Can you please answer the questions for me, I don't need the SPSS done just the questions?? THANK YOU Scenario: Imagine that Alpha Shoe Company wants to do a second study on the vertical lift basketball players can gain from their shoes. Recall that they believe that how high a player can jump is affected by the type of shoe that player wears. They identified 25 professional basketball players and randomly assigned each of them to wear one of the five types of shoe, then measured how high each player jumped. Each player's jumping height is given below in inches: Pluto Omega II Beta Super Delta Gamma 29.1 29.2 28.5 28.4 27.7 29.8 29.1 28.9 28.0 27.9 30.0 28.8 29.2 28.8 28.0 29.0 28.7 28.3 29.0 28.2 31.1 28.8 30.0 28.9 28.0 Assignment: To complete this Assignment, submit by Day 7 answers to the following. Use SPSS to compare the means of the scores of these five shoes with a one-way ANOVA. Save and submit both your SPSS data file and your output. Before comparing the scores with an ANOVA, state your null and alternative hypotheses in words (not formulas). Identify the independent and dependent variables. Name the levels in your identified factor. State the within-group degrees of freedom and explain how you calculate it. State the between-group degrees of freedom and explain how you calculate it. Identify the obtained F value. Identify the p value. Explain whether the F test is significant. Explain how you know and what it tells you. Explain what you can conclude about the effect of shoe choice on vertical lift (jumping height). Should you conduct a post hoc test? Why or why not? If yes, conduct a Tukey HSD post hoc analysis. Explain what the results tell you about type of shoe choice and vertical lift. Submit three documents for grading: your text (Word) document with your answers and explanations to the application questions, your SPSS Data file, and your SPSS Output file. Provide an APA reference list. Hypothesis Testing 1 Hypothesis testing in ANOVA Introduction: The case study deals with hypothesis testing in ANOVA. Where we have more than two samples. The samples are denoted by treatment also. We compare that whether the average effect of all the treatments is same or they differ significantly. Or we compare the independent mean and we conclude that whether the mean is same for all the populations or it differs significantly. Case Study: We have picked 5 shoes Pluto, Omega II, Beta super, Delta and Gamma. We measured the jump heights of all the players wearing these shoes. Now we have to test that whether any specific shoes has the significant effect on the Jump height. Or all the shoes are same. That means average effect of all the shoes are same or whether it varies significantly. If the effect varies significantly then how it varies among different shoes. Hypothesis Testing 2 The data that has been noted down is as follows Trial Pluto Omega II Beta Delta Gamma Super 1 29.1 29.2 28.5 28.4 27.7 29.8 29.1 28.9 28.0 27.9 30.0 28.8 29.2 28.8 28.0 29.0 28.7 28.3 29.0 28.2 31.1 28.8 30.0 28.9 28.0 149 144.6 144.9 143.1 2 3 4 5 Total 139.8 Solution to the case study: Now here we have 5 independent categorical variable or we have 5 treatments Pluto, Omega II, Beta super, Delta and Gamma. We have one response variable called jump height. Stating Hypothesis Null Hypothesis, H0: 1 = 2 = 3 = 4 = 5 That means we assume that average jump height by all the shoes are same Alternative Hypothesis, H1: 1 2 3 4 5 That means average jump height by all the shoes are not same, balls are significantly different. For testing the hypothesis we need to make ANOVA table, the format of ANOVA table is as follows Hypothesis Testing 3 Source of variation Between Treatments Residuals Total Degrees of Freedom k-1 n-k n-1 Sum of Squares SSB SSR SST Mean Squares SSB /(k - 1) SSR/(n - k) The relevant calculations are as follows k = Total number of samples or treatment = 5 n - sum total of all the data points of all the sample = (5 + 5 + 5 + 5 + 5) = 25 SST = SSB + SSR i - stands for number of treatment j - stands for number of response the first treatment is Pluto, second is Omega II, third is beta super, fourth is delta and fifth is gamma. yij2 = (29.1 + 29.8 + 30 + 29 + 31.1 ) 2 2 2 2 2 + (29.22 + 29.12 + 28.82 + 28.72 + 28.82) + (28.52 +28.92 + 29.22 + 28.32 + 302) + (28.42 + 282 + 28.82 + 292 +28.92) + (27.72 + 27.92 + 282 + 28.22 + 282) = 20831.22 Hypothesis Testing 4 (y..) = (29.1 + 29.8 + 30 + 29 + 31.1) + (29.2 + 29.1 + 28.8 + 28.7 + 28.8 ) + (28.5 + 28.9 + 29.2 + 28.3 + 30 ) + (28.4 + 28 + 28.8 + 29 +28.9 ) + (27.7 + 27.9 + 28 + 28.2 + 28 ) = 721.4 SST = 20831.22 - (721.42/25) = 14.50 SSB = ( 1492 5 + 144.6 2 5 + 144.92 143.12 139.82 + + 5 5 5 )-( 721.4 2 25 = 8.84 The ANOVA table will be as follows Source of variation Between Treatments Residuals Total Degrees of Freedom 4 20 24 Sum of Squares 8.84 5.66 14.5 Mean Squares 2.21 0.283 Hypothesis Testing Now the F statistic = 5 2.21 0.283 = 7.80 The critical value at 5% significance level on (4,20) degrees of freedom is 3.493 which means our null hypothesis is rejected. So we can conclude that the effect of all the shoes are not same, as per the selection of shoes the response variable which is jump height varies. Now since our null hypothesis is rejected that means we should do Post hoc analysis We will perform the Tukey HSD Test since all the samples have same sizes The HSD value for Tukey test will be q* MS with n q is a value taken from Q score Tukey table MS within = 0.283 n=5 q as given in Tukey table = 4.23( Tukey table has been given at the end of report) 0.283 The HSD will be = 4.23* 5 = 1.006 Now if the difference of mean between any two shoes is greater than Tukey HSD value then we can say that those two shoes have statistically different effect on jump height (Response variable) Hypothesis Testing 6 Majors Mean difference HSD value Is Mean difference > HSD Are The Shoes Different Pluto - Omega II (29.8-28.92)= 0.88 1.006 No No Pluto- Beta super (29.8- 28.98) = 0.82 1.006 No No Pluto - delta (29.8-28.62) = 1.18 1.006 Yes Yes Pluto - gamma (29.8-27.96)= 1.84 1.006 Yes Yes Omega II- Beta Super (28.92- 28.98) = -0.06 1.006 No No Omega II- delta (28.92-28.62) = 0.3 1.006 No No Omega II- gamma (28.92- 27.96) = 0.96 1.006 No No Beta super - delta (28.98-28.62) = 0.36 1.006 No No Beta super - gamma (28.98- 27.96) = 1.02 1.006 Yes Yes Delta - gamma (28.62-27.96) = 0.66 1.006 No No Conclusion The Shoe Pluto and delta, shoes Pluto and gamma and shoe beta supper and gamma have statistically different effect on the jump height as per Tukey HSD test. The average jump height of Pluto is more than delta, the average jump height of Pluto is more than gamma, and the Average jump height of shoe beta is more than gamma. Hypothesis Testing Now we will answer different questions on the basis of above study Q1) Before comparing the scores with an ANOVA, state your null and alternative hypotheses in words (not formulas). Answer) Stating Hypothesis Null Hypothesis, H0: 1 = 2 = 3 = 4 = 5 That means we assume that average jump height by all the shoes are same Alternative Hypothesis, H1: 1 2 3 4 5 That means average jump height by all the shoes are not same, balls are significantly different. Q2) Identify the independent and dependent variables. Answer) Dependent Variable is Jump height Independent variable is different shoes Q3) Name the levels in your identified factor. Answer) There are 5 independent levels in the Question Pluto, Omega, Beta super, Delta and Gamma. 7 Hypothesis Testing 8 Q4) State the within-group degrees of freedom and explain how you calculate it. Answer) Within group degrees of freedom = Total number of all the observations - Total number of samples. Within group degrees of freedom = 25 - 5 = 20 Q5) State the between-group degrees of freedom and explain how you calculate it. Answer ) Between group degrees of freedom = Total number of samples - 1 Between group degrees of freedom = 5 - 1 = 4 Q6) Identify the obtained F value Answer) Now the F statistic = 2.21 0.283 = 7.80 Q7) Identify the P value Answer ) P(F4,20 > 7.8) = 0.0005 Q8) Explain whether F test is significant. Explain how knows it and what it tells you? Hypothesis Testing 9 Answer) If our null hypothesis is rejected at significance level, then F test is said to be significant. In this case F test is significant because at the significance level of 5% null hypothesis rejected. Null hypothesis is rejected because F statistic value 7.8 is greater than critical value of 3.493 Q9) Explain what you can conclude about the effect of shoe choice on vertical lift (jumping height). Answer ) On the basis of testing we can say that effect of all the shoes on jumping height is not same. Q10) Should you conduct a post hoc test? Why or why not? If yes, conduct a Tukey HSD post hoc analysis. Explain what the results tell you about type of shoe choice and vertical lift. Answer) Since null hypothesis has been rejected, so we should carry the post hoc test. Post Hoc (Tukey test) The HSD value for Tukey test will be q* MS with n Hypothesis Testing 10 q is a value taken from Q score Tukey table MS within = 0.283 n=5 q as given in Tukey table = 4.23( Tukey table has been given at the end of report) The HSD will be = 4.23* 0.283 5 = 1.006 Now if the difference of mean between any two shoes is greater than Tukey HSD value then we can say that those two shoes have statistically different effect on jump height (Response variable) Majors Mean difference HSD value Is Mean difference > HSD Are The Shoes Different Pluto - Omega II (29.8-28.92)= 0.88 1.006 No No Pluto- Beta super (29.8- 28.98) = 0.82 1.006 No No Pluto - delta (29.8-28.62) = 1.18 1.006 Yes Yes Pluto - gamma (29.8-27.96)= 1.84 1.006 Yes Yes Omega II- Beta Super (28.92- 28.98) = -0.06 1.006 No No Omega II- delta (28.92-28.62) = 0.3 1.006 No No Omega II- gamma (28.92- 27.96) = 0.96 1.006 No No Beta super - delta (28.98-28.62) = 0.36 1.006 No No Hypothesis Testing 11 Beta super - gamma (28.98- 27.96) = 1.02 1.006 Yes Yes Delta - gamma (28.62-27.96) = 0.66 1.006 No No Conclusion The Shoe Pluto and delta, shoes Pluto and gamma and shoe beta supper and gamma have statistically different effect on the jump height as per Tukey HSD test. The average jump height of Pluto is more than delta, the average jump height of Pluto is more than gamma, and the Average jump height of shoe beta is more than gamma. Hypothesis Testing 12 Hypothesis Testing 1 Hypothesis testing in ANOVA Introduction: The case study deals with hypothesis testing in ANOVA. Where we have more than two samples. The samples are denoted by treatment also. We compare that whether the average effect of all the treatments is same or they differ significantly. Or we compare the independent mean and we conclude that whether the mean is same for all the populations or it differs significantly. Case Study: We have picked 5 shoes Pluto, Omega II, Beta super, Delta and Gamma. We measured the jump heights of all the players wearing these shoes. Now we have to test that whether any specific shoes has the significant effect on the Jump height. Or all the shoes are same. That means average effect of all the shoes are same or whether it varies significantly. If the effect varies significantly then how it varies among different shoes. Hypothesis Testing 2 The data that has been noted down is as follows Trial Pluto Omega II Beta Delta Gamma Super 1 29.1 29.2 28.5 28.4 27.7 29.8 29.1 28.9 28.0 27.9 30.0 28.8 29.2 28.8 28.0 29.0 28.7 28.3 29.0 28.2 31.1 28.8 30.0 28.9 28.0 149 144.6 144.9 143.1 2 3 4 5 Total 139.8 Solution to the case study: Now here we have 5 independent categorical variable or we have 5 treatments Pluto, Omega II, Beta super, Delta and Gamma. We have one response variable called jump height. Stating Hypothesis Null Hypothesis, H0: 1 = 2 = 3 = 4 = 5 That means we assume that average jump height by all the shoes are same Alternative Hypothesis, H1: 1 2 3 4 5 That means average jump height by all the shoes are not same, balls are significantly different. For testing the hypothesis we need to make ANOVA table, the format of ANOVA table is as follows Hypothesis Testing 3 Source of variation Between Treatments Residuals Total Degrees of Freedom k-1 n-k n-1 Sum of Squares SSB SSR SST Mean Squares SSB /(k - 1) SSR/(n - k) The relevant calculations are as follows k = Total number of samples or treatment = 5 n - sum total of all the data points of all the sample = (5 + 5 + 5 + 5 + 5) = 25 SST = SSB + SSR i - stands for number of treatment j - stands for number of response the first treatment is Pluto, second is Omega II, third is beta super, fourth is delta and fifth is gamma. yij2 = (29.1 + 29.8 + 30 + 29 + 31.1 ) 2 2 2 2 2 + (29.22 + 29.12 + 28.82 + 28.72 + 28.82) + (28.52 +28.92 + 29.22 + 28.32 + 302) + (28.42 + 282 + 28.82 + 292 +28.92) + (27.72 + 27.92 + 282 + 28.22 + 282) = 20831.22 Hypothesis Testing 4 (y..) = (29.1 + 29.8 + 30 + 29 + 31.1) + (29.2 + 29.1 + 28.8 + 28.7 + 28.8 ) + (28.5 + 28.9 + 29.2 + 28.3 + 30 ) + (28.4 + 28 + 28.8 + 29 +28.9 ) + (27.7 + 27.9 + 28 + 28.2 + 28 ) = 721.4 SST = 20831.22 - (721.42/25) = 14.50 SSB = ( 1492 5 + 144.6 2 5 + 144.92 143.12 139.82 + + 5 5 5 )-( 721.4 2 25 = 8.84 The ANOVA table will be as follows Source of variation Between Treatments Residuals Total Degrees of Freedom 4 20 24 Sum of Squares 8.84 5.66 14.5 Mean Squares 2.21 0.283 Hypothesis Testing Now the F statistic = 5 2.21 0.283 = 7.80 The critical value at 5% significance level on (4,20) degrees of freedom is 3.493 which means our null hypothesis is rejected. So we can conclude that the effect of all the shoes are not same, as per the selection of shoes the response variable which is jump height varies. Now since our null hypothesis is rejected that means we should do Post hoc analysis We will perform the Tukey HSD Test since all the samples have same sizes The HSD value for Tukey test will be q* MS with n q is a value taken from Q score Tukey table MS within = 0.283 n=5 q as given in Tukey table = 4.23( Tukey table has been given at the end of report) 0.283 The HSD will be = 4.23* 5 = 1.006 Now if the difference of mean between any two shoes is greater than Tukey HSD value then we can say that those two shoes have statistically different effect on jump height (Response variable) Hypothesis Testing 6 Majors Mean difference HSD value Is Mean difference > HSD Are The Shoes Different Pluto - Omega II (29.8-28.92)= 0.88 1.006 No No Pluto- Beta super (29.8- 28.98) = 0.82 1.006 No No Pluto - delta (29.8-28.62) = 1.18 1.006 Yes Yes Pluto - gamma (29.8-27.96)= 1.84 1.006 Yes Yes Omega II- Beta Super (28.92- 28.98) = -0.06 1.006 No No Omega II- delta (28.92-28.62) = 0.3 1.006 No No Omega II- gamma (28.92- 27.96) = 0.96 1.006 No No Beta super - delta (28.98-28.62) = 0.36 1.006 No No Beta super - gamma (28.98- 27.96) = 1.02 1.006 Yes Yes Delta - gamma (28.62-27.96) = 0.66 1.006 No No Conclusion The Shoe Pluto and delta, shoes Pluto and gamma and shoe beta supper and gamma have statistically different effect on the jump height as per Tukey HSD test. The average jump height of Pluto is more than delta, the average jump height of Pluto is more than gamma, and the Average jump height of shoe beta is more than gamma. Hypothesis Testing Now we will answer different questions on the basis of above study Q1) Before comparing the scores with an ANOVA, state your null and alternative hypotheses in words (not formulas). Answer) Stating Hypothesis Null Hypothesis, H0: 1 = 2 = 3 = 4 = 5 That means we assume that average jump height by all the shoes are same Alternative Hypothesis, H1: 1 2 3 4 5 That means average jump height by all the shoes are not same, balls are significantly different. Q2) Identify the independent and dependent variables. Answer) Dependent Variable is Jump height Independent variable is different shoes Q3) Name the levels in your identified factor. Answer) There are 5 independent levels in the Question Pluto, Omega, Beta super, Delta and Gamma. 7 Hypothesis Testing 8 Q4) State the within-group degrees of freedom and explain how you calculate it. Answer) Within group degrees of freedom = Total number of all the observations - Total number of samples. Within group degrees of freedom = 25 - 5 = 20 Q5) State the between-group degrees of freedom and explain how you calculate it. Answer ) Between group degrees of freedom = Total number of samples - 1 Between group degrees of freedom = 5 - 1 = 4 Q6) Identify the obtained F value Answer) Now the F statistic = 2.21 0.283 = 7.80 Q7) Identify the P value Answer ) P(F4,20 > 7.8) = 0.0005 Q8) Explain whether F test is significant. Explain how knows it and what it tells you? Hypothesis Testing 9 Answer) If our null hypothesis is rejected at significance level, then F test is said to be significant. In this case F test is significant because at the significance level of 5% null hypothesis rejected. Null hypothesis is rejected because F statistic value 7.8 is greater than critical value of 3.493 Q9) Explain what you can conclude about the effect of shoe choice on vertical lift (jumping height). Answer ) On the basis of testing we can say that effect of all the shoes on jumping height is not same. Q10) Should you conduct a post hoc test? Why or why not? If yes, conduct a Tukey HSD post hoc analysis. Explain what the results tell you about type of shoe choice and vertical lift. Answer) Since null hypothesis has been rejected, so we should carry the post hoc test. Post Hoc (Tukey test) The HSD value for Tukey test will be q* MS with n Hypothesis Testing 10 q is a value taken from Q score Tukey table MS within = 0.283 n=5 q as given in Tukey table = 4.23( Tukey table has been given at the end of report) The HSD will be = 4.23* 0.283 5 = 1.006 Now if the difference of mean between any two shoes is greater than Tukey HSD value then we can say that those two shoes have statistically different effect on jump height (Response variable) Majors Mean difference HSD value Is Mean difference > HSD Are The Shoes Different Pluto - Omega II (29.8-28.92)= 0.88 1.006 No No Pluto- Beta super (29.8- 28.98) = 0.82 1.006 No No Pluto - delta (29.8-28.62) = 1.18 1.006 Yes Yes Pluto - gamma (29.8-27.96)= 1.84 1.006 Yes Yes Omega II- Beta Super (28.92- 28.98) = -0.06 1.006 No No Omega II- delta (28.92-28.62) = 0.3 1.006 No No Omega II- gamma (28.92- 27.96) = 0.96 1.006 No No Beta super - delta (28.98-28.62) = 0.36 1.006 No No Hypothesis Testing 11 Beta super - gamma (28.98- 27.96) = 1.02 1.006 Yes Yes Delta - gamma (28.62-27.96) = 0.66 1.006 No No Conclusion The Shoe Pluto and delta, shoes Pluto and gamma and shoe beta supper and gamma have statistically different effect on the jump height as per Tukey HSD test. The average jump height of Pluto is more than delta, the average jump height of Pluto is more than gamma, and the Average jump height of shoe beta is more than gamma. Hypothesis Testing 12