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For data that exhibited a normal distribution, parametric tests were employed. For non- normally distributed data, equivalent non-parametric tests were chosen. Some authors such as Lix, Keselman and Keselman (1996) assert that parametric tests such as ANOVA

(analysis of variance) are not particularly sensitive to departures from normality, especially at larger sample sizes (McDonald, 2014) and where the group sizes are equal (Laerd Statistics, 2016). For this reason, for some of the key tests, especially where the histograms appeared to be broadly similar, a parametric test was used to support the findings of the non-parametric alternative.

Parametric Tests

Independent Samples t-test

A t-test is used in hypothesis-testing when examining the differences between groups on one or more variables. When there are two groups be included, and the participants are not being tested more than once, a t-test for independent samples is indicated. (Hawkins, 2014)

The test has six assumptions:

1. There is one dependent variable that is measured at the continuous level, (i.e. numeric and on a scale that can be infinitely divisible).

2. There is an independent variable that consists of two groups

3. There is independence of observations (i.e. no relationship between the groups, different participants in each group).

4. There should be no extreme outliers in each group regarding the independent variable.

5. The dependent variable should follow a normal distribution

6. The variance of the dependent variable is homogenous (i.e. the same for both groups).

The aim of the t-test is to determine whether any differences between the sample means reflect a difference in the population that the samples represent. The findings may be

generalisable and inferences can be made about the population being tested (Donnelly, 2007).

One-Way Analysis of Variance (ANOVA)

This test is used to determine whether there are any statistically significant differences between the means of more than two samples (Hawkins, 2014). The test has what is known as an omnibus test-statistic, in that it can only detect a difference between groups. It cannot specifically identify which groups were different. However, post hoc (follow-up) tests can be performed to make this discrimination. ANOVA makes six main assumptions:

1. There is one independent variable, measured at the continuous level 2. There is one dependent variable that consists of more than two categorical,

independent groups.

3. There is independence of observations

4. There should be no extreme outliers in each group in terms of the independent variable.

5. The dependent variable should follow a normal distribution

6. The variance of the dependent variable is homogenous (i.e. the same for all groups).

The ANOVA test is used to determine whether any differences between groups can be attributed to sample error alone rather than variance caused by the independent variable. (Laerd Statistics, 2016)

Pearson’s Correlation Test

Pearson’s correlation was used to measure the strength and direction of any association between any two continuous variables. The test makes the following assumptions (Hawkins, 2014):

1. There are two variables measured on a continuous scale 2. The variables are paired

3. There is a linear relationship between variables 4. There are no significant outliers

5. There should be bivariate normality

Pearson’s correlation coefficient (r) has a range of values from -1 representing a perfect negative linear relationship between variables, to +1 where there is a perfect positive linear relationship. A value of 0 indicates no relationship.

Non - Parametric Tests Kruskal-Wallis Test

The Kruskal-Wallis test is considered to be a non-parametric equivalent of the One-way ANOVA, used when data do not meet the normality assumption required. This test makes four main assumptions (Hawkins, 2014; McDonald, 2014):

1. There is one dependent variable measured at the continuous or ordinal level 2. There is one independent variable consisting of two independent groups or

categories

3. There is independence of observations

It may be used to test for differences between groups, between conditions, or between change scores. The Kruskal-Wallis test is appropriate for this study when testing for a difference between learners when grouped by the screen size of their devices.

Mann-Whitney U test

The Mann-Whitney U test was formerly known as the Wilcoxon Rank Sum test and provides an alternative to the t-test. It is used when the data are not paired, and the data do not follow a normal distribution (Hawkins, 2014). It may be used to test for differences between groups, between conditions, or between change scores. This makes the Mann- Whitney test appropriate for this study where two independent groups were tested under different conditions and a difference in the change between pre and post-test scores was measured between groups. This Mann-Whitney U test makes four main assumptions:

1. There is one dependent variable measured at the continuous or ordinal level 2. There is one independent variable consisting of two independent groups or

categories

3. There is independence of observations

4. The data from each group should have a similar distribution (same shape)

The test was chosen as it is thought to offer stronger evidence than other non-parametric tests because it compares the distribution of the samples as well as the medians. Conroy (2012) states that strictly-speaking, the test should not be described as “non-parametric” because it calculates a parameter; namely the Mann-Whitney test statistic. This can be useful in clinical trials, as a measure of effect size when measuring scales that are not interval. Conroy gives examples such as measuring moods and attitudes. The Mann- Whitney U test was, therefore, appropriate for analysing the NASA TLX data collected in this study. The test employs different computations depending upon the sample sizes used and the normality of the distribution of the values in each sample. For smaller

sample sizes (such as found in the smartphone (n=36) and tablet-learner (n=25) groups) the test calculates a u-statistic. For large sample sizes (such as found in the control group (n=65) and experimental group (n=65) the value of U approaches a normal distribution and a z-test may be used.

Spearman’s Correlation

Spearman’s correlation was used to measure the strength and direction of any association between any two variables. The test makes the following assumptions (Hawkins, 2014):

1. the variables can be measured on a continuous, or ordinal scale

2. there are paired observations, namely that a single participant will be affected by the score of two variables, for example, performance and pre/post-test result 3. there is a monotonic relationship between variables, namely that one variable

increases (or decreases) with the other.

Spearman’s correlation was used in preference to Pearson’s correlation where the data were not normally distributed.

Shapiro-Wilk’s Test

The Shapiro-Wilk’s test (1965) can detect departures from normality due to Skewness and Kurtosis (Razali and Wah, 2011) Skewness describes an asymmetry between the tails of the Gaussian curve, Kurtosis refers to the shape of the peak. Salkind (2008), explains that a peak having a taller, sharper profile than a normal distribution is described as

leptokurtic, and a peak having a flatter profile as platykurtic. Kurtosis, in turn, relates to the number of non-typical values seen in data-points from outliers as these will affect the thickness (height) of the tails. A Shapiro-Wilk test was therefore performed on all of the data to determine normality.