1. HYPOTHESIS TESTS

2. Good answers come from good questions not from esoteric analysis
Good answers come from good questions not from esoteric analysis. (Schoolman et al., (1968)

3. Introduction
We can now build on the ideas of the previous lessons. We will use the ideas of estimation and hypothesis testing. Other important ideas are the relation between the analysis and the research design and the nature of the observations.
We are going to deal comparing groups of observations with respect to continous data, starting with the simplest case where we wish to compare a single group of observations with some prespecified value and moving through to the case where we have sevaral sets of observations on each of a group individuals. Parametric approaches to analysis are introduced.

4. Choosing an appropriate method of analysis
When choosing an appropriate method of analysis there are several aspects of data that we must consider,
relating to the design of the study,
the nature of the data,
and the purpose of the analysis.

5. 1. The number of groups of the observations
Choosing an appropriate method of analysis
1. The number of groups of the observations
Although methods of dealing with several groups of observations can be used for just one or two groups it is convenient to consider the one and two group cases seperately, as the methods can be simplified, and there are fewer problems of interpretation. The two group case is the most common type of statistical analysis.

6. 2. Independent or dependent group of observations
Choosing an appropriate method of analysis
2. Independent or dependent group of observations
When there are two or more sets of observations there are two types of design that must be distinguish:
The observations relate to independent groups of individuals. Ex: groups of patients with different diseases.
Each set of observation is made on the same group of individuals. Ex: we may have antenatal and postnatal blood pressure measurements from one group of women. We call such data paired.

7. Choosing an appropriate method of analysis
3. The type of data
The distinction between continous and categorical data were discussed in the previous lessons.
Specifically, parametric methods are based on calculating means and standart deviations, so they are inappropriate for ordered categorical data such as Apgar score.

8. 4. The distrubition of data
Choosing an appropriate method of analysis
4. The distrubition of data
For independent groups, parametric methods require the observations within each group to have an approximately Normal distribution, and the standard deviations in each group should be similar. If the raw data do not satisfy these conditions, a transformation may be successful. Otherwise a non parametric method should be used.
For paired data relating to two or more observations on the same people there is no assumption that each set of observations should be Normally distributed, but there is a different assumption of Normality.

9. 5. The objective of the analysis
Choosing an appropriate method of analysis
5. The objective of the analysis
Hypotesis testing are considered throughout this lesson. However, with three or more groups of data there are several possible comparisons between groups. The choice of which to investigate should follow directly from objectives of the study.

10. Hypothesis Tests Number of Samples One Sample Two More Than
Two Samples

11. Descriptive Statistic
Hypothesis Tests
Descriptive Statistic
Arith. Mean
Median
Proportion
Variance

12. Hypothesis Tests
Assumptions
Parametric Tests
Non-Parametric Tests

13. One Sample Descriptive Statistic Arith. Mean Significance Test
for Pop. Mean
Median
Sign Test
Proportion
for Pop. Prop.
Variance
for Pop. Variance

14. for Population Variance
Examples for
One Sample
Tests
Significance Test
for
Population Mean
Sign Test
for Population
Proportion
for Population Variance
Examples
A researcher wants to test whether a new drug reduces the blood pressure more than standard drugs. If it is known that standard drugs reduce blood pressure 10 mmHg, is this new drug better or not?
H0 : µ = 10 mmHg, H1 : µ > 10 mmHg
It is believed that median apgar scores of new borns is 8 in a clinic. If in a given day the apgar scores are derived as , is this belief true or not?
H0 : M = 8, H1 : M > 8
Lung cancer prevalance is assumed to be in a region. Is this assumption true, if the prevalance is found as after studying randomly selected 500 people from this region?
H0 : P= 0, H1 : P ≠ 0,002
It is believed that variance of cholesterol is lower than 1500 for adults in a region. Is this belief true if the variance is found as 1400 in a study carried out on 800 randomly selected people?
H0 : 2= H1 : 2 < 1500

15. Two Samples (parametric)
Independent
Dependent
Descriptive
Statistic
Descriptive
Statistic
Significance Test for Two Independent Samples
Testing the difference between systolic blood pressure means of males and females above 50 years old
Significance Test for Two Dependent (Paired) Samples
Testing the difference between blood sugar level means before and after anesthesia
A. Mean
A. Mean
Significance Test for Two Independent Proportions
Testing recovery proportions of treatment and control groups
Significance Test for Two Dependent (Paired) Proportions
Investigating the reduction in rates of complaints about movement limitations after treatment relative to before treatment
Prop.
Prop.
Median Test
Investigating the similarity between language skill test scores of pre-school children in two different age groups
Significance Test for Two Dependent (Paired) Proportions
Investigating the reduction in scores of complaints about movement limitations after treatment relative to before treatment
Median
Median
Homogeneity of Variances Test (F Test)
Testing the homogeneity of variances of systolic blood pressures of males and females aged above 50
Homogeneity of Variances Test (t Test)
Testing the reduction in variability of bone density of women with osteoporosis after treatment
Variance
Variance

16. Two Samples (non-parametric)
Independent
Dependent
Descriptive
Statistic
Descriptive
Statistic
Wilcoxon Sign Test
Testing the difference between white blood cells of patients before and after having chemotherapy
Mann Whitney U Test
Investigating the difference between number of white blood cells of breast cancer patients with and without lymph node
A. Mean
A. Mean
2 x 2 Chi – Square (Exact Chi-Square)
Comparing frequency of low birth weights in women with and without hypertension
Mc-Nemar Test
Testing the reduction in pain complaints after treatment relative to before treatment
Prop.
Prop.
2 x 2 Chi – Square (Exact Chi-Square)
Comparing frequency of low birth weights in women with and without hypertension
Mc Nemar Test
Testing the reduction in pain scores after treatment relative to before treatment
Median
Median
Kolmogorov- Smirnov Two Samples Test
Comparing distributions of apgar scores of premature and mature new borns
Bowker Test*
Testing the difference between distributions of pain scores before and after treatment
Variance
Variance

17. K Samples (parametric)
Independent
Dependent
Descriptive
Statistic
Descriptive
Statistic
One Way Analysis of Variance
Comparing survival times of breast cancer patients in different phases
Analysis of Variances for Repeated Measures
Investigating the difference between three anxiety score measurements after treatment
A. Mean
A. Mean
Chi-Square
Comparing proportions of hospitilization of children with acute respiratory infections in different regions
Cochran Q Test
Investigating the efficiency of a drug in reducing high cholesterol levels to normal levels
Prop.
Prop.
Median Test (Multiple)
Investigating the similarity of median of apgar scores according to number of pregnancies
Cochran Q Test
Investigating the success of a drug in reducing cholesterol in different periods
Median
Median
Homogeneity of Variances Test (F Test)
Comparing variances of survival times of breast cancer patients in different phases
Homogeneity of Variances Test (Sphericity)
Testing the assumption of sphericity for analysis of variances in repeated measures
Variance
Variance

18. K Samples (non-parametric)
Independent
Dependent
Descriptive
Statistic
Descriptive
Statistic
Kruskal Wallis Test
Comparing fasting blood sugar measurements in Underweight-Normal-Overweight groups
Friedman Variance Analysis
Investigating the difference in 3 auditory threshold scores after treatment
A. Mean
A. Mean
Chi – Square
Comparing distributions of obesity in 4 different groups
Cochran Q Test
Comparing the efficiency of 4 different drugs used for same patients
Prop.
Prop.
Cochran Q Test
Investigating the success of a drug in reducing cholesterol in different periods
Median Test (Multiple)
Investigating the similarity of median of apgar scores according to number of pregnancies
Median
Median
Chi-Sqaure
Comparing distributions of survival times
of breast cancer patients in different phases
Homogeneity of Variances Test* (Sphericity)
This test may be used after transformation of data
Variance
Variance