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Quantitative methods

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Table of Contents-

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.

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