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1-131-131-2 Descriptive and Inferential 1-2 Descriptive and Inferential
StatisticsStatistics
Inferential statisticsInferential statistics consists of generalizing from samples to populations, performing hypothesis testing, determining relationships among variables, and making predictions.
A study conducted at Manatee Community College revealed that students who attended class 95% to 100% of the time usually received an A in the class. Students who attended class 80% to 90% of the time usually received a B or C in the class. Students who attended class less than 80% of the time usually received a D or an F or eventually withdrew from the class.
Answer the following questions:1. What are the variable under study?2. What are the data in the study?3. Are descriptive, inferential, or both types of
statistics used?4. What is the population under study?5. Was a sample collected? If so, from where?6. From the information given, comment on the
1-161-16 1-3 Variables and Types of Data1-3 Variables and Types of Data
Qualitative variablesQualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute. For example, gender (male or female).
1-171-17 1-3 Variables and Types of Data1-3 Variables and Types of Data
Quantitative variablesQuantitative variables are numerical in nature and can be ordered or ranked. Example: age is numerical and the values can be ranked.
1-201-20 1-3 Variables and Types of Data1-3 Variables and Types of Data
The nominal level of measurementnominal level of measurement classifies data into mutually exclusive (non-overlapping), exhausting categories in which no order or ranking can be imposed on the data.
1-211-21 1-3 Variables and Types of Data1-3 Variables and Types of Data
The ordinal level of measurementordinal level of measurement classifies data into categories that can be ranked; precise differences between the ranks do not exist.
1-221-22 1-3 Variables and Types of Data1-3 Variables and Types of Data
The interval level of measurementinterval level of measurement ranks data; precise differences between units of measure do exist; there is no meaningful zero.
1-231-231-3 Variables and Types of Data1-3 Variables and Types of Data
The ratio level of measurementratio level of measurement possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist for the same variable.
A lottery draw is a good example of simple random sampling. A sample of 6 numbers is randomly generated from a population of 45, with each number having an equal chance of being selected.
If a systematic sample of 500 students were to be carried out in a university with an enrolled population of 10,000, the sampling interval would be:
I = N/n = 10,000/500 =20 All students would be assigned sequential numbers.
The starting point would be chosen by selecting a random number between 1 and 20. If this number was 9, then the 9th student on the list of students would be selected along with every following 20th student. The sample of students would be those corresponding to student numbers 9, 29, 49, 69, ........ 9929, 9949, 9969 and 9989.
1-321-321-4 Data Collection and Sampling 1-4 Data Collection and Sampling Techniques Techniques
Stratified samplesStratified samples are selected by dividing the population into groups (strata) according to some characteristic and then taking samples from each group.
The committee of a company of 1,000 employees wishes to assess any reaction to the re-introduction of security system into the company. To ensure a representative sample of employees from all departments, the committee uses the stratified sampling technique.
In this case the strata are the departments. Within each strata the committee selects a sample. So, in a sample of 100 employees, all departments would be included. The employees in the sample would be selected using simple random sampling or systematic sampling within each strata
Suppose an organization wishes to find out which lung cancer treatment doctors are recommending in across Malaysia. It would be too costly and take too long to survey every doctor, or even some doctors from every hospital. Instead, 100 hospitals are randomly selected from all over Malaysia.
These hospitals are considered to be clusters. Then, every doctor in these 100 hospitals is surveyed. In effect, doctors in the sample of 100 hospitals represent all doctors in Malaysia.
In an observational study, the researcher merely observes what is happening or what has happened in the past and tries to draw conclusions based on these observations.
(a) Subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. After 6 months, the numbers of respiratory tract infections each group had were compared.
(d) Subjects are randomly assigned to four groups. Each group is placed on one of four special diets – a low-fat diet, a high-fish diet, a combination of low-fat diet and high-fish diet, and a regular diet. After 6 months, the blood pressures of the groups are compared to see if diet has any effect on blood pressure.