Two-way
mixed design ANOVA compares the means of two or more independent variables (Field,
2013). It involves a fixed effects factor (between-subjects factor) and a random
effects factor (within-subjects factor) (Seltman, 2009).

This research
investigates the effect of two independent variables, anxiety level and armed
or unarmed offenders, on one dependent variable, number of shots. The aim is to
find out whether anxiety helps people in handling stress. If anxiety helps
people to deal with stress, then the hypothesis should be when anxiety
increased, the shooting accuracy increased, that is, the armed offender will
receive more shots.

The
between-subjects factor of this research is the level of anxiety and has two
levels, low level of anxiety and high level of anxiety. The within-subjects factor
also has two levels, whether the offenders are armed or unarmed.

This
design will present the result of two groups; the low level of anxiety (the
control group) and the high level of anxiety. 
Each group will contain the number of shots at armed and unarmed
offenders. By assessing the result of the two groups will demonstrate whether
participants are more accurate with higher anxiety level.

Q2.

Firstly, normality of both the between- and within- groups
should be assessed. This can be done via the histogram or the Normal Q-Q plot. Additionally,
the Shapiro-Wilk Test (sample size < 50), the Kolmogorov-Smirnov Test, or the Z-test can also be used to test for normality (Field, 2013). If normality is violated, the F-statistic of ANOVA is still quite robust provided that the group sizes are equal (Donaldson, 1968) and the degree of freedom is at least 20 degrees (Lunney 1970). Secondly, homogeneity of variances means that the variance of each set of data should be approximately equal and is normally tested by Levene's test (Field, 2013). This assumption should be met for between-groups analysis. If it is violated, the Welch and Brown-Forsythe tests and then a post hoc test of Games-Howell can be used. Lastly, sphericity assumes the level of dependence between the groups is approximately the same (Field, 2013). Sphericity is assessed using the Mauchly's test for within-groups with three or more levels. For this research design, the within-group variable only has two levels (armed and unarmed) and sphericity can be ignored.  However, if sphericity is violated, the Bonferroni method can be used (Field, 2013).   Q3. Univariate Tests is one of the simple effects analysis for two-way ANOVA. It offers two tests. In this case, the first test compares the mean shots between the two groups (low anxiety and high anxiety) at unarmed offender. The second test compares the mean shots between the two groups at armed offenders. If the p-value < .05 means that the mean shots between the two groups are significantly different. However, this figure does not tell us the direction of the difference, that is, which group is higher and which is lower. This information can be obtained from the plot.  The graph will show which group is higher and which is lower (Monash University, 2018a). The other method is the pairwise comparisons, which is used for assessing the interaction effect (Monash University, 2018b). Multiple pairwise comparisons performed at the level of the interaction could determine which group differences are statistically significant (p < .05). It computes a p-value for each pair of between-groups levels. The number of pairs of factor levels to be compared depends on the research design. Pairwise comparison is only applicable when there are three or more between-groups levels, therefore, not applicable here (Monash University, 2018a).

Two-way
mixed design ANOVA compares the means of two or more independent variables (Field,
2013). It involves a fixed effects factor (between-subjects factor) and a random
effects factor (within-subjects factor) (Seltman, 2009).

This research
investigates the effect of two independent variables, anxiety level and armed
or unarmed offenders, on one dependent variable, number of shots. The aim is to
find out whether anxiety helps people in handling stress. If anxiety helps
people to deal with stress, then the hypothesis should be when anxiety
increased, the shooting accuracy increased, that is, the armed offender will
receive more shots.

The
between-subjects factor of this research is the level of anxiety and has two
levels, low level of anxiety and high level of anxiety. The within-subjects factor
also has two levels, whether the offenders are armed or unarmed.

This
design will present the result of two groups; the low level of anxiety (the
control group) and the high level of anxiety. 
Each group will contain the number of shots at armed and unarmed
offenders. By assessing the result of the two groups will demonstrate whether
participants are more accurate with higher anxiety level.

Q2.

Firstly, normality of both the between- and within- groups
should be assessed. This can be done via the histogram or the Normal Q-Q plot. Additionally,
the Shapiro-Wilk Test (sample size < 50), the Kolmogorov-Smirnov Test, or the Z-test can also be used to test for normality (Field, 2013). If normality is violated, the F-statistic of ANOVA is still quite robust provided that the group sizes are equal (Donaldson, 1968) and the degree of freedom is at least 20 degrees (Lunney 1970). Secondly, homogeneity of variances means that the variance of each set of data should be approximately equal and is normally tested by Levene's test (Field, 2013). This assumption should be met for between-groups analysis. If it is violated, the Welch and Brown-Forsythe tests and then a post hoc test of Games-Howell can be used. Lastly, sphericity assumes the level of dependence between the groups is approximately the same (Field, 2013). Sphericity is assessed using the Mauchly's test for within-groups with three or more levels. For this research design, the within-group variable only has two levels (armed and unarmed) and sphericity can be ignored.  However, if sphericity is violated, the Bonferroni method can be used (Field, 2013).   Q3. Univariate Tests is one of the simple effects analysis for two-way ANOVA. It offers two tests. In this case, the first test compares the mean shots between the two groups (low anxiety and high anxiety) at unarmed offender. The second test compares the mean shots between the two groups at armed offenders. If the p-value < .05 means that the mean shots between the two groups are significantly different. However, this figure does not tell us the direction of the difference, that is, which group is higher and which is lower. This information can be obtained from the plot.  The graph will show which group is higher and which is lower (Monash University, 2018a). The other method is the pairwise comparisons, which is used for assessing the interaction effect (Monash University, 2018b). Multiple pairwise comparisons performed at the level of the interaction could determine which group differences are statistically significant (p < .05). It computes a p-value for each pair of between-groups levels. The number of pairs of factor levels to be compared depends on the research design. Pairwise comparison is only applicable when there are three or more between-groups levels, therefore, not applicable here (Monash University, 2018a).