The statistical techniques and tools help in analysing relationship between various variables (Weiss and Weiss, 2012, pp. 23). Moreover, the feasibility of various tests can be evaluated through adoption of appropriate statistical techniques. The report presented herewith helps in conducting an in-depth evaluation of different sets of information extracted. The application of statistical techniques helps in generating valid and reliable outcomes. The report provides deep understanding of statistical tools that can be adopted through SPSS for the purpose of generating valid and reliable outcomes.
Question: A researcher wanted to determine if psychological factors could predict the number of games won in tennis players across a range of ages. Once the regression equation has been established the validity of this measure needs to be assessed.
The statistical techniques are applied to study whether psychological factors are capable to predict number of games won in tennis players across a range of ages. The following hypothesis is tested for the purpose of identifying relationship between variables.
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In context to research design of the present study that examines relationship of psychological factors to performance of tennis players. As per the hypothesis, it can be claimed that the analysis is based on casual effect design. The research design helps in testing cause and effect relationship between the variables identified (Pallant, 2013, pp. 54). The analysis assists in identifying whether the significant relationship exists between psychological factors and number of games won by tennis player. It emphasizes on identifying impact of various psychological factors on performance of tennis players. The causal research design is suitable since it helps in identifying cause and effect relationship between two variables.
The data collected will be analysed through adoption of regression analysis. It is through multiple regressions that the relationship between the psychological factors and age group of tennis players is assessed (Cohen, Cohen, West and Aiken, 2013, pp. 78). The dependent variable in present case is identified as performance of tennis player based on number of games won out of 70 matches. On the other hand factors such as age, anxiety and mental toughness score are considered as independent factors for multiple regression analysis. It is through support of SPSS that the multiple regressions are applied in order to assess the relationship between the variables identified. This in turn helps in testing the hypothesis framed for the purpose of analysis. The multiple regression analysis is adopted to determine that whether psychological factors are capable to predict number of games won in tennis players across a range of ages. Besides, the normality test is applied to examine that whether the sample distribution has shape of normal curve or not. It is through application of normality test that distribution of information accumulated can be identified. The test helps in evaluating whether the data for number of matches won is normally distributed over the age of tennis players. The analysis through multiple regression helps in identifying direction and degree of relationship between variables. As per the null hypothesis it is assumed that performance of tennis player is not significant dependent on any of psychological factors. The outcomes generated will help in testing the hypothesis created
The outcomes generated by way of analysis are enclosed in Appendix section. The first table of model summary indicates value of R-square. This in turn helps in identifying proportion of variation in Y or dependent variable with change in x or independent variables. The value is estimated at .860 which indicates the proportionate change of approximately 86% in performance of tennis players.
The second table of outcome indicates F-statistic and significance value so as to test the hypothesis. The significance value is estimated at 0.000 that is significantly lower than 0.05. The probability is significantly lower than 0.05 which indicates the F-statistic is large enough to reject the null hypothesis. This in turn indicates that alternative hypothesis is accepted in present case. Henceforth, it can be said that the significant relationship exists between psychological factors and number of games won in tennis players. Finally, the table of coefficients indicates degree and direction of relationship between variables. The value of coefficient is estimated at -0.819, 0.124 and -0.064 respectively for anxiety score, mental toughness and age in years. This in turn indicates that inverse and strong relationship exists between anxiety scores and number of games won in tennis players. On other hand, direct and weak relationship exists between mental toughness and number of games won in tennis players. Finally, the relationship between age and number of games won is established to be highly weak and negative in nature. The normality tests help in identifying whether the data is normally distributed or not. The null hypothesis for normality tests indicates data is normality distributed. Alternative hypothesis on other hand assumes data is not normally distributed. The significance vale for age group 1 that includes players below 38 years is estimated at .280 which is significantly higher than .05. This in turn indicates acceptance of null hypothesis. On other hand, significance value for age group 2 that includes players of above 38 years is estimated at 0.020 which is lower than .05. Henceforth, the null hypothesis is rejected for this group. It can be therefore said that performance of team players of age group below 38 years is normally distributed. However, the performance of players above 38 years is not normally distributed.
The evaluation of data helps in identifying distribution of information accumulated and relationship between variables. It is seen that that performance of individuals below 38 years follows normal distribution. However, performance of individuals above 38 years does not follow normal distribution. Moreover, the alternative hypothesis is accepted for testing the relationship. It is seen that number of games won by players decreases with increase in age. Moreover, with increase is anxiety level of 1% results in decrease in performance by 81%. Finally, the performance increases with rise in mental toughness due to positive relationship. As per the analysis it can be said that the significant relationship exists between psychological factors and number of games won in tennis players.
Question: An investigator was interested in determining whether any differences existed in football attendance over three months at two different country locations (north and south).
The analysis conducted herewith aims at evaluating whether significant difference exists in football attendance over three months at two different locations. It is through creation and testing of hypothesis that the difference between variables can be tested (Hanneman, 2008, pp. 256). In case of two-way ANOVA three hypotheses are created and analysed. The hypotheses created for the purpose of analysis are presented underneath.
The research or study design helps in identifying manner in which research can be conducted. The study into consideration is based on two- variable design since it studies the distribution of attendance in different months and location (Lucey, 2002, pp. 45). The analysis into consideration helps in understanding difference that exists between attendances. The evaluation studies attendance of two locations in different periods. The same can be analysed by way of adoption of two-variable design (Jaisankar, 2009, pp. 36). The appropriate statistical techniques are adopted for the purpose of analysis.
In order to identify the difference that exists in attendance of different months and locations, the technique of two-way ANOVA is adopted. The ANOVA that implies analysis of variances helps in understanding difference that exists in variables into considerations (Hawks, 2010, pp. 48). The two-way ANOVA is considered to be applicable when affect of multiple factors is judged. In present case the difference in attendance needs to be judged for two different locations and three different months. Henceforth, two-way ANOVA helps in identifying impact of multiple factors on dependent variable. In present case attendance is considered as dependent variable. Two factors on which difference in attendance needs to be identified are locations (north and south) and months (September, December and February). The first hypothesis helps in identifying the difference existed between attendances over three different months. The second hypothesis emphasizes on studying the difference in attendance over two locations. Finally, the third hypothesis helps in studying the level of interaction between two variables. It can be therefore said that outcomes generated by way of two-way ANOVA test helps in identifying difference that exists in football attendance (Cortina, Jose and Nouri, 2000, pp. 38). Moreover, normality tests are adopted to test the distribution of attendance over period of time. It is through normality tests that the distribution of data into consideration can be tested. Henceforth, it can be said that two-way ANOVA is adopted for testing hypothesis and normality tests is applied to test the distribution of data into consideration.
The appendix two shows outcomes generated through two-way analysis. The table of descriptive statistics shows average value of attendance for different months and locations. The table: 6 that are test of between subject effects helps in proving the hypothesis formulated. The tabulated value of F is compared to calculated value of F so as to test the hypothesis.
Months are considered as Variable 1 in this case since value of mean square is comparatively higher. The tabulated value for F is considered for degrees of freedom of 2 for V1 and 30 for V2.
The calculated value of F is estimated to be lower than its tabulated value. This in turn indicates that null hypothesis is true in the case (Newbold and et. al., 2009, pp. 24). It can be therefore said that the no significant difference exists between football attendances of three months.
The value of mean square for location is higher than error which makes location as V1. The tabulated values for degrees of freedom of 1 for V1 and 30 for V2 are considered in present case.
It is seen that calculated value of F is significantly higher than tabulated value. Henceforth, the null hypothesis is rejected in present case. It can be therefore said that alternative hypothesis is true which suggest significant difference exists in football attendance of two countries.
The hypothesis test level of interaction between two factors taken into consideration. The variable location*months is considered to be V2 in the case since its value is comparatively lower. The tabulated value for F is considered for degrees of freedom of 30 for V1 and 2for V2.
It is seen that calculated value is lower than tabulated value in above case. This in turn indicates supports decision to accept the null hypothesis. It can be therefore said that no significant interaction occurs between months and location for football attendance.
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As per the hypothesis testing, it can be said that significant difference exists in attendance of north and south location. However, attendance for September, December and February does not differ significantly. Moreover, the location and duration for record of attendance does not interact significantly. As per the post hoc analysis it can be said that mean difference is significant for attendance of two locations in different months (Bland and Altman, 2003, pp. 89). This is due to reason that the significance level is estimated to be higher than .05 in all the cases. Moreover, the estimated mean graph indicates attendance for two locations follow same structure. However, the mean attendance for north location is significantly lower than south. In addition, test of normality indicates the football attendance is normally distributed for September, December and February since significance value is for all the three is estimated at .20 which is higher than .05. Henceforth, it can be said that the football attendance is normally distributed in all three months.
The analysis presented above helps in evaluating the distribution of attendance in three months and two locations. As per the analysis it is concluded that the significant difference exists in attendance of two locations. However, the attendance of different months does not vary significantly. Finally, no significant interaction exists between months and location for football attendance. Finally, the attendance is normally distributed for month of September, December and February.
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