4 - Testing hypothesis and their limits

Question 1

How can we obtain confidence intervals?

Answer 1

From the variance and standard deviation of the mean

Question 2

Measures of dispersion

Answer 2

Variance and standard deviation

Question 3

Standard Deviation

Answer 3

most common measure used for normal or near normal distributions.
• Defined by a statistical formula, but remember that:
• The mean +/- one SD contains about 2/3 of the observations.
• the mean +/- 2 SD’s includes about 95% of the observations.

Question 4

Variance

Answer 4

• first compute the mean and store it
• subtract the mean from every sample, Xi, square it and store the result
• sum all the squared values
• divide the sum by n-1

Question 5

95% confidence interval

Answer 5

(h - 1.96 x s.e(h)) (h + 1.96 x s.e(h))

Question 6

normal distribution

Answer 6

A function that represents the distribution of variables as a symmetrical bell-shaped graph.

Question 7

measures of central tendency

Answer 7

mean, median, mode - in a normal distribution, all are equal

Parametric statistical methods assume a distribution with known shape

Question 8

Negative + positive skew

Answer 8

negative - Bell of curve is to the right

positive - Bell of curve is to the left

Question 9

Two things that lead to narrower (or wider) confidence intervals:

Answer 9

• a larger sample size implies a smaller standard error = narrower.
• If the variance is small, the population will be fairly homogeneous and thus there will be little variation in any particular sample taken from the population = narrower.

Question 10

Classical Hypothesis Testing:Steps

Answer 10

1. Define the null hypothesis
2. Define the alternative hypothesis
3. Calculate a p value
4. Accept or reject the null hypothesis based on the p value
5. If the null hypothesis is rejected, then accept the alternative hypothesis

Question 11

The Null Hypotheses

Answer 11

no difference between the two groups to be compared

Question 12

The Alternative Hypothesis

Answer 12

there is a difference between the 2 groups to be compared

• Example: Difference in Pain Score on 100mm VAS of 13mm or greater

Question 13

The p value

Answer 13

probability of obtaining the results observed, if the null hypothesis were true
• If p = 0.7, then the chance of obtaining the same results as the experiment is 70%
• accept the null hypothesis
• If p= 0.01 then the chance of obtaining the same results as the experiment is 1%
- Very unlikely due to chance!
- So we reject the null hypothesis

Question 14

Rejecting the Null Hypothesis

Answer 14

• The cut-point for rejecting the null hypothesis is arbitrary (a)
• Typically, a = 0.05
• If the null hypothesis is rejected, then the alternative hypothesis is accepted as true

Question 15

Limitations of the p Value

Answer 15

• p < 0.05 tells us that the observed treatment difference is “statistically significantly” different
• p < 0.05 does not tell us:
• The uncertainty around the point estimate
• The likelihood that the true treatment effect is clinically important

Question 16

t-test

Answer 16

It is based on t-value, a ratio of the difference between two means and their pooled standard errors.
Larger is the t-value, more significant is the difference.
However, this value is not used. And commonly decisions are made based on p-values.
p-values are obtained considering the size of the population (degrees of freedom)

Question 17

Contingency tables

Answer 17

Categorical data arranged in a table of rows and columns in which the Individual entries are counts.

Question 18

Chi-square

Answer 18

compares Proportions

Categorical variable,more than 5 patients inany particular “cell”