Pharmaceutics Assignment-MAH_130115_25370_2_49566

We have to compare the three batches in terms of their arithmetic mean tablet weight. For this comparison purpose, we have to see some descriptive statistics for these three batches. We have to use the one way ANOVA test for comparison of means of three batches. We have to use the SPSS for statistical analysis purpose. Let us see all this comparison in detail.

First we have to see the descriptive statistics for the first batch. We know that descriptive statistics consist of the mean, standard deviation, variance, minimum, kurtosis, etc. All descriptive statistics for the first batch is given in the following table:

Descriptive Statistics

N

Minimum

Sum

Mean

Std. Deviation

Variance

Batch1

20

.35

7.37

.3686

.01546

.000

Valid N (listwise)

20

Some other descriptive statistics for the first batch are given in the following table:

Descriptive Statistics

N

Range

Maximum

Mean

Skewness

Kurtosis

Statistic

Statistic

Statistic

Std. Error

Statistic

Std. Error

Statistic

Std. Error

Batch1

20

.05

.39

.00346

.103

.512

-1.418

.992

Valid N (listwise)

20

The box plot for the weights of first batch is given below:

 

Now, let us see the descriptive statistics for the weights of second batch. All descriptive statistics for the weights of second batch are given in the following two tables:

Descriptive Statistics

N

Minimum

Sum

Mean

Std. Deviation

Variance

Batch2

20

.35

7.40

.3699

.01636

.000

Valid N (listwise)

20

Descriptive Statistics

N

Range

Maximum

Mean

Skewness

Kurtosis

Statistic

Statistic

Statistic

Std. Error

Statistic

Std. Error

Statistic

Std. Error

Batch2

20

.05

.39

.00366

-.020

.512

-1.657

.992

Valid N (listwise)

20

The box plot for the weights of the second batch is given as below:

 

Now, we have to see the some descriptive statistics for the weights of the third batch. The descriptive statistics for the weights of third batch are given in the following table:

Descriptive Statistics

N

Minimum

Sum

Mean

Std. Deviation

Variance

Batch3

20

.38

7.95

.3974

.00885

.000

Valid N (listwise)

20

Descriptive Statistics

N

Range

Maximum

Mean

Skewness

Kurtosis

Statistic

Statistic

Statistic

Std. Error

Statistic

Std. Error

Statistic

Std. Error

Batch3

20

.03

.41

.00198

-.440

.512

-1.107

.992

Valid N (listwise)

20

The box plot for the weights of the third batch is given as below:

 

Now, we have to compare these three batches or average weights of these three batches. For comparison of means of weights of these three batches, we have to use the one way ANOVA test. We take significance level for this test as alpha = 0.05.

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The means of weights for all three batches are same.

Alternative hypothesis: Ha: The means of weights for all three batches are not same.

In statistical words, these hypotheses are written as below:

H0: µ1 = µ2 = µ3 V/s Ha: µ1 ≠ µ2 ≠ µ3

Where, µ1 is the mean for weights for the first batch, µ2 is the mean for weights for the second batch and µ3 is the mean for weights of third batch.

The ANOVA table by using SPSS is given as below:

ANOVA

Weight

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

.011

2

.005

27.191

.000

Within Groups

.011

57

.000

Total

.022

59

For this ANOVA table, we get the p-value as 0.000 and we have level of significance or alpha value = 0.05. We know the decision rule is given as below:

We reject the null hypothesis if the p-value is less than the alpha value or level of significance and we do not reject the null hypothesis if the p-value is greater than the alpha value or level of significance.

Here we have alpha value = 0.05 and p-value = 0.05

That is, here p-value < alpha value

So, we reject the null hypothesis that the means of weights for all three batches are same.

In the next topic we have to compare the means and standard deviations for the tablet tensile strength and tablet porosity. Also we have to find the some intervals for means. Let us see the descriptive statistics for tensile strength and porosity in detail. The means and standard deviations are given in the following table:

Descriptive Statistics

N

Mean

Std. Deviation

TSB1

10

10.5460

.02066

TSB2

10

10.0500

.00000

TSB3

10

10.4200

.12293

TPB1

10

3.5290

.02234

TPB2

10

3.6650

.15219

TPB3

10

3.6800

.31903

Valid N (listwise)

10

TSB1 = Tensile strength for batch 1

TSB2 = Tensile strength for batch 2

TSB3 = Tensile Strength for batch 3

TPB1 = Tablet porosity for batch 1

TPB2 = Tablet porosity for batch 2

TPB3 = Tablet porosity for batch 3

The overall mean and standard deviation for the strength and porosity is given as below:

Descriptive Statistics

Mean

Std. Deviation

N

Strength

10.3387

.22508

30

Porosity

3.6247

.20905

30

One standard deviation limits from the mean for the strengths and porosity of these three batches are given as below:

Batch

Tensile strength

Porosity

Lower

Upper

Lower

Upper

Batch 1

10.52534

10.56666

3.50666

3.55134

Batch 2

10.05

10.05

3.51281

3.81719

Batch 3

10.29707

10.54293

3.36097

3.99903

Now, in the next topic we have to see the relationship between the strength and porosity. We have to check whether there is any linear relationship or association between the strength and porosity exists or not. For this purpose we have to find the correlation coefficient between the two variables strength and porosity.

The SPSS output for the correlation coefficient is given as below:

Correlations

Strength

Porosity

Strength Pearson Correlation

1

-.092

Sig. (2-tailed)

.627

N

30

30

Porosity Pearson Correlation

-.092

1

Sig. (2-tailed)

.627

N

30

30

The correlation coefficient between the two variables strength and porosity is found as 0.627, this is a positive correlation coefficient. This indicates that there is positive considerable linear relationship or association exists between the two variables strength and porosity.

Let us see regression analysis for above two variables. The SPSS output is given below:

Descriptive Statistics

Mean

Std. Deviation

N

Strength

10.3387

.22508

30

Porosity

3.6247

.20905

30

Below is the correlation coefficient for these two variables.

Correlations

Strength

Porosity

Pearson Correlation Strength

1.000

-.092

Porosity

-.092

1.000

Sig. (1-tailed) Strength

.

.314

Porosity

.314

.

N Strength

30

30

Porosity

30

30

The description for the variables is given in the following table:

Variables Entered/Removeda

Model

Variables Entered

Variables Removed

Method

1 Porosityb

.

Enter
a. Dependent Variable: Strength
b. All requested variables entered.

The model summary for the regression analysis is given below:

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

Durbin-Watson

1

.092a

.009

-.027

.22808

.556

a. Predictors: (Constant), Porosity
b. Dependent Variable: Strength

For the above model summary, we get the coefficient of determination as 0.009, this means that only 0.9% of the variation in the dependent variable is explained by the independent variable.

The ANOVA table for the regression analysis is given below:

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1 Regression

.013

1

.013

.241

.627b

Residual

1.457

28

.052

Total

1.469

29

a. Dependent Variable: Strength
b. Predictors: (Constant), Porosity

For above ANOVA, we get the p-value as 0.627 which is greater than the level of significance or alpha value = 0.05, so we do not reject the null hypothesis that the given regression model is significant.

The coefficients for the regression equation are given below:

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

95.0% Confidence Interval for B

Collinearity Statistics

B

Std. Error

Beta

Lower Bound

Upper Bound

Tolerance

VIF

1 (Constant)

10.699

.736

14.546

.000

9.192

12.206

Porosity

-.099

.203

-.092

-.491

.627

-.514

.316

1.000

1.000

a. Dependent Variable: Strength

Collinearity Diagnosticsa

Model Dimension

Eigenvalue

Condition Index

Variance Proportions

(Constant)

Porosity

1 1

1.998

1.000

.00

.00

2

.002

35.299

1.00

1.00

a. Dependent Variable: Strength

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

10.2914

10.3908

10.3387

.02079

30

Residual

-.30007

.28871

.00000

.22412

30

Std. Predicted Value

-2.274

2.510

.000

1.000

30

Std. Residual

-1.316

1.266

.000

.983

30

a. Dependent Variable: Strength

Chart

 

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