Interpret statistical output

Student name:

Institution name:

Tittle: A statistical analysis of video games

Problem description

This report details the outcomes of the data analysis of a video game data set. The analysis involved carrying out various hypothesis tests to ascertain the validity of particular claims about the data. The data analysis was carried out using the statistical software for social sciences (SPSS). The statistical tests conducted were Student’s t-test for the difference in means between groups along with descriptive and visual analysis of the data (Kim, 2015). T-tests were used because each of the grouping variables (independent variables) consisted of only two categories (Rhemtulla, Brosseau-Liard, & Savalei, 2012). The specific questions to be addressed were whether the number of video games visits varied with the type of video game on show and whether the amount of visit time in a video game are different for the type of video game on show. Additionally, questions of whether the number of video game visits and the time taken for each visit varied with whether or not an advertisement of the video game was carried out.

Hypotheses were formulated and tested to help answer the above research questions. Given that each independent/grouping variable was associated with two research questions, a total of 4 hypotheses were formulated. The hypotheses were as below;

Video game type and number of video game visits

H0: There is no difference in the mean number of video game visits for the two types of video games (police or thief).

H1: There is a difference in the mean number of video game visits for the two types of video games (police or thief).

Video game type and the amount of visiting time

H0: There is no difference in the mean amount of visiting time for the two types of video games on offer (police or thief).

H1: There is a difference in the mean amount of visiting time for the two types of video games on offer (police or thief).

Advertising and the number of video games visits

H0: Advertising has no influence on the number of times a video game is visited/ the mean number of times a video game is visited is the same with or without advertisement.

H1: Advertising has an influence on the number of times a video game is visited/ the mean number of times a video game is visited varies with whether or not an advertisement is carried out.

Advertising and the amount of visiting time for a video game

H0: The amount of visiting time for a video game does not vary with whether or not an advertisement is carried out for the video game/ the mean amount of visiting time for a video game is the same with or without advertisement.

H1: The amount of visiting time for a video game does vary with whether or not an advertisement is carried out for the video game/ the mean amount of visiting time for a video game is dependent on whether or not an advertisement is carried out for the video game.

All the above hypotheses were tested at the 0.05 level of significance (Wasserstein & Lazar, 2016). This implies that the null hypothesis is rejected if the obtained p-value is less than 0.05 while we fail to reject it if the obtained p-value is greater than 0.05 (Anderson, Burnham, & Thompson, 2000).

The data

As already mentioned, the data used for this analysis is a video game data recording various aspects of the games such as the type of game, whether or not an advertisement was carried out, the number of times a video game was visited, the amount of visiting time for each visit, the total amount of time for each visit on a particular day and the day the visit occurred. The data has a total of 6 variables each with 44 observations. Two of the variables of interest were re-coded in SPSS to transform them from type string to type numeric to allow for the appropriate data analysis procedure (Escalera, Pujol, & Radeva, 2010). These variables were Game and Advertising which needed to be converted to numeric categorical/grouping variables. Of the six variables, two, that is Date and Totaltime, were not used in the analysis. The table below illustrate each of the variable in the data;

Variable	Type	Description	Re-coded as	Re-coded as type
Date	String	The day of the week on which the video game visit took place.
Visits	Numeric	The number of video game visits on a particular day of the week
VisitTime	Numeric	How long each video game visit lasted.
TotalTime	Numeric	The total amount of time a video game was visited on a particular day of the week
Game	String	A string variable denoting the type of game on show (police or thief)	Gamerecoded Values of 2 and 3 were used to denote whether the game was police or thief respectively.	Numeric
Advertising	String	A string variable denoting whether an advertisement was carried out for the video game or not (yes for advertisement and no for no advertisement).	Advertisingrecoded Values 1 and 4 were used to denote whether or not an advertisement was carried out for the video game (1 for no and 4 for yes).	Numeric

Descriptive statistics and visualizations

Before data analysis was carried out to answer the research questions, descriptive statistics as well as visualization of the variables in the data were carried out to give an idea of the distribution as well as the central tendencies of the variables. The table below illustrates the results of the descriptive analysis;

Descriptive Statistics
	N	Range	Minimum	Maximum	Mean	Std. Deviation
Visits	44	10	0	10	1.45	2.672
VisitTime	44	4.44	.00	4.44	.7050	1.09071
TotalTime	44	28.45	.00	28.45	2.8702	6.00944
Gamerecoded	44	1	2	3	2.50	.506
Advertisingrecoded	44	3	1	4	2.50	1.517
Valid N (listwise)	44

As can be seen from the table, the highest number of visits in a particular day was 10 while the least was 0. The mean number of visits was 1.45 with a standard deviation of 2.672. The longest visit lasted a maximum of 4.44 hours with some visits lasting as little as 0.00 hours. The mean amount of visiting time was 0.705 hours with a standard deviation of 1.091. The highest total amount of time a video game was visited in a particular day was 28.45 hours. The mean total visit amount was 2.8702 with a standard deviation of 6.0094. The type of video game was either police (2) or thief (3) while a video game was either advertised (1) or not (4). All the observations in each of the variables were valid.

To assess the distribution of the variables, histograms of the important ones (visits, visittime) were plotted. The histogram for each variable is as displayed below;

The number of visits follow no particular distribution with the range 0-1 capturing the most data points. This implies that the video games received no visitors on a frequent basis.

Most video game visits lasted between 0 and 2 hours on the maximum with a good number of the remaining visits lasting between 2-3 hours.

T-tests, results and discussion

Independent sample t-test for the difference in means were carried out to test the hypotheses formulated in the first section above. The results of each of the tests were as displayed in the below tables

Group Statistics
	Gamerecoded	N	Mean	Std. Deviation	Std. Error Mean
VisitTime	Police	22	.5250	.90210	.19233
	Theif	22	.8850	1.24671	.26580

Independent Samples Test
	Levene's Test for Equality of Variances	t-test for Equality of Means
	F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
								Lower	Upper
VisitTime	Equal variances assumed	1.955	.169	-1.097	42	.279	-.36000	.32808	-1.02210	.30210
	Equal variances not assumed			-1.097	38.259	.279	-.36000	.32808	-1.02402	.30402

Dependent variale; visittime: independent variable; Gamerecoded

The 2-tailed p-value (significance) assuming unequal variances is 0.279 which is higher than the 0.05 level of significance. We therefore fail to reject the null hypothesis and conclude that there is no difference in the mean amount of visiting time for the two types of video games on offer (police or thief).

The t-test results for the number of visits to the video games and type of game are as displayed in the tables below;

Group Statistics
	Gamerecoded	N	Mean	Std. Deviation	Std. Error Mean
Visits	Police	22	1.41	2.594	.553
	Theif	22	1.50	2.807	.599

Independent Samples Test
	Levene's Test for Equality of Variances	t-test for Equality of Means
	F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
								Lower	Upper
Visits	Equal variances assumed	.025	.875	-.112	42	.912	-.091	.815	-1.736	1.554
	Equal variances not assumed			-.112	41.741	.912	-.091	.815	-1.736	1.554

Dependent variable; Visits: Independent variable; Gamerecoded

From the test results above, the p-value is once again 0.912>0.05. Again, we fail to reject the null hypothesis and conclude that there is no difference in the mean number of video game visits for the two types of video games (police or thief).

The t-test results for the video game visits as well as visiting time are as displayed in the below tables;

Group Statistics
	Advertisingrecoded	N	Mean	Std. Deviation	Std. Error Mean
VisitTime	No	22	.2441	.69344	.14784
	Yes	22	1.1659	1.22881	.26198
Visits	No	22	.23	.685	.146
	Yes	22	2.68	3.315	.707

Independent Samples Test
	Levene's Test for Equality of Variances	t-test for Equality of Means
	F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
								Lower	Upper
VisitTime	Equal variances assumed	8.405	.006	-3.064	42	.004	-.92182	.30082	-1.52890	-.31474
	Equal variances not assumed			-3.064	33.144	.004	-.92182	.30082	-1.53374	-.30990
Visits	Equal variances assumed	50.261	.000	-3.401	42	.001	-2.455	.722	-3.911	-.998
	Equal variances not assumed			-3.401	22.792	.002	-2.455	.722	-3.948	-.961

Dependent variables; Visittime and visit: Independent variable; Advertisementrecoded

From the analysis results above, the p-value for the visit time is 0.004 <0.05. The null hypothesis is therefore, rejected and the conclusion that the amount of visiting time for a video game does vary with whether or not an advertisement is carried out for the video game is drawn. On the other hand the p-value for the number of visits is 0.002<0.05. The null hypothesis is again rejected and the conclusion that advertising has an influence on the number of times a video game is visited is drawn.

References Anderson, D. R., Burnham, K. P., & Thompson, W. L. (2000). Null hypothesis testing: problems, prevalence, and an alternative. The journal of wildlife management, 912-923. Escalera, S., Pujol, O., & Radeva, P. (2010). Re-coding ECOCs without re-training. Pattern Recognition Letters. Pattern Recognition Letter. Kim, T. K. (2015). T test as a parametric statistic. Korean journal of anesthesiology, 540. Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological methods, 354. Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: context, process, and purpose. The American Statistician, 129-133.