Know the concept of probability;
Know the application of Probability and the Normal Distribution
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics
Sampling error: natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter
distribution of the sample, means: a collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population
1. sample means should be relatively close to the population mean
2. Sample means should form a normal-shaped distribution (centered around the mean)
3. the larger the sample size, the closer the sample means should be to the population mean
sampling distribution: distribution of statistics obtained by selecting all the possible samples of a specific size from a population
𝑛 = ________________
NON-PROBABILITY SAMPLING
- involves non-random selection based on convenience or other criteria, allowing you to easily collect data.
CONVENIENCE SAMPLING
- selection of the samples based on the convenience of the researcher.
- Also called the accidental sampling.
PURPOSIVE SAMPLING
- the selection of the sample is based on the selective judgment of the researcher.
- also called judgmental sampling
- there is a criterion set by the researchers that is relevant to the topic under study
- Disadvantage: The researcher's judgment may be in error.
QUOTA SAMPLING
- the researcher identifies population sections or strata and decides how many participants are required from each section.
- usually, the stratification is based on variables relevant to the study.
- allows a better representation of the population.
SNOWBALL SAMPLING
- a technique wherein initial sample members are asked to refer other people who meet the criteria required by the researcher.
- based on the assumption that people who share the same traits or experiences know each other.
- useful for subjects who are hard to find
PROBABILITY SAMPLING
- involves random selection, allowing you to make strong statistical inferences about the whole group.
SIMPLE RANDOM SAMPLING
- most basic probability sampling technique.
- selection of sample is purely based on chance and each member of the population has an equal chance of being selected as a sample.
- EX: Fishbowl technique
SYSTEMATIC SAMPLING
- a process of selecting the kth element in the population until the desired number of samples is attained.
- the researchers set the sample size (n); the size of the population is known (N); then through dividing N by n, the sampling interval width (k) is determined.
SAMPLING INTERVAL
- the standard distance between elements chosen for the sample. EX: The researcher sets 100 as the sample size from a population of 2,000 students found in the student directory:
K = 2,000 ÷ 100
K = 20
In other words, every 20th student from the list would be sampled
STRATIFIED SAMPLING
- the population is divided into subgroups or strata. After the stratification, an appropriate number of elements are selected from each stratum randomly.
CLUSTER SAMPLING
- is a method of selecting clusters from a population that is large and widely dispersed over a wide geographical area.
- also known as multi-stage sampling
- the resulting design is described in terms of the number of sampling stages (three-stage cluster sampling)
Central Limit Theorem: for any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will have a mean of μ and a standard deviation of σ/square root n and will approach a normal distribution as n approaches infinity
-describes the distribution of sample means for any population, no matter what shape, mean, or standard deviation-distribution of sample means <<approaches>> a normal distribution very rapidly
-distribution of sample means is almost perfectly normal if:
1. the population from which the samples are selected is a normal distribution;
2. the number of scores (n) in each sample is relatively large, around 30 or more
the expected value of M: the mean of the distribution of sample means is always identical to the population mean
-when all of the possible sample means are obtained, the average value is identical to μ;
-sample mean is an example of an unbiased statistic, on average the sample statistic produces a value equal to the corresponding population parameter.
The Standard Error of M
the standard deviation for the distribution of sample means (σM);
1. describes the distribution of sample means and provides a measure of how much difference is expected from one sample to another
-when the standard error is small, all the sample means are close together and have similar values
-when the standard error is large, the sample means are scattered over a wide range and there are big differences from one sample to another.
2. measures how well an individual sample mean represents the entire distribution-provides a measure of how much distance is reasonable to expect between a sample mean and the overall mean for the distribution of sample means.
magnitude of the standard error is determined by two factors:
1. sample size: as sample size increases, the error between the sample mean and the population mean should decrease
-law of large numbers: the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean
2. the population standard deviation: when the sample consists of a single score(n=1), the standard error is the same as the standard deviation;
the original population of scores
the sample that is selected from the population;
distribution of sample means;
Whenever you have a probability question about a sample mean, you must use the distribution of sample means
z-Score for Sample Means
1. sign tells whether the sample mean is located above(+) or below (-) the mean for the distribution (population mean, μ)
2. number tells the distance between the sample mean and μ in terms of the number of standard errors•z= (M-μ)/σM