Questionnaire: Quantitative analysis

Research Question 1 investigated Greek-Cypriot EFL learners’ attitudes towards error- related issues, and the relationship between learners’ attitudes and other individual difference concepts. These questions were approached via quantitative inquires, and the analysis of the questionnaire operated the use of statistics with the IBM SPSS Statistics 23 software.

Firstly, before performing any statistical tests, I checked the missing values of all the different variables from the student questionnaire, and I found that none of the variables with missing values achieved more than 5% of the total case distribution. Therefore, the missing values were not imputed before performing the statistical tests to avoid bias. Secondly, the implementation of statistical analysis required me to test my sample for violations of the assumptions of the statistical tests that I was planning to perform.

The levels of measurement of variables which were represented by the relationship between what was being measured, and the number that it was being represented by, were the criteria determining the choice of the statistical tests that were performed (Connor- Linton, 2010; Field, 2013). The questionnaire had categorical, ordinal, and continuous items, which were measured at the nominal, ratio, and interval level respectively. For different quantitative inquiries, different statistical tests were performed, according to the levels of measurements of the variables in question. Nominal variables represented items for which the number was the name of the category, whereas ordinal variables used numbers to indicate ranks. Normal arithmetic operations could not be operated with ranks because they did not have a quantitative content, namely the rank scale did not have equal intervals. In contrast, for continuous variables, the number represented a quantity which could be manipulated, since equal intervals on a scale represented equal intervals on what was being measured (Field, 2013).

In order to discover students’ attitudes towards error production and CF, I performed descriptive statistics. The questionnaire items that related to these attitudinal dimensions were represented by variables which were measured at the nominal and ratio levels, therefore frequencies and multiple response frequencies were performed (Pallant, 2011). In Table 3.3, the categorical and the ordinal questionnaire items are listed. As is evident in the Table, attitudinal dimensions measuring error production and error correction included both nominal and ordinal items, whereas dimensions assessing affective responses to CF, as well as attitudes towards different CF types were represented by ordinal variables.

NOMINAL VARIABLES ORDINAL VARIABLES Error production

Section C – item 1: oral error production, item 2: written error production, item 3: reasons for error production, item 4: L1 knowledge helps

-

CF -

Section C – question 7: items 1-5: degree of correction, question 8 items 1-4: degree of correction for different error types Affective responses to CF

- Section C – question 6: items 1-8 CF types

- Section C – question 9: items 1-8

Table 3. 3: Nominal and ordinal dependent variables measuring attitudes towards error- related issues.

In addition to descriptive statistics, I performed inferential statistics to test specific hypotheses. In particular, I run the following tests: chi-square tests for goodness of fit, chi-square tests for independence, binary logistic regressions, and ordinal logistic regressions.

Firstly, for the investigation of students’ attitudes towards error-related issues I performed chi-square tests for goodness of fit to test the following null hypothesis: Ho = Oi = Ei,

i.e. students’ responses were equally spread across the yes/no options of a statement. The null hypothesis was tested as opposite to the alternative hypothesis: Ha = Oi ≠ Ei, i.e.

students’ responses were not equally spread across the yes/no options of a statement. An

alpha level (α) of .05 was set as the cutoff of the probability value to test the statistical

significance for all tests (Rumsey, 2010). The current sample met the assumptions for a chi-square for goodness of fit test, which requires one categorical variable, the expected frequencies in each group of categorical variables to be at least five, and to have independence of observations (Pallant, 2011). I performed chi-square tests for the variables that were measured in frequencies, but not for the items that were measured in multiple response frequencies, because the later violates the assumption of independent responses in chi-square tests (Laerd statistics, 2015).

Moreover, I performed post-hoc pairwise binomial tests for all variables in order to test all possible pairs of the response categories. Due to the fact that there were five response categories for each variable, I performed ten pairwise tests for each variable. Since the response items were based on five-point Likert-type scales, I tested the following combinations: one with two, one with three, one with four, one with five, two with three, two with four, two with five, three with four, three with five, and four with five. Each number represented the agreement, frequency, or evaluation items on the Likert-type items. To test the significance of the tests, I applied the Bonferroni correction to control for Type I error (Pallant, 2011). Hence, the alpha level (α) was set to .005.

Moreover, the investigation of the relationship between students’ attitudes and other individual differences required the operation of inferential statistics. The statistical tests that were performed tested the impact of a set of predictors i.e. independent variables, on the variables that were to be predicted or explained i.e. dependent variables. In particular, I followed the traditional approach, thus I tested the null hypothesis: Ho = no relationship

between X and Y, which stated that there was no relationship between the independent

and the dependent variables. In contrast, the alternative hypothesis: Ha = X and Y are

related, claimed that there was a relationship between the independent and the dependent

variables (Sheskin, 2011; Creswell & Creswell, 2018).

Depending on the combinations of independent and dependent variables and their levels of measurement (Table 3.3), different analytical procedures were followed. Due to the fact that the dependent variables were either nominal or ordinal, I chose to perform

logistic regressions. Logistic regressions allowed me to test the probability that certain

outcomes were based on one or more independent variables. In other words, I was able to test which of my regression models, and specific independent variables, had a statistically significant effect on my dependent variables. Binary/binomial logistic regressions were performed when the dependent variables were nominal and dichotomous. Moreover, ordinal logistic regressions were performed when the dependent variables were ordinal (Laerd statistics, 2015).

One of the assumptions of the binary logistic regression is that there should be no significant outliers and high leverage points. Moreover, an assumption of the ordinal logistic regression is that there should be no proportional odds (Pallant, 2011). These assumptions are documented were relevant in the findings, in Chapter 4. Moreover, the logistic regression models were tested for multicollinearity, and the details are presented in section 3.4.4 Models and multicollinearity. In the next section, I explain how the ordinal variables were recoded before creating the new Likert scales of independent variables.