# Analyzing Data Using Two-Way ANOVA- SPSS Statistics Sample

QUESTION

In the given data set you will notice that this dataset contains three variables: Country (1 = Argentina; 2 = Brazil), Sex (1 = Male; 2 = Female) and Life satisfaction (1 = Dissatisfied…10 = Satisfied). Choose the appropriate test to inform whether there are any significant differences in life satisfaction between Brazilians and Argentinians and between men and women. Report all the descriptive statistics and assumptions tests.
write interpretation in below style:
The study investigated the effect of easy and difficult statistics activities in the first and last week of term on students’ statistics anxiety. First, parametric assumptions were tested. Then, a repeated-measures factorial ANOVA showed a significant main effect of difficulty of the statistics activity: F(1, 9) = 15.31, p = .004, ηp 2 = .630; a significant main effect of the week of the term: F(1, 9) = 18.16, p = .002, ηp 2 = .669; and a significant two-way interaction: F(1, 9) = 10.55, p = .010; ηp 2 = .540.
 Country Sex LifeSatisfaction Country: 1 = Argentina; 2 = Brazil 1 1 7 Sex: 1 = Male; 2 = Female 1 1 7 1 1 5 1 1 9 1 1 5 1 1 6 1 1 8 1 1 4 1 1 8 1 1 9 1 1 6 1 1 9 1 1 8 1 1 10 1 1 7 1 1 9 1 1 4 1 1 7 1 1 2 1 1 9 1 1 3 1 1 3 1 1 8 1 1 5 1 1 5 1 1 7 1 1 10 1 1 7 1 1 1 1 1 8 1 1 4 1 1 7 1 1 10 1 1 7 1 1 1 1 6 1 1 7 1 1 10 1 1 5 1 1 10 1 1 9 1 1 8 1 1 7 1 1 8 1 1 5 1 1 6 1 1 6 1 1 10 1 1 1 1 1 4 1 2 6 1 2 5 1 2 6 1 2 8 1 2 6 1 2 5 1 2 2 1 2 8 1 2 6 1 2 8 1 2 5 1 2 7 1 2 2 1 2 3 1 2 10 1 2 5 1 2 7 1 2 7 1 2 5 1 2 8 1 2 6 1 2 10 1 2 9 1 2 7 1 2 6 1 2 5 1 2 5 1 2 7 1 2 10 1 2 10 1 2 8 1 2 5 1 2 10 1 2 3 1 2 7 1 2 5 1 2 5 1 2 2 1 2 10 1 2 3 1 2 8 1 2 5 1 2 10 1 2 8 1 2 8 1 2 5 1 2 7 1 2 7 1 2 5 1 2 4 1 1 6 1 1 10 1 1 8 1 1 9 1 1 5 1 1 10 1 1 5 1 1 9 1 1 6 1 1 7 1 1 7 1 1 8 1 1 7 1 1 7 1 1 7 1 1 10 1 1 8 1 1 5 1 1 10 1 1 6 1 1 7 1 1 10 1 1 8 1 1 5 1 1 7 1 1 8 1 1 9 1 1 9 1 1 6 1 1 4 1 1 9 1 1 9 1 1 6 1 1 8 1 1 8 1 1 10 1 1 8 1 1 3 1 1 7 1 1 7 1 1 5 1 1 10 1 2 8 1 2 7 1 2 8 1 2 10 1 2 10 1 2 10 1 2 10 1 2 8 1 2 2 1 2 8 1 2 8 1 2 8 1 2 10 1 2 9 1 2 8 1 2 8 1 2 10 1 2 8 1 2 7 1 2 5 1 2 6 1 2 5 1 2 10 1 2 8 1 2 7 1 2 7 1 2 8 1 2 10 1 2 10 1 2 7 1 2 7 1 2 8 1 2 7 1 2 3 1 2 8 1 2 8 1 2 8 1 2 3 1 2 7 1 2 8 1 2 9 1 2 8 1 2 9 1 2 9 1 2 5 1 2 8 1 2 8 1 2 6 1 2 7 1 2 9 1 2 8 1 2 9 1 2 10 1 2 7 1 2 8 1 2 8 1 2 7 1 2 9 2 1 8 2 1 8 2 1 10 2 1 7 2 1 9 2 1 10 2 1 10 2 1 10 2 1 10 2 1 8 2 1 10 2 1 5 2 1 10 2 1 5 2 1 5 2 1 7 2 1 10 2 1 10 2 1 7 2 1 10 2 1 10 2 1 3 2 1 7 2 1 6 2 1 10 2 1 5 2 1 8 2 1 9 2 1 5 2 1 7 2 1 2 2 1 10 2 1 5 2 1 7 2 1 7 2 1 8 2 1 5 2 1 5 2 1 8 2 1 9 2 1 10 2 1 10 2 1 10 2 1 10 2 1 6 2 1 8 2 1 10 2 1 10 2 1 8 2 1 10 2 1 5 2 1 8 2 1 9 2 1 9 2 1 5 2 1 8 2 1 5 2 1 10 2 1 7 2 2 5 2 2 8 2 2 10 2 2 6 2 2 6 2 2 10 2 2 2 2 10 2 2 10 2 2 10 2 2 3 2 2 7 2 2 7 2 2 2 2 9 2 2 8 2 2 4 2 2 10 2 2 7 2 2 9 2 2 6 2 2 10 2 2 6 2 2 10 2 2 7 2 2 7 2 2 5 2 2 8 2 2 5 2 2 9 2 2 10 2 2 10 2 2 8 2 2 6 2 2 5 2 2 9 2 2 10 2 2 6 2 2 5 2 2 8 2 2 10

ANSWER

Two Way ANOVA

We can analyze our data using two-way ANOVA, if the data satisfies six assumptions that are required for a two-way ANOVA to give us a valid result. To check these six assumptions means that we have a few more procedures to run through in SPSS Statistics.

When analyzing our own data using SPSS Statistics, one or more of these assumptions can be violated (i.e., is not met). This is not uncommon when working with real-world data. First, let’s take a look at these six assumptions:

1: Dependent variable should be measured at the continuous level (i.e., they are interval or ratio variables). Examples of continuous variables include exam performance (measured from 0 to 100), height (measured in cm).

2: Two independent variables should each consist of two or more categoricalindependent groups. Example independent variables that meet this criterion include illness (low, high, severe), sex (2 groups: male or female) and so forth.

3: Should have independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group.

4: There should be no significant outliers. Outliers are data points within your data that do not follow the usual pattern. The problem with outliers is that they can have a negative effect on the two-way ANOVA, reducing the accuracy of your results.

5: The dependent variable should be approximately normally distributed for each combination of the groups of the two independent variables. The two-way ANOVA requires approximately normal data, this is because it is quite “robust” to violations of normality, meaning the assumption can be a little violated and still provide valid results. We can test for normality using the Shapiro-Wilk test for normality.

6: There needs to be homogeneity of variances for each combination of the groups of the two independent variables. We can test this assumption in SPSS Statistics using Levene’s test for homogeneity of variances.

 Tests of Normalitya Kolmogorov-Smirnovb Shapiro-Wilk Statistic df Sig. Statistic df Sig. LifSat .178 39 .003 .895 39 .002 a. Argentina,Brazil = Brazil, Sex = Female b. Lilliefors Significance Correction

As the Sig. value under the Shapiro-Wilk column is less than 0.05, we can conclude that “LifSat” for this particular subset of individuals is not normally distributed.

Hence we consider non parametric version of the anova test.We use Mann-Whitney U test. When we choose to analyse our data using a Mann-Whitney U test, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a Mann-Whitney U test. let’s look at these four assumptions:

1: Dependent variable should be measured at the ordinal or continuous level. Examples of ordinal variables include Likert items (e.g., a 3-point scale from “severe” through to “low”), amongst other ways of ranking categories (e.g., a 5-point scale explaining how much a customer liked a service, ranging from “Not very much” to “Yes, a lot”). Examples of continuous variables include revision time (measured in seconds), height (measured in cm)

2: Independent variable should consist of two categoricalindependent groups. Example independent variables that meet this criterion include sex(2 groups: male or female), disease (2 groups: yes or no).

3: Independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group

4: A Mann-Whitney U test can be used when your two variables are not normally distributed

The Ranks table is the first table that provides information regarding the output of the actual Mann-Whitney U test. It shows mean rank and sum of ranks for the two groups tested (i.e., the 2 countries Argentina,Brazil).Brazil has higher mean rank hence it has more life satisfaction.

 Ranks Country N Mean Rank Sum of Ranks LifeSatisfaction Argentina 199 139.92 27844.00 Brazil 98 167.44 16409.00 Total 297

This table shows us the actual significance value of the test. Specifically, the Test Statistics table provides the test statistic, U statistic, as well as the asymptotic significance (2-tailed) p-value.

 Test Statisticsa LifeSatisfaction Mann-Whitney U 7944.000 Wilcoxon W 27844.000 Z -2.633 Asymp. Sig. (2-tailed) .008 a. Grouping Variable: Country

From this data, it can be concluded that life satisfaction in the Brazil group was statistically significantly higher than the Argentina group ( p = .008).

/M-W= LifeSatisfaction BY Sex(1 2)

/STATISTICS=DESCRIPTIVES QUARTILES

Mann-Whitney Test

The Ranks table is the first table that provides information regarding the output of the actual Mann-Whitney U test. It shows mean rank and sum of ranks for the two groups tested (i.e., the male and female groups):

 Ranks Sex N Mean Rank Sum of Ranks LifeSatisfaction Male 150 150.68 22601.50 Female 147 147.29 21651.50 Total 297

The table above is very useful because it indicates which group can be considered as having the higher life satisfaction, overall; namely, the group with the highest mean rank. In this case, the male group had the highest life satisfaction.

 Test Statisticsa LifeSatisfaction Mann-Whitney U 10773.500 Wilcoxon W 21651.500 Z -.345 Asymp. Sig. (2-tailed) .730 a. Grouping Variable: Sex

From this data, it can be concluded that life satisfaction in the male group was not statistically significantly higher than the female group (p = .730).

The study investigated whether there are any significant differences in life satisfaction between Brazilians and Argentinians and between men and women. First parametric assumptions were tested for 2-way ANOVA. Then we found that data was not normally distributed. We couldn’t continue further as assumption was violated. Then we proceeded with Mann Whitney U test which is a non-parametric test.All the required assumptions have been listed above.

We conclude that life satisfaction in the Brazil group was statistically significantly higher than the Argentina group (p = .008). We conclude that life satisfaction in the male group was not statistically significantly higher than the female group (p = .730).

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