of potential relationships between variables:
Any indication of the hypothesised relationship between Independent and dependent variables?
Any indication of data multicollinearity ? (association between independent variables?)
In SPSS, go to:
Analysis  Correlate  Bivariate, and
Move All variables of interest into Variables
Under Correlation Coefficient: Select Pearson (Parametric data)
Under Test of Significance: Select Two-tailed (because the direction of association is not known in advance)
Select: Flag significant correlations
Under Options – Missing Values: Select Exclude cases pairwise
Click OK for the output

19. (c) Examination of potential relationships
Measures of collinearity – IVs correlation
Tolerance
% of variance in IV, not accounted by other IVs
1 – R2, 0.2 or less is commonly considered problematic
Variance Inflation Factor (VIF)
Degree to which std errors are inflated by collinearity
The reciprocal of Tolerance = 1/(1 – R2),
VIF of 5 or more - problematic

20. (d) Inferential statistics – testing of hypotheses Key question:
Is there a relationship between the dependent variable (DV) and several independent variables (IVs) as suggested by existing theory/theories (and as deduced in the hypotheses)?
H0 = there is no relationship between DV and the IVs
OLS regression (parametric data), Logistic regression (non- parametric)
Research question: What variables in a financial report are associated with (predict) market value of equity?
Remember: the hypotheses/regression model to be tested in order to answer this research question should not include the variable PAT because we already know that the correlation between PAT and MV is not significant.

21. (d) Inferential statistics – testing of hypotheses
Given the research question and the data-set Exercise 1 MANG_6322_Excel_Datafile.xls, we can state the following hypotheses
Hypothesis 1: Sales revenue is positively associated with market value of equity. Hypothesis 2: Research and development expenditure is positively associated with market value of equity. Hypothesis 3: Dividend paid/declared is positively associated with market value of equity. Hypothesis 4: Audit fees is positively associated with market value of equity. Hypothesis 5: Book value of equity is positively associated with market value of equity. Hypothesis 6: Non-audit services fees is positively associated with market value of equity.

22. (d) Inferential statistics – testing of hypotheses
The formal expression of the regression equation is:
y = β0 + β1x β6x6 + ε
Where:
y is the dependent variable; firm’s market value of equity (MV) as measured in a stock exchange
x x6 are the 6 independent variables.
β0 is the constant.
β β6 are the coefficients for x x6 respectively
ε is the error term

23. Performing a multiple linear regression analysis
Assuming our data meets the assumptions of a linear equation (see Collis and Hussey, 2014, p. 282), then we use the following SPSS procedures.
SPSS procedures
Select Analyse  Regression  Linear …
Move the dependent (outcome) variables into Dependent and the independent (predictor) variable(s) into Independent.
If we have theoretical reasons for choosing the predictor variables (i.e. our hypotheses are based on theory), accept the default method, ‘enter’, which means the variables will be entered simultaneously as one block.
Click on the Options button and under Statistics and Plots, and select any additional statistics we want to help us assess the fit of the model to the data and click continue.
Click OK for the results.

24. (d) Interpreting the OLS regression results: SPSS output – 1
Report Adj. R2
Proportion of total variability in MV that is explained by the IVs
Large differences between R2 and Adj. R2 signals redundant IVs
Nagelkerke R2 for Logistic regression

25. (d) Interpreting the OLS regression results: SPSS output – 2
Report F-Value
H0 = Model has no explanatory power
i.e. all the IV coefficients are zero, and IVs do not help to predict the DV
Reject or not reject H0 look the p-value (Sig.)
Sig. < 0.05, REJECT H0
Hosmer and Lemeshow test (Logistic regression)
H0 = observed frequencies (actual counts) are not associated with expected frequencies (theoretical counts)
Rejecting H0 means there is good fit between data and model

26. (d) Interpreting the OLS regression results: SPSS output – 3
Measures of collinearity – are IVs correlated?
Tolerance
% of variance in IV, not accounted by other IVs
1 – R2, 0.2 or less is commonly considered problematic
e.g. Sales, DIV and AF
Variance Inflation Factor (VIF)
Degree to which std errors are inflated by collinearity
The reciprocal of Tolerance = 1/(1 – R2),
VIF of 5 or more - problematic

27. (d) Interpreting the OLS regression results: SPSS output – 4
Most important – the significance of each coefficient
Relationship between IV and DV
Null for t-statistic, H0 = the coefficient for the respective IV is zero
The IV does not help to predict the MV
Assess the significance of each IV
t-statistic and related p-value
All IV are Sig. < 0.05, REJECT H0 (IVs are not zero)

28. (d) Interpreting the OLS regression results: SPSS output – 5
Unstandardised Coefficients (B)
Does the sign make sense?
Does theory suggests negative or positive relationship?
Interpretation of the coefficient
e.g. more AF or NAS expenses reduces the MV, holding other IV constant
£1 increase in AF is associated with £1, decrease in MV

29. (d) Interpreting the OLS regression results: SPSS output – 6
Standardised Coefficients (Beta)
Measures the sensitivity of the DV to changes in the IV
e.g. for a 1 SD increase in DIV, the model predicts that MV will increase by by (48%)
Indicates which one of the IVs is more important than others

30. Weeks 5& 6: Student learning activities (contd
Weeks 5& 6: Student learning activities (contd.) Exercise 2: Based on real data used in Collis and Hussey (2009; 2014, Chapters 11 & 12)
Purpose of exercise 2 - opportunity to exercise the use of SPSS to perform the following quantitative data analysis:
Tests of differences between two independent samples.
Tests of association/correlation between quantitative variables.
Run a multiple regression analysis to test a number of hypotheses.
Interpret the results of quantitative data analysis using the SPSS outputs in 3 above.

31. Exercise 2 Study Background Purpose of the study:
Some companies qualified for audit exemption; but decided to continue having their accounts audited.
Commissioned by the UK government (Collis, 2003)
Purpose of the study:
To assess the impact on take-up levels of audit exemption, of a proposal to raise the UK turnover threshold for audit exemption from £1m to £4.8m.
To identify the factors that have significant influence on the directors’ decision regarding a voluntary audit

32. Exercise 2 Research Question:
Literature review - empirical & theoretical:
Size Factors
Emphasis on turnover in company law implied a relationship between firm size and cost/benefit of audit, and directors’ decision to have a voluntary audit.
Agency factors
Agency Theory (Jenson and Meckling, 1976)
audit would be required where there is information asymmetry between ‘agents’ (e.g. directors), and principals (e.g. external shareholders)
In small firms, principals may include lenders and/or creditors
Management factors
Audit increases the quality of the information in the accounts
Audit acts as an independent check on internal controls to reduce the chance of material error
educational profile may be a proxy for formal knowledge of the costs and benefits of the audit
Research Question:
What are the factors that have a significant influence on the demand for the audit among companies with a maximum turnover of £4.8m?

33. Exercise 2: Box 12.1 Hypotheses to be tested
Size Factors
H1 Voluntary audit (VA) is positively associated with turnover.
Management Factors
H2 VA is positively associated with agreement that the audit provides a check on accounting records and systems.
H3 VA is positively associated with agreement that it improves the quality of the financial information.
H4 VA is positively associated with agreement that it improves the credibility of financial information.
H5 VA is positively associated with agreement that it has a positive effect on the credit rating score.
H6 VA is positively associated with the directors having qualifications or training in business or management.
Agency Factors
H7 VA is negatively associated with the company being family-owned.
H8 VA is positively associated with the company having shareholders without access to internal financial information.
H9 VA is positively associated with demand from the bank and other lenders.

34. Exercise 2: Variable definition and measurement
Definition/Description
Measurement
Hypothesis
Expected Sign
VOLAUDIT
Whether company would have a voluntary audit
1 = Yes
0 = No
TURNOVER
Turnover in 2002 accounts £k H1 +
CHECK
Audit provides a check on accounting records and systems
5 = Agree …
1 = Disagree H2
QUALITY
Audit improves the quality of the financial information H3
CREDIBILITY
Audit improves the credibility of the financial information H4
CREDITSCORE
Audit has a positive effect on the credit rating score H5
EDUCATION
Whether respondent has degree/qualifications/training H6
FAMILY
Whether company is wholly family-owned H7 _
EXOWNERS
Whether company has external shareholders H8
BANK
Whether statutory accounts are given to bank/lenders H9

35. Exercise 2: Research Design
Research methodology:
Survey
Method of data collection
Data collection instrument
Postal questionnaire (see C&H, p. 229)
Strategy to deal with non-response: used government logo and sent one reminder and
Sampling method
Population: Fame database, contains data from the annual report and accounts of 2.8m companies in UK and Ireland.
Sampling frame: 2,633 companies with registered accounts for and did not exceed £4.8m turnover, £2.4m balance sheet total and 50 employees (proposed higher thresholds)
Sample: 790 companies = 30% response rate (high rate due to permission to use government logo)
Method of data analysis
Descriptive and inferential statistics (e.g. Mann-Whitney Tests, and Logistic regression analysis)

36. Exercise 2: Required Test the no difference hypothesis - (b)(i)
H0 – there is no difference between voluntary audit companies and non-voluntary audit companies, in relation to – TURNOVER, CHECK, QUALITY, CREDIBILITY and CREDITSCORE.
Test the no association hypothesis - (c)(i)
H0 - there is no association between VOLAUDIT and FAMILY, EXOWNERS, BANK and EDUCATION.
Test the no correlation hypothesis – (c)(ii)
H0 - there is no correlation between any two of the following variables (TURNOVER, CHECK, QUALITY, CREDIBILITY and CREDITSCORE)
Perform a multiple regression analysis (d)(i)
DV – VOLAUDIT
IVs - TURNOVER, CHECK, QUALITY, CREDIBILITY, CREDITSCORE, FAMILY, EXOWNERS and BANK.
Interpret the results and conclude
Answers: Please read Collis & Hussey (2014, pp )

37. Summary of what to present and how to interpret results of OLS regression analysis
Model summary:
Report Adjusted R2.
Proportion of total variability in a DV that is explained/predicted by IVs (i.e. explanatory/predictor variables).
ANOVA:
Report F-value and related p-value.
If F-value is not significant, then there is no need to continue because it indicates all Bs are Zero, and no IV that predicts the DV in the model.
Coefficients:
Report t-statistic and related p-value.
Coefficients (Bs) – does the signs make sense? – Theory?
Standardised beta – indicate importance of Bs.
Overall interpretation:
Hypotheses rejected/not rejected?
Link to existing empirical literature.

38. REMEMBER! Diagnostic Statistics
Helps to establish whether the required conditions/assumptions of the adopted statistical test/technique have been met or breached
For example – does the data meet the assumptions of an OLS regression technique?
normality of data for all variables
normality of residuals
no significant multicollinearity between independent variables (as measured by tolerance >,= 0.2, VIF <,= 5)
Homoscedasticity – homogeneity of error variances
minimal outliers – scatter plot

39. End - Week 6 Topics Student learning activities [Weeks 5 & 6]:
Exercise 1 – with suggested solution.
Exercise 2 – with suggested solution.