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When the aim of study is to appraise the margin of effect of a dichotomous or interval/ratio predictor element of measure on a ratio/interval principle variable, linear regression is an suitable analysis. Multiple regression and linear regression do not have that much of a difference but the application of an equation like draws a line for measuring; y = b1*x + c, where c is a constant, y is an estimated dependent variable, b is a regression coefficient, and x is an independent variable (Fidell, & Tabachnick 2006; pp. 45-89). In linear regression unlike multiple linear regressions, it is not important to assess the lack of multi-collinearity due to the predictor variable.

The conduction of linear regression determines if assessing of independent variable affects the dependent variable by performing the F test. R2 is highlighted and used to determine how the level of variation can be accounted for by the autonomous variable. Beta coefficients are utilized to determine the level of effect of the prediction of the independent variable as opposed to the use of t test in the determination of the predictor’s importance. In the case of a significant predictor and all units of predictor, dependent variables either increase or decrease with the range of unstandardized beta coefficients.

Assumptions concerning and involving linear regression requires linearity and homoscedasticity to be assessed. Linearity assumes a direct link between predictor and criterion variable therefore resulting to a straight line while on the other hand; homoscedasticity assumes that the distribution of scores takes place along specific points on the line. Scatter plots are used to examine homoscedasticity and linearity (Stevens, 2009; pp. 23-25).

The use of t tests and linear regressions is adapted to answer the research questions. More participants are required to find significance in linear regression. Analysis involving power has been conducted in G POWER to define a sample size by the use of 0.05, 0.08 power, and medium size effect (f2 = 0.15) (Erdelder, Faul, Lang & Buchner, 2008; pp. 290-311). The sample size of this research is 55 participants based on the assumptions mentioned earlier.. In most cases, an alpha value below the standard 0.05 is always rejected for null hypotheses, but in special cases type I error occurs, if the null hypothesis is true. Considering the research questions, we have been searching for evidence to reject the null hypotheses and this gives a margin of error. Jacob Cohen (1989) argues that all null hypotheses are false in their double-tailed forms. As much as we investigate an issue from a sample of a particular size, we are aiming at finding evidence to support or reject a hypothesis (Richard, 1984; pp. 114-116).

In regard with the heads up by Jacob, the issue of the null hypothesis effect and a sample size are applied to ensure of much accurate parameters (Tabachnick, & Fidell, 2006; pp.13-22). For this to be achieved, a large enough sample gives greater possibility of finding the evidence of what we are looking for. A sample size makes sure that a large sample will provide reliable effect in the process of investigation (Stevens, 2009; Tabachnick, & Fidell, 2007; p. 76).

Since a sample size concerns researchers, an error is likely to occur in every situation, especially when using the G* POWER to determine analysis (Trochim, & William, 2006; p. 200). The hypotheses, we thrive to prove or disprove, has a potential of being actual findings of the research in the case of type I error and type II error. A true null hypothesis can be rejected in the case of type I error, while a false null hypothesis can be accepted in type II error. In order to reduce chances of error with the use of G*POWER analysis for linear regressions (Vance, 2011; p. 83), a sample size is to be 55 participants.

Data analysis

Data collected from the sample and gathered from different sources are organized and fed to SPSS software version 18.0 for Windows (Mac operating systems are avoided for simplicity reasons). As a form of the mixed method of data collection, qualitative and quantitative methods are merged to give descriptive statistics of the data collected (Abelson, 1995). In regard with the research sample size and variables for consideration, descriptive statistics is useful, for it outlines variables, specifies constants and differentiates consistent elements with random ones. The population of students reviewed can be monitored or defined to fit in a specific margin and this is classified under consistent elements. The curriculum is a major appraisal mechanism defining grading for the vast number of students and this is a constant that descriptive statistics outlines clearly (Adèr, &Mellenbergh, 2008: p 17). Whether games affect grades of high school students or not, their mental abilities, time spent playing games, time spent studying and efforts drawn to achieve better grades apply as a unit of varying elements whose definitive characteristic depends on the nature and type of an individual. Regarding the use of descriptive statistics, an in-depth analytical approach to determining frequencies of variables plays an important role for data analysis.

As a critical requirement for research data analysis, calculations are to be developed considering the nature and amount of data. When considering the size of the sample, a small one requires a model for calculating different elements and variables. Considering that there are a number of factors influencing grades for high school students, only those related to gaming are relevant for this research. To achieve the right results and to present a reliable data analysis, frequencies of time, influence, character and a need to play games are calculated alongside the respective percentage of the sample for nominal (categorical/dichotomous) data.

Continuous data are calculated following means/standard deviations; this is effective and important for determining ratios and intervals of occurring. In data analysis, these calculations play a great role, since an appraisal for occurrence in one group or setting can be compared with another one to draw a line (ASTM International; 2002: pp. 35-37). An interval of occurrence is of great importance, since dependent variables are determined and identified for a better and concise analysis. Through nominal and continuous data calculations, research findings are traced back to physical numbers and descriptive statistics clarifies conflicting variables (Chow, 1996; p. 77).

RESEACRH QUESTIONS

Research Question 1

Controlling for income level, does the ratio of hours spent playing video games to hours spent studying predict high school GPA?

Determinants for hours spent studying are continuous and nominal calculations. As a result, it should be determined from the fact how many hours are spent playing and studying. To determine this, the calculation of percentage, frequency and intervals of playing and studying are used to reflect the total amount of time spent gaming and studying. When these hours are determined, an analysis to clear issues of special cases determines the correct number of consistent activity (Chuang, & Chen, 2009; pp. 100-103; pp. 21-25). It is done to set up a foundation and basis for clear and reliable data analysis. In the event when some data are considered coincidental or happen by chance, adding this to the final research requires the basis of occurrence and frequency by assessing a cause. For example, as discussed in the literature review, high school students’ grades are affected differently by the same game concerning sex, age, mental ability and their creativity in games as opposed to schoolwork (Cohen, 1989; p. 215).

Taking into account an income level, the prediction of the ratio of hours spent playing video games to hours spent studying will influence or affect grades is determined by a close examination of prevailing and presumably recurring events. A sample with gaming problems or a sample with studying disorders may not necessarily give the same results that will determine the ratio of gaming to studying. Equivocally, students with gaming problems are expected to score lower grades as compared to those who balance studying and playing video games (Dodge, 2003; pp. 90-93). Why does it happen? Mental abilities and a focus vary from one individual to another, while at the same time there is an issue of an educationally unmotivated group of students. Taking these as random issues, the ratio of hours spent playing video games to hours spent studying is a factor determined by personal, mental and motivational variables. There is a task to find a reliable method used to measure variables. It requires assumptions to be used for reassuring that the data presented and gathered are only connected with the context of video game playing and high school students’ grades. Such assumptions that grades of high school students are affected by video game playing and studying respectively and the number of hours spent on them deter recording of irrelevant data (Faul, Erdfelder, Buchner & Lang, 2008; pp.56-57).

H1_{0}: Controlling an income level, the ratio of hours spent playing video games to hours spent studying does not predict high school GPA.

The first research question and probably the rest questions do not have a definitive final response to prove or to disapprove. However, assuming this is a case, data collection and literature review either object or support that predetermined result (Greenberg, et, al., 2008: p. 115). This being an open research, questions are to be answered satisfactorily through the provision of evidence to support one side of the issue or another. In a rather unexpected turn of events, the research question may not be answered in favor of any argument, for variations are evident in both sides of the question.

Considering the first possible argument that controlling an income level the ratio of hours spent playing video games to hours spent studying does not predict high school GPA, multiple linear regressions are conducted to determine this fact. With the above discussed assumptions, there are two elements for comparison, while a common variable is an expected unit of calculation. The unit of calculation may not be quantifiable numerically (Kappes, & Thompson, 1985; p. 317), but considering a descriptive statistics approach for defining sample demographics, it is possible to formulate understandable results.

H1_{a}: Controlling an income level, the ratio of hours spent playing video games to hours spent studying predicts high school GPA.

Research Question 1 discussed above is not a close-ended question and any result cannot be realized through a careful calculation and assumptions. In this case, it can either be proved that controlling an income level, ratio of hours spent playing video games to hours spent studying predicts high school GPA. The assumptions of normality, homoscedasticity and absence of multi-collinearity are assessed to ensure that results are within context and the purpose of research is obeyed.

For the examination of Research Question 1, multiple regressions are conducted to assess whether the ratio of hours spent playing video games to hours spent studying predicts high school GPA after an income level has been controlled. Before measuring hours spent either playing games or studying, schedules for a sample group are determined over the period of schooling and holidays. During school days, the number of hours spent on such active school activities as attending lectures, physical exercises, visiting a library and tackling assignments are taken as study time. On the other hand, travel time, house chores, cleaning and dining are not counted as video game playing time. The percentage of time supposed to be hobby time, keeping other factors constant, makes up video game playtime. For these reasons, the time for playing video games is measured by calculating the number of hours spent by a student out of class within his or her free time. Free time is considered recreational time. If n is an amount of time, when a student is free to play games and na is an amount of time spent without playing video games, then time for playing video games is measured by n-na= playtime.

Hours spent studying over a period of one day or a week are measured by calculating the allocated number of hours for active school attendance or attendance of lectures added to the amount of time spent in the library and tackling exams and assignments. If time t is the total amount of time, a high school student is expected to be active in class, and ts is the amount of time spent attending lectures, visiting library and tackling assignments and exams, then t-ts is an amount of actual study time.

For the calculation of the ratio of hours spent playing video games to hours spent studying, n-na/t-ts determines the ratio. The previous equation can be modified to give other results, for example, when the ratio is known and one of variables isn’t. Besides, the calculation of time for every activity can be done separately to avoid complications and then division of playtime and study time is performed. The use of the division or obtaining the ratio creates a continuous independent variable. This independent variable is applied to determining whether more or less time spent playing video games or studying predicts high school GPA.

Controlling an income level for the determination of playtime to study the time ratio can be taken as a constant or can be scrapped from the picture. However, it cannot be controlled if it is not an important variable. For this case, the measurement of an income level is attained through assessing and comparing the effect of playtime and study time with overall grades of students. For example, playing games longer affects grades negatively. By using a benchmark for expected minimum grades, an income level can be measured to determine the level of change. An income level is attained as a whole number or a fraction considering the result of the ratio and is treated as a level variable. With respect to the assumptions of normality, homoscedasticity and absence of multi-collinearity, a dependent variable measures GPA.

Research Question 2a

RQ 2a: Controlling an income level, do hours spent playing video games predict hours spent studying?

Determinants of hours spent playing and hours spent studying are continuous and nominal calculations. As a result, it should be determined from samples how many hours are spent playing and of studying. To determine this, the calculation of percentage, frequency and intervals between playing and studying are used to reflect the total amount of time spent gaming and studying. When these hours are determined, an analysis to clear issues of special cases determines the correct number of consistent activities. It is done to set up a foundation and basis for clear and reliable data analysis. In the event, when some data are considered coincidental or happen by chance, adding this to the final research requires the basis of occurrence and frequency by assessing a cause. For example, as discussed in the literature review, high school students’ grades are affected differently by the same game concerning sex, age, mental ability and their creativity in games as opposed to schoolwork.

H 2a_{0}: Controlling an income level, hours spent playing video games do not predict hours spent studying.

Taking into account an income level, the prediction of hours spent playing video games based on the number of hours spent studying is determined by a close examination of prevailing and presumably recurring events. A sample with a gaming problem and a sample with studying disorders are not necessarily to give the same results determining the ratio of gaming to studying. Students with gaming problems do not have their problems as a condition predicting hours spent studying. Why does it happen? Mental abilities and a focus vary from one individual to another, while at the same time there is an issue of an educationally unmotivated group of students. Taking these as random issues, the prediction of hours spent studying on the basis of hours spent playing video games is a factor determined by personal, mental and motivational variables. However, all discrepancies concerning this research question are respected and considered. Assumptions that grades of high school students are affected by video game playing and studying respectively and the number of hours spent on them deter recording of irrelevant data.

The nature of research questions does not have a definite final response to prove or to disapprove arguments. However, assuming this is a case, data collection and literature review either obligate or support that predetermined result. This being an open research, questions are to be answered satisfactorily through the provision of evidence to support one side of the issue or another. Concerning the nature of the first question as opposed to the nature of the second one, there is a similarity and unless a neutral point is drawn, no side of an argument can be supported with sufficiency of dependent variables.

Considering the first possible argument that controlling an income level, hours spent playing video games predict hours spent studying, multiple linear regressions are conducted to determine this. With the above-discussed assumptions, there are two elements for comparison, while a common variable is an expected result. The unit of calculation may not be quantifiable numerically, but considering a descriptive statistics approach for defining sample demographics, it is possible to formulate understandable results in regard with the impact of video game playtime on study time.

H 2a_{a}: Controlling an income level, hours spent playing video games predict hours spent studying.

Similar to Research Question 1, results from calculated data support or disagree with the selected sides of the question. In this case, it can be proven that controlling an income level, hours spent playing video games predicts hours spent studying. The assumptions of normality, homoscedasticity and absence of multi-collinearity are assessed to make sure that results are within the context and that the tenacity of the research is obeyed.

To examine Research Question 2a, multiple regressions are conducted to assess whether hours spent playing video games predict hours spent studying after an income level has been controlled. Before measuring hours spent playing games or studying, schedules for a sample group are determined over a period of schooling and holidays similar to Research Question 1. During school days, the number of hours spent on active school activities, namely attending lectures, physical exercises, visiting a library and tackling assignments is taken as study time. On the other hand, travel time, house chores, cleaning and dining are counted as video game playing time. The percentage of time supposed to be free time, keeping other factors constant, makes up video game playtime. For these reasons, time spent playing video games is measured by calculating the number of hours spent by a student out of class within his or her free time. Responding to the question, it is to be determined how playing video games affects the choice of hours for studying. In this case, the percentage of time for studying taken or consumed for playing video games determines the margin of the impact of playtime on study time. If the time spent studying is originally supposed to be y hours, and playing video games consumes x% of that study time, then study time in respect to playtime is measured by y-(y x x% (Keren, and Lewis, 1993; pp. 87-88).

Hours spent studying over a period of one day or a week are measured by calculating the allocated number of hours for active school attendance or attendance of lectures added to the amount of time spent in library and tackling exams and assignments. If time t is the total amount of time, a high school student is expected to be active in class, and ts is the amount of time spent attending lectures, visiting a library and tackling assignments and exams, then t – ts is the amount of actual study time. However, considering the previous tool for measurement, this study time consumes time spent playing video games subtracted from it.

Considering these measurements of playtime and study time, these two variables are taken as independent. These independent variables in respect to prediction of study time are compared in different platforms to determine the relation and how videogame playtime predicts study time.

Controlling an income level, the determination of the impact of playtime on the prediction of study time can be taken as a dependent variable, for grades of students are not independent variables. In this case, when independent variables are known and the controlled variable depends on them, it is measured through its lenience towards either the direction of the question requirement. Then it is treated as either 0 or a level in regard with the side it supports concerning the research question. For example, playing games longer affect grades negatively. By using a benchmark for expected minimum grades, an income level can be measured to determine the level of change. An income level is attained as a means and its frequency is treated as a nominal level variable. With respect to the assumptions of normality, homoscedasticity and absence of multi-collinearity, a dependent variable measures the effect of playtime on study time.

Research Question 2b

RQ 2b: Considering the top 50th percentile of GPAs and controlling an income level, do hours spent playing video games predict hours spent studying?

Determinants of hours spent playing video games and hours spent studying are continuous and nominal calculations. As a result, it should be determined from samples how many hours of playing video games and studying are spent for the top 50th percentile of GPAs. To determine this, the calculation of percentage, frequency and intervals between playing and studying is used to reflect the total amount of time spent gaming and studying. When these hours are determined, the top 50th percentile of GPAs is determined by setting a benchmark for a maximum degree of GPA. There is no chance that the top 50th percentile will have study time predetermined by time spent playing video games. However, research predictions may not be supported by actual data and it is through this a tool for measurement is applied to determine actual results. According to the top 50th percentile of observation, it is likely that more time will be spent studying than playing video games. Actually, the GPA depends strictly on what amount of time is allocated for an activity (Kraemer, and Theimann, 1987; pp. 15-19).

H 2b0: Considering the top 50th percentile of GPAs and controlling an income level, hours spent playing video games do not predict hours spent studying.

Considering the top and the bottom 50th percentiles of GPAs, time spent playing video games on time spent studying may be directly linked or a case of naturally occurring event. This may be true if assumptions of this research are lenient on this particular question. For the fact that it is not, linear regressions are conducted to determine whether considering the top 50th percentile of GPAs and controlling an income level, hours spent playing video games do not predict hours spent studying. Assuming that nature of Research Question 2b is close-ended, data collection and literature review either object or support that predetermined argument. This being an open research, questions are treated as vector quantities with direction. Supporting an argument, a hypothesis is a positive or affirmative response to that question, while objecting it is opposite. In research, there is the prevalence of related issues of mutually opposing variables that depict an action-reaction nature.

Considering the first possible argument that controlling an income level and the top 50th percentile of GPAs affect the fact that, hours spent playing video games do not predict hours spent studying, multiple linear regressions are conducted to assess this. With the above discussed assumptions, time spent playing video games and time spent studying are elements for comparison for the top 50th percentile. The unit of calculation may not be quantifiable arithmetically, but considering a descriptive statistics approach for defining sample demographics, it is possible to formulate an equation for determining a connection between playtime and study time.

H 2b_{a}: Considering the top 50th percentile of GPAs and controlling an income level, hours spent playing video games predict hours spent studying.

Controlling an income level, hours spent playing video games predict hours spent studying for the top 50th percentage. To prove or object this, linear progressions are used as in the instances of the above research questions. When linear regressions are determined, Hypothesis 1 is compared with Hypothesis 2 by considering the difference between them.

Examining Research Question 2b, multiple linear regressions are conducted for the top 50th percentile of GPAs and controlling an income level; then hours spent playing video games predict hours spent studying. Before measuring hours spent playing games or studying, schedules for a sample group making up the top 50th percentile are determined over the period of schooling and holidays. During school days, the number of hours spent on active school activities, namely attending lectures, physical exercises, visiting a library and tackling assignments is taken as study time. On the other hand, travel time, house chores, cleaning and dining are not counted as video game playing time. The percentage of time supposed to be hobby time, keeping other factors constant makes up video game playtime. For these reasons, time spent playing video games is measured by calculating the number of hours, during which the top 50th percentile spent out of class within students’ free time. Considering the top 50th percentile of GPAs controlling an income level, hours spent playing video games are measured by dividing the number of samples into two groups of the top and bottom 50th percentile. The top 50th percentile is taken as p1, while the bottom one is taken as p2, whereas P1 is used for this analysis. Time spent playing video games and time spent studying are taken as continuous independent variables, while an income level is treated as a dependent level variable. A dependent level variable is a constant affecting any variables and if applied affects both continuous independent variables.

Hours spent studying over a period of one day or a week is measured by calculating the allocated number of hours for active school attendance or attendance of lectures added to the amount of time spent in a library and tackling exams and assignments. If time t is the total amount of time, during which a high school student is expected to be active in class, and ts is the amount of time spent attending lectures, visiting a library and tackling assignments and exams, then t – ts is the amount of actual study time.

Considering the top 50th percentile of GPAs, controlling an income level is measured by assessing how time spent playing video games influences study time. The income control is used to determine how study time is dependent on playtime. This variable is treated as an ‘a’ level variable in regard with Hypothesis 2b.

Research Question 2c

RQ 2c: Considering the bottom 50th percentile of GPAs and controlling an income level, do hours spent playing video games predict hours spent studying?

Determinants of hours spent playing video games and studying are continuous and nominal calculations. As a result, it is determined based on samples how many hours are spent on playing and studying. To determine this, the calculation of percentage, frequency and intervals between playing and studying is used to reflect the total amount of time spent gaming and studying. When these hours are determined, an analysis to clear issues of special cases determines the correct number of consistent activities. Performing these calculations, it is important to set up a foundation and basis for clear and reliable data analysis. For example, as discussed in the literature review, high school students’ grades are affected differently by the same game concerning sex, age, mental ability and their creativity in games as opposed to schoolwork. However, these determinants and affecting factors are used for this kind of analysis, because the research is strict on assumptions.

The bottom 50th percentile of GPAs and controlling an income level, when hours spent playing video games predict hours spent studying, are determined by a close examination of prevailing and presumably recurring events (frequency of variables). A sample with a gaming problem and a sample with studying disorders are not necessarily to give results determining this case. Equivocally, students with gaming problems are expected to score lower grades as compared to those who balance studying and playing video games. Considering this argument, the bottom 50th percentile is to have more students whose study time is predicted by the number of hours spent playing video games. If the above statement is true, Hypothesis 1 of Research Question 2c is supported. If the number of students regarding the bottom 50th percentile of GPAs has its’ study time free from the influence of the number of hours they spend playing video games, Hypothesis 2 of Research Question 2c is supported. Assumptions play a great role in this analysis to make sure that no irrelevant variables are considered outside the scope of variables (Murphy and Myors, 2003; pp. 67-109)

H 2c_{0}: Considering the bottom 50th percentile of GPAs and controlling an income level, hours spent playing video games do not predict hours spent studying.

Like all other research questions, Research Question 2c does not have a definitive final response to prove or to disapprove. However, it is dual-faced and an argument can fall on the one side or the other concerning the similarity of answers to hypothetical question. Since the analysis measures variables with various tools, results of such analysis render that a hypothetical suggestion is either true or false. Unless other variables and factors are allowed for consideration through lifting assumption restrictions, there is no middle ground for arguing that both hypotheses are applied equally to a certain section or the whole sample.

Considering the first possible argument as opposed to Hypothesis 1, because of the bottom 50th percentile of GPAs and controlling an income level, hours spent playing video games do not predict hours spent studying. Multiple linear regressions are conducted to determine the truth of this hypothesis. According to the assumptions discussed above, there are two elements for comparison, while a common variable is an expected unit of the calculation. The unit of calculation may not be quantifiable numerically, but considering a descriptive statistics approach for defining sample demographics, it is possible to formulate understandable results (Olson, 2010; p. 53).

H 2c_{a}: Considering the bottom 50th percentile of GPAs and controlling an income level, hours spent playing video games predict hours spent studying.

Research Question 2c allows for a trial-and-error type of calculation, upon which two hypotheses can be proven by the application of measurement tools with results expected from a careful calculation in respect to assumptions. In this case, controlling an income level for the bottom 50th percentile of GPAs, hours spent playing video games predict hours spent studying The assumptions of normality, homoscedasticity and absence of multi-collinearity are assessed to ensure that results are within the context and the purpose of the research is obeyed.

Examining Research Question 2c, when multiple regressions are conducted to assess the bottom 50th percentile of GPAs and controlling an income level, hours spent playing video games predict hours spent studying. Before measuring hours spent playing games or studying, schedules for a sample group are determined over the periods of schooling and holidays. During school days, the number of hours spent on active school activities, namely attending lectures, physical exercises, visiting a library and tackling assignments are taken as study time. On the other hand, travel time, house chores, cleaning and dining are not counted as video game playing time. The percentage of time supposed to be hobby time, keeping other factors constant, makes up video game playtime. For these reasons, time spent playing video games is measured by calculating the number of hours spent by a student out of class within his or her free time. Free time is considered recreational time. If n is an amount of time, during which a student is free to play games and na is an amount of time spent without playing video games, then time spent playing video games is measured by n –na= playtime. Hours spent playing video games and hours spent studying are treated as continuous independent variables

Hours spent studying over a period of one day or a week are measured by calculating the allocated number of hours for active school attendance or attendance of lectures added to the amount of time spent in a library and tackling exams and assignments. If time t is the total amount of time, during which a high school student is expected to be active in class, and ts is an amount of time spent attending lectures, visiting a library and tackling assignments and exams, then t – ts is an amount of actual study time. Only the bottom 50th percentile of GPAs is used in this analysis. The assumptions of normality, homoscedasticity and absence of multi-collinearity are assessed.

Determining whether hours spent playing video games predict hours spent studying considering the bottom 50th percentile with controlling an income level, there is a model for assessing the impact of continuous independent variable, that is, time spent playing video games, on time spent studying. The formula for measuring each variable is used to provide the number of hours applied to playing video games and studying.

For the bottom 50th percentile of GPAs, controlling an income level is measured by assessing how time spent playing video games influences study time. The income control is used to determine how study time is dependent on playtime. This variable is treated as a level variable in regard with Hypothesis of Research Question 2b.

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