Statistical Analysis Essay On O2 Max Test Technique For Sedentary Teenagers Before And After Training.

You are required to complete the appropriate statistical analysis and report the analysis as it would be written in a report or journal article..

The following points should be considered:

1. a) The clarity and style with which the report is written
2. b) Use of research skills together and use relevant data analysis literature
3. c) Ability to interpret and report the results of the analyse 

The following learning outcomes are assessed by this coursework:

1. Display proficiency in the use of appropriate computer packages
2. Handle data, complete simple statistical procedures and interpret the outputs 

Report contents

The contents required in each section and marking criteria are included below.  There are a total of 25 marks available that will then be multiplied by 4 to provide your final grade as a percentage. The report should use the following headings and the information described in each section should be included. 

1) Aims and Hypotheses (4 marks)

State the aim and the null and alternative hypotheses for the study Remember if there are two aims there will be two sets of null and alternative hypotheses  

2) Methods

1. a) Study design (1 mark)

Describe the research design of the study

1. b) Data Analyses (4 marks)

Report the methods used to analyse the data. This section should include the names of the tests used and the reason for using them.

The following information should be included: State the name of the tests of normality of distribution, tests of difference and tests of correlation used. Include a rationale for the use of each test and the P value used to accept or reject the null hypothesis  

3) Results (9 Marks)

Report the results in the text, using full sentences.

You should report:

• Descriptive data,
• Statistics (from the tests of normality, difference and correlation, do not put the SPSS tables in this section)
• Include graphs that reflect the analysis performed for the tests of difference and correlation. The appearance of the graphs should be of the quality found in academic journals.

Where possible state the direction of any statistically significant differences or significant relationships.

          Remember:

• There are two aims there should be two graphs.
• The appearance of the graphs should be of the quality found in academic journals 

4) Conclusion (5 marks)

   What can you conclude from these results (can you accept or reject your null

hypotheses)? Put the results into context so that readers with little statistical knowledge could understand what was found. Remember there should be two sets of hypotheses. Also include a so what statement or statement about how the results could be used. 

5) References (1 mark)

Reference work in the accepted format (APA 6th) 

6) Relevant SPSS outputs (1 mark)

Include only the relevant outputs and highlight the information used within each output.

1) Aims and Hypothesis

The researcher wants to know about the effect of O₂ max test technique on the sedentary teenagers before and after a training. To find the evidence about the effect of O₂ max test technique, he completed the training program twice over the sedentary teenagers, first while consuming a 200 mL beetroot juice supplement and other one with a placebo.

The objective of the study is to find the difference in change in O₂ max and association between the changes in O₂ max performance for the two training programs.The hypothesis to find the evidence of performance difference between the two training programs is defined as below:

Null Hypothesis: The difference exists between the mean percentage changes in O₂ max after each program. Mathematically it is defined as:Alternate hypothesis: There is a difference between the mean percentage changes in O₂ max after each program. Mathematically it is defined as: 

Here,  is the mean percentage changes in O₂ max after providing beetroot supplement and  is the mean percentage changes in O₂ max after providing placebo supplement. The hypothesis to find the evidence of a relationship exists in O₂ max performance between the two training programs is defined as below:

Null Hypothesis: The population correlation coefficient between the change O₂ max in performance of two training is equal to 0:Alternate hypothesis: The population correlation coefficient between the change O₂ max in performance of two training is not equal to 0: 

2) Methods

1. a) Study design:

The data can be divided into two categories as qualitative or quantitative. The qualitative data contains the qualitative values in different levels as binary, nominal and ordinal and the quantitative data contains the numeric values (Tesch, 2013). Thus, in this case the data for O₂ max test technique on the sedentary teenagers before and after a training is quantitative.

The statistical tests applies on the basis of research design, type of variable and the distribution of data. If the data is distributed normally, then the parametric tests used for analysis, and if the data is not normally distributed then the non-parametric tests use for the analysis. 

1. b) Data Analysis:

The t-test applied to test whether the mean of a sample is a characteristic of the population or not. The t-test applied on the samples which contains quantitative values and variables measured in the interval or ratio level. The sample size of t-test should be less than 30 and the population standard deviation is unknown. (Davis, 2013). Thus, the one sample is tested twice with two training programs, so the samples are related to each other. Hence, to test that there is a difference in O₂ max performance between the training programs, the dependent sample t-test will be used.

Methods

In this problem Percentage change in VO₂ max pre and post, so two samples of Training with Beetroot supplement and Training without Beetroot supplement (Placebo) are dependent and two paired-samples t-test will be used to understand whether there was a difference in O₂ max performance between the two samples.

Assumptions of the paired-samples t-test:

1. Dependent variable must contain continuous scale.
2. Independent variable must be contain two categorical groups, "related groups" or "matched pairs". 
3. The major outliers should not exists between the differences of two group values.
4. The distribution between the differences of two group values should be approximately normal. 

To check the assumptions of normality and outliers, follow the below process:

1. Write the provided data into SPSS data editor.
2. Click on “Analyze > Descriptive statistics > Explore”, a new dialog box will appear, select the dependent variables as “Training without beetroot supplement and training with beetroot supplement”.

iii. Now, click on the “Plots” option and select the “Normality plots with tests”.Click on the “Continue” option and then press “OK” to get the results.

The obtained results are shown below:  The obtained boxplots are shown below: 

        The t-test procedure:To test that difference in O₂ max performance exists, use SPSS software, the procedure is as follows:

• Click on the Analyze > Compare means > Paired sample t- test, A new dialog box will appear. Select the variable 1 as “Training with Beetroot supplement” and variable 2 as “Training with Beetroot supplement”
• Click on the “Option” button in the above dialog box, a new dialog box will appear, select the confidence interval percentage as 95% and then press “Continue” option to go back old dialog box.

iii. Press “OK” option in the above dialog box to get output. The screenshot of the obtained output is shown below:      Test of relationship:Scatterplot: The scatterplot indicates the visual relationship between two variables. One variable can be consider as independent and other as dependent. If value of one variable increases and the corresponding value of another variable also increases then it indicates positive association between the variables.

If value of one variable increases and the corresponding value of another variable also decreases then it indicates negative association between the variables. (Cohen, Cohen, West, & Aiken, 2013). To make the scatterplot, follow the below procedure in SPSS software:

• Graphs > Legacy dialogs > Scatterplot/dot, a new dialog box will appear, select the y-axis and x-axis variables.
• Press “OK” option in the above dialog box, the obtained scatterplot is shown below:

 Correlation: It is a degree of relationship between the two numeric variables which contain a numeric value between -1 to +1.  (Jolley & Mitchell, 2012) The negative value of correlation coefficient (r) indicates a negative association between the variables and the positive value of correlation coefficient (r) indicates a positive association between the variables.

The Pearson correlation used to know whether correlation coefficient is 0 or not.

Thus, the one sample is tested twice with two training programs, so to know about the relationship between the changes O₂ max in performance between the two training programs the Pearson product-moment correlation will be used.

Consider the level of significance for the test as (α = 0.05).

Assumptions:

1. Two variables must contain numeric values.
2. Two variables should be linearly related.
3. There should be no significant outliers in the data.
4. Variables should be approximately normally distributed.

The SPSS procedure is given as below:

1. Click on Analyze > Correlation > Bivariate, a new dialog box will appear.
2. Select the variables as “training with Beetroot supplement and training without Beetroot supplement”.

iii. Press “OK” option in the above dialog box. 

The screenshot of the obtained output is shown below:

 3) ResultsAssumptions of t-test:The variables, Training with Beetroot supplement and Training without Beetroot supplement are measured in continuous scale. So, this assumption 1 is met for t-test.The two variables, Training with Beetroot supplement and Training without Beetroot supplement indicates the same subjects and includes in the both samples. So, this assumption 2 is met for t-test.The Shapiro-Wilk test provide more appropriate results for the sample size less than 50, thus in this case the data is less than 50 which indicates Shapiro-Wilk will be appropriate to test the normality.

The p-value for the Shapiro-Wilk test for both samples is greater than 0.05 level of significance, which indicates that data is normal.The obtained boxplot for the data of two samples does not indicates strong outliers, so there are no strong outliers in the dataset.The obtained boxplots are shown below:           Hence, all the conditions for the matched pair t-test are satisfied.The calculated value of test statistic is 0.373 and the degree of freedom is 14. The obtained P-value corresponding to the test statistic value is 0.715. So, the P­-value is larger than the level of significance 0.05, which indicates that the null hypothesis does not gets rejected. Thus it can be concluded that there is no significance difference in change in O₂ max performance between the two training programs.

Assumptions for Pearson correlation: The variables, Training with Beetroot supplement and Training without Beetroot supplement are measured in continuous scale. So, this assumption 1 is met.The scatterplot indicates a positive relationship indicates a positive linear relationship between the training with beetroot supplement and training without beetroot supplement. As the training without beetroot supplement increases the training with beetroot supplement also increases. So the assumption of linear relationship is met.The Shapiro-Wilk test provide more appropriate results for the sample size less than 50, thus in this case the data is less than 50 which indicates Shapiro-Wilk will be appropriate to test the normality.

The p-value for the Shapiro-Wilk test for both samples is greater than 0.05 level of significance, which indicates that data is normal.The obtained boxplot for the data of two samples does not indicates strong outliers, so there are no strong outliers in the dataset.Hence, all the conditions for the Pearson correlation are satisfied.The Scatterplot for the correlation between the training with Beetroot supplement and training without Beetroot supplement is shown below:         The above scatterplot indicates a positive relationship indicates a positive linear relationship between the training with beetroot supplement and training without beetroot supplement. As the training without beetroot supplement increases the training with beetroot supplement also increases.

Correlation result, the value of correlation coefficient (0.905) indicates that two variables are very strongly related.Pearson correlation coefficient result, the P-value of Pearson correlation coefficient is 0.000. So, the P-value is smaller than the level of significance 0.05. Thus it can be conclude that the population correlation coefficient is not 0. 

4) Conclusion

The null hypothesis of no significance difference in change in O₂ max performance between the two training programs does not gets rejected, thus it can be conclude that there is no difference between the Percentage change in VO₂ max test technique before and after a training intervention study.The value of correlation coefficient (0.905) indicates that two variables are very strongly related.As effect of training with Beetroot supplement increases the effect of training without Beetroot supplement (Placebo) also increases.The population correlation coefficient is not 0, so there is a relationship exists between the training with Beetroot supplement increases and training without Beetroot supplement (Placebo).

 5) References

Cohen, J., Cohen, P., West, S., & Aiken, L. (2013). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. Routledge.Davis, C. (2013). SPSS for Applied Sciences: Basic Statistical Testing. Csiro Publishing.Jolley, J., & Mitchell, M. (2012). Research Design Explained. Cengage Learning.Tesch, R., (2013). Qualitative Research: Analysis Types and Software. Routledge: Education.                 , 

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
Training_with_Beetroot_supplement	15	93.8%	1	6.2%	16	100.0%
Training_without_Beetroot_supplement	15	93.8%	1	6.2%	16	100.0%
Tests of Normality
	Kolmogorov-Smirnova			Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
Training_with_Beetroot_supplement	.142	15	.200*	.942	15	.411
Training_without_Beetroot_supplement	.142	15	.200*	.923	15	.213
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
Paired Samples Statistics
		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	Training_with_Beetroot_supplement	9.33	15	4.821	1.245
	Training_without_Beetroot_supplement	9.13	15	4.688	1.211
Paired Samples Correlations
		N	Correlation	Sig.
Pair 1	Training_with_Beetroot_supplement & Training_without_Beetroot_supplement	15	.905	.000
Paired Samples Test
		Paired Differences					t	df	Sig. (2-tailed)
		Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
					Lower	Upper
Pair 1	Training_with_Beetroot_supplement - Training_without_Beetroot_supplement	.200	2.077	.536	-.950	1.350	.373	14	.715
Correlations
		Training_with_Beetroot_supplement	Training_without_Beetroot_supplement
Training_with_Beetroot_supplement	Pearson Correlation	1	.905**
	Sig. (2-tailed)		.000
	N	15	15
Training_without_Beetroot_supplement	Pearson Correlation	.905**	1
	Sig. (2-tailed)	.000
	N	15	15
**. Correlation is significant at the 0.01 level (2-tailed).
Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
Training_with_Beetroot_supplement	15	93.8%	1	6.2%	16	100.0%
Training_without_Beetroot_supplement	15	93.8%	1	6.2%	16	100.0%
Tests of Normality
	Kolmogorov-Smirnova			Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
Training_with_Beetroot_supplement	.142	15	.200*	.942	15	.411
Training_without_Beetroot_supplement	.142	15	.200*	.923	15	.213
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
Paired Samples Statistics
		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	Training_with_Beetroot_supplement	9.33	15	4.821	1.245
	Training_without_Beetroot_supplement	9.13	15	4.688	1.211
Paired Samples Correlations
		N	Correlation	Sig.
Pair 1	Training_with_Beetroot_supplement & Training_without_Beetroot_supplement	15	.905	.000
Paired Samples Test
		Paired Differences					t	df	Sig. (2-tailed)
		Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
					Lower	Upper
Pair 1	Training_with_Beetroot_supplement - Training_without_Beetroot_supplement	.200	2.077	.536	-.950	1.350	.373	14	.715
Correlations
		Training_with_Beetroot_supplement	Training_without_Beetroot_supplement
Training_with_Beetroot_supplement	Pearson Correlation	1	.905**
	Sig. (2-tailed)		.000
	N	15	15
Training_without_Beetroot_supplement	Pearson Correlation	.905**	1
	Sig. (2-tailed)	.000
	N	15	15
**. Correlation is significant at the 0.01 level (2-tailed).