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# Quantitative methods

### Introduction:

Present study is aimed to test whether daily exercise enhance the memory in people with moderate dementia. For this study patients have been chosen randomly and out of total sample 20 has undergone half an hour of supervised treadmill waling at the university on daily basis for a month. 20 people out of sample were asked to visit the university and have conversation with the researcher for half an hour each day for a month. All the relevant data related to the memory has been stored by the researcher before the treatment period, during the test and at the end of the treatment. Each participant had scope to achieve highest marks of 100 and researcher scored them as per the memory test after the complete test. Considering the achieved marks statistical analysis has been done and outcome has been presented below.

### Justification of analysis method:

For the present study, two way mixed Anova method has been utilised because there were two independent variable. As per the stored data, time points and exercise levels were the two independent variables. Besides this time has been considered as a variable for the study and it is repeated measure that means participants in all three conditions of the Anova test were dependent. Other four conditions of the Anova were independent measures where different participants were contested under different conditions.

### Analysis:

The analysis has been done meeting all the assumptions for the two way mixed anova. As per the first assumption of two way mixed Anova method, dependent variable should be measured at a continuous level. As per the present case, dependent variable (Memory), has been set to continuous level so as to meet the first assumption. Second assumption of the two way mixed Anova method depicts that within subject factors, there should be at least two categorical matched groups that represent same subjects within both groups. As per the present case, there were two categorical variable that makes the test justified with second assumption as well.

 Within-Subjects Factors Measure: MEASURE_1 health Dependent Variable 1 Baseline 2 Two_weeks 3 Four_weeks

 Between-Subjects Factors N Group Exercise 19 No_exercise 20

Thirdly two way mixed Anova method need to have at least two independent groups between subjects factor independent variable. As per the group distribution it can be seen that there has been no significant outlier within the chosen data set apart from one participant within the exercise group. Moreover, significant outlier should not be present within the dataset. Thus, outlier has been removed and not considered for the test (Kuznetsova et al. 2015).

 Multivariate Testsa Effect Value F Hypothesis df Error df Sig. health Pillai's Trace .985 1160.498b 2.000 36.000 .000 Wilks' Lambda .015 1160.498b 2.000 36.000 .000 Hotelling's Trace 64.472 1160.498b 2.000 36.000 .000 Roy's Largest Root 64.472 1160.498b 2.000 36.000 .000 health * Group Pillai's Trace .963 472.543b 2.000 36.000 .000 Wilks' Lambda .037 472.543b 2.000 36.000 .000 Hotelling's Trace 26.252 472.543b 2.000 36.000 .000 Roy's Largest Root 26.252 472.543b 2.000 36.000 .000 a. Design: Intercept + Group  Within Subjects Design: health b. Exact statistic

As per the multivariate test it can be seen that health group has showcased significant outcome with degrees of freedom 2. F Value was high and makes the test aligned with the assumption 5 that argues dependent variable should normally distributed (Parnaudeau et al. 2015).

 Mauchly's Test of Sphericitya Measure: MEASURE_1 Within Subjects Effect Mauchly's W Approx. Chi-Square df Sig. Epsilonb Greenhouse-Geisser health .966 1.234 2 .539 .967

 Mauchly's Test of Sphericitya Measure: MEASURE_1 Within Subjects Effect Epsilon Huynh-Feldt Lower-bound health 1.000 .500 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.a a. Design: Intercept + Group  Within Subjects Design: health b. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.

 Tests of Within-Subjects Effects Measure: MEASURE_1 Source Type III Sum of Squares df Mean Square F health Sphericity Assumed 3430.762 2 1715.381 1095.397 Greenhouse-Geisser 3430.762 1.935 1773.198 1095.397 Huynh-Feldt 3430.762 2.000 1715.381 1095.397 Lower-bound 3430.762 1.000 3430.762 1095.397 health * Group Sphericity Assumed 1557.131 2 778.565 497.172 Greenhouse-Geisser 1557.131 1.935 804.807 497.172 Huynh-Feldt 1557.131 2.000 778.565 497.172 Lower-bound 1557.131 1.000 1557.131 497.172 Error(health) Sphericity Assumed 115.883 74 1.566 Greenhouse-Geisser 115.883 71.587 1.619 Huynh-Feldt 115.883 74.000 1.566 Lower-bound 115.883 37.000 3.132

Homogeneity of variance for each combination of the groups of factors are mandatory for the at least two independent groups. Tests within the subject effect showcase that F value for each health group was high enough and sphericity was justified as the two way mixed anova analysis..

 Tests of Within-Subjects Effects Measure: MEASURE_1 Source Sig. health Sphericity Assumed .000 Greenhouse-Geisser .000 Huynh-Feldt .000 Lower-bound .000 health * Group Sphericity Assumed .000 Greenhouse-Geisser .000 Huynh-Feldt .000 Lower-bound .000 Error(health) Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound

This section of the analysis showcase the within subject effect where the significance of the groups were valid to make the assumption that exercise enhance memory power of the people with slight dementia.

 Tests of Within-Subjects Contrasts Measure: MEASURE_1 Source health Type III Sum of Squares df Mean Square F Sig. health Linear 2681.899 1 2681.899 2075.396 .000 Quadratic 748.863 1 748.863 407.047 .000 health * Group Linear 778.689 1 778.689 602.591 .000 Quadratic 778.442 1 778.442 423.125 .000 Error(health) Linear 47.813 37 1.292 Quadratic 68.071 37 1.840

Within subject contrasts showcase sum of square for the health and health group are good enough to make the chosen mode demonstrate as a good fit model. As the type III sum of squares are much higher and distributed uniformly within the subject they are significant to showcase the model it good fit (Vardigan et al. 2015).

 Tests of Between-Subjects Effects Measure: MEASURE_1  Transformed Variable: Average Source Type III Sum of Squares df Mean Square F Sig. Intercept 354812.373 1 354812.373 180397.935 .000 Group 2954.752 1 2954.752 1502.290 .000 Error 72.773 37 1.967

Estimated Marginal Means

 1. Group Measure: MEASURE_1 Group Mean Std. Error 95% Confidence Interval Lower Bound Upper Bound Exercise 60.114 .186 59.738 60.490 No_exercise 50.060 .181 49.693 50.427

 2. health Measure: MEASURE_1 health Mean Std. Error 95% Confidence Interval Lower Bound Upper Bound 1 47.432 .225 46.977 47.887 2 58.666 .238 58.183 59.149 3 59.163 .154 58.851 59.475

Estimated marginal means demonstrate health status was better for the group who performed exercise compared to the other who performed conversation with the researcher.

 3. Group * health Measure: MEASURE_1 Group health Mean Std. Error 95% Confidence Interval Lower Bound Upper Bound Exercise 1 47.474 .322 46.822 48.125 2 67.342 .341 66.651 68.033 3 65.526 .220 65.080 65.973 No_exercise 1 47.390 .313 46.755 48.025 2 49.990 .332 49.316 50.664 3 52.800 .215 52.365 53.235

Profile Plots

As per the estimated marginal measure variances of the differences between the groups of the between subject factor can be observed. It showcase that people who performed exercise had better mental condition compared to the other.

### Leverage point:

Leverage was checked using the calculation as follows:

v is the number of predictors in the model and n is the number of data point

Thus, Leverage point is = 2[(2+1)/39]

= .15

### Conclusion:

From the above analysis it can be seen that physical exercise has enhanced the memory of the participants by a large extent compared to the people who belonged to the non-exercise group. In certain cases as per the test it can be observed that during the mid-weeks participants scored better than the end result who were in exercise group and reverse can be observed in case of no exercise group. Thus, it can be entailed as per the test that prolonged exercise enhance the memory, however, that do not last for long time. On the other hand, if exercise is not performed and only conversation therapy is utilised for the people with light dementia, it could enhance the memory marginally. All the conditions for the Anova test has been met and it also showcase that data collected by the researcher were justified.

### Reference:

Kuznetsova, A., Christensen, R.H., Bavay, C. and Brockhoff, P.B., 2015. Automated mixed ANOVA modeling of sensory and consumer data. Food Quality and Preference40, pp.31-38.

Parnaudeau, S., Taylor, K., Bolkan, S.S., Ward, R.D., Balsam, P.D. and Kellendonk, C., 2015. Mediodorsal thalamus hypofunction impairs flexible goal-directed behavior. Biological psychiatry77(5), pp.445-453.

Vardigan, J.D., Cannon, C.E., Puri, V., Dancho, M., Koser, A., Wittmann, M., Kuduk, S.D., Renger, J.J. and Uslaner, J.M., 2015. Improved cognition without adverse effects: novel M1 muscarinic potentiator compares favorably to donepezil and xanomeline in rhesus monkey. Psychopharmacology232(11), pp.1859-1866.