Civil Engineering statistics and probability

Probability and statistics

1. Sampling and data collection methodes Areas to be covered: Sample and population Sampling techniques.

2. Sampling Techniques Meaning of Sampling Technique In a study, all subjects ( human or objects)of a particular interest are referred to as population while part of the population statistically selected is referred to as a sample. The process of selecting subjects from a population to form a sample is called sampling while the method used to select a sample is called sampling method or sampling technique . When conducting a study, a sample is used instead of the whole population to cut cost or to save time. When selecting a sample bias can be avoided by making the sampling random ( every subject in the population to have the same chance of being include in the sample ).

3. Sampling Techniques There are several different sampling methods/techniques available, and they can be subdivided into two groups: probability sampling and non-probability sampling . In probability(random) sampling, all eligible individuals have a chance of being chosen for the sample while in non-probability (non-random) sampling, some individuals have no chance of being selected. Probability(random) Sampling techniques Simple random sampling : Consider a population of size(N)=850, and you want to have a sample of size(n)= 100. To do a simple random sampling, you assign numbers to the 850 subjects then randomly select 100 subjects between 1 and 850 manually or using a computer.

4. Sampling Techniques Systematic Sampling : Individuals are selected at regular intervals from the sampling frame. Consider N= 800, and you want to select a sample of size(n)= 100 from this population. Using systematic sampling technique you first number the 800 subject, calculate a sample fraction given by n/N in this case, n/N=1/8 then draw random number between 1 and 8 as your random start . Then select every 8th subject from the random start. Stratified Sampling : In this case the given population is divided according to some characteristics eg age group, gender, race, religion to form groups called strata then determine sample size from each stratum which is given by , then do simple random sampling in each stratum.  

5. Sampling Techniques Example : Suppose you have a population consisting of 80 female subjects and 120 male subjects and you want to draw a sample of 70 subjects from the population. Solution Stratified random sampling. Firstly, working out the number of students from each stratum Stratum 1 (females subjects) = = 28   Stratum 2 ( male subjects) =   Secondly , randomly select 28 students and 42 students from the females and males subjects.  

6. Cluster Sampling : In a clustered sample, subgroups of the population are used as the sampling unit, rather than individuals. The population is divided into subgroups, known as clusters, which are randomly selected to be included in the study. Clusters are usually already defined, for example individual practices or towns/ villanges /families could be identified as clusters . Multistage sampling : This sampling technique has three stages: Primary stage sampling where you sample enumeration areas eg villages, communities. Secondary stage sampling where you sample house holds/clusters within each selected enumeration area. Tertiary stage sampling where you sample individual in the sampled house holds/clusters.

7. Sampling Techniques Example Let’s say you wanted to find out which subjects Malawian secondary school children preferred. A population list is a list of all Malawi secondary school children which would be near-impossible to come by, so you cannot take a  sample  of the population . Instead, you divide the population into Districts and take a simple random sample of Districts( as a primary stage). For the secondary stage, you might take a simple random sample of schools from within those Districts. Finally you could perform simple random sampling on the students within the schools to get your sample.

8. Sampling Techniques Non-Probability(non random) Sampling techniques Convenience sampling : In convenience sampling participants are selected based on availability and willingness to take part. Useful results can be obtained, but the results are prone to significant bias, because those who volunteer to take part may be different from those who choose not to (volunteer bias), and the sample may not be representative of other characteristics, such as age or sex. Note: volunteer bias is a risk of all non-probability sampling methods. Snowball Sampling : In this case you use convenience sampling and then ask respondents to give you other contacts(subjects ).

9. Sampling Technique Quota Sampling :   Researchers can select elements using their knowledge of target traits and personalities to form strata. Members of various strata can then be chosen to be a part of the sample as per the researcher’s understanding . For example, an interviewer might be told to go out and select 20 adult men, 20 adult women, 10 teenage girls and 10 teenage boys so that they could interview them about their television viewing. Ideally the quotas chosen would proportionally represent the characteristics of the underlying population.   Purposive/Judgement/Selective/subjective sampling : This technique relies on the judgement of the researcher when choosing who to ask to participate. This approach is often used in qualitative research eg the media when canvassing the public for opinions and in.