Biostatistics 📊✅

Define chi-squared test

1. The chi-squared test is a statistical test used to determine the statistical significance of any difference between the expected and observed results, and the probability that such difference is due to chance.

Define p-value of chi-squared test

1. p-value is the probability that the difference between the expected and observed results is due to chance.

2. The chance events could be due to small sample size or counting error.

Perform the chi-squared test and state a suitable conclusion for the null hypothesis to not be rejected [5m]

Null hypothesis: There is no significant difference between the expected and observed results.

Alternative hypothesis: There is significant difference between the expected and observed results.

Calculations:

Conclusion:

1. For () degrees of freedom and level of significance p= (), calculated chi-squared value of () is less than critical chi-squared value of ().

2. The probability that the difference is due to chance is more than 0.05.

3. The difference between the expected and observed results is statistically insignificant and due to chance.

4. Do not reject null hypothesis.

5. Therefore, the observed results are consistent with the expected ratio of 9:3:3:1/ 1:1:1:1.

Perform the chi-squared test and state a suitable conclusion for the null hypothesis to be rejected

Null hypothesis: There is no significant difference between the expected and observed results.

Alternative hypothesis: There is significant difference between the expected and observed results.

Calculations:

Conclusion:

1. For () degrees of freedom and level of significance p= (), calculated chi-squared value of () is more than critical chi-squared value of ().

2. The probability that the difference is due to chance is less than 0.05.

3. The difference between the expected and observed results is statistically significant and not due to chance.

4. Reject null hypothesis.

5. Therefore, the observed results are not consistent with the expected ratio of 9:3:3:1/ 1:1:1:1.

Define standard deviation

1. Standard deviation measures the spread of the data about the mean.

Describe the distribution of data for a typical normal distribution curve

1. 99.7% between +- 3s.d.

2. 95.4% between +- 2s.d.

3. 68.3% between +-1s.d.

Define t-test

1. The t-test is a statistical test used to compare the means of two sets of data and determine if there is any significant difference between them.

Define p-value of t-test

1. p-value is the probability that the difference between the means of sample 1 and sample 2 is due to chance.

Perform the t-test and state a suitable conclusion for the null hypothesis to not be rejected [5m]

Null hypothesis: There is no significant difference between the means of sample 1 and 2.

Alternative hypothesis: There is significant difference between the means of sample 1 and 2. OR The mean of sample 1 is significantly smaller/ greater/ shorter/ longer than that of sample 2.

Table: Mean (), Standard deviation and Sample size.

Calculations:

Conclusion:

1. For () degrees of freedom, calculated t value of () is less than critical t value of ().

2. The probability that the difference is due to chance is more than 0.05.

3. The difference between the means of the 2 samples is not statistically significant and due to chance.

4. Do not reject null hypothesis.

5. Therefore…

Perform the t-test and state a suitable conclusion for the null hypothesis to be rejected [5m]

Null hypothesis: There is no significant difference between the means of sample 1 and 2.

Alternative hypothesis: There is significant difference between the means of sample 1 and 2. OR The mean of sample 1 is significantly smaller/ greater/ shorter/ longer than that of sample 2.

Table: Mean (), Standard deviation and Sample size.

Calculations:

Conclusion:

1. For () degrees of freedom, calculated t value of () is more than critical t value of ().

2. The probability that the difference is due to chance is less than 0.05.

3. The difference between the means of the 2 samples is statistically significant and not due to chance.

4. Reject null hypothesis.

5. Therefore…