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:

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

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:

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:

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: H_a: 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 H_a: 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:

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:

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:

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

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:

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:

Below is the correlation coefficient for these two variables.

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

The model summary for the regression analysis is given below:

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:

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:

Chart

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