Sampling Error
is the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.
Distribution of sample means
The ability to predict sample characteristics is based on the distribution of sample means.
The distribution of sample means is the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a populat
Sampling Distribution
is a distribution of statistics obtained by selecting all the possible samples of a specific size from a population.
Sample means
Is an example of a sampling distribution. Often called the sampling distribution of M.
1. The sample means should pile up around the population mean.
2. The pile of sample means should tend to form a normal-shaped distribution.
3. In general, the larger t
Central Limit Theorem*
For any population with mean ? and standard deviation ?, the distribution of sample means for sample size n, will have a mean of ? and a standard deviation of ?/?n and will approach a normal distribution as n approaches infinity.
Value of the Central Limit Theorm
1st - it describes the distribution of sample means for any population, no matter what shape, mean, or standard deviation.
2nd - the distribution of the sample means "approaches" a normal distribution very rapidly
By the time the sample size reaches n = 3
The shape of the distribution of the sample means: 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.
Expected value of M
The mean of the distribution of sample means is equal to the mean of the population of scores, ?, and is called the expected value of M.
The Standard error of M (?M)
The mean of the distribution of the sample means always is identical to the population mean.
The standard deviation of the distribution of sample means, ?M, is called the standard error of M. The standard error provides a measure of how much distance is e
?M
The symbol for the standard error is ?M. The ? indicates that this value is a standard deviation, and the subscript M indicates that it is the standard deviation for the distribution of sample means.
The magnitude of a standard error is determined by two factors:
(1) the size of the sample and (2) the standard deviation of the population from which the sample is selected.
Law of large numbers
The law of large numbers states that the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.
The population standard deviation
when n = 1, standard error = ?M = ? = standard deviation
standard error = ?M ( ? / ?n)
Three Different Distributions
1. First, we have the original population of scores. This population contains the scores for thousands or millions of individual people, it has its own shape, mean and standard deviation.
2). Next, we have a sample that is selected from the population. Th
Hypothesis Test
A statistical method that uses sample data to evaluate a hypothesis about a population.
A formalized procedure that follows a standard series of operations. So researchers have a standard method for evaluating the results of their research studies.
1. Fir
null hypothesis Ho
The null hypothesis states that the treatment has no effect; no change, no effect, no difference--nothing happened.
H (hypothesis) 0 (zero-effect)
Ho: ? with supplement = 80 (Even with the supplement, the mean test score will still be 80).
scientific, or alternative hypothesis H1
This hypothesis states that the treatment has an effect on the dependent variable.
There will be some type of change; doesnt specific direction
The alternative hypothesis (H1) states that there is a change, a difference, or a relationship for the general
Step 2: Set the criteria for a decision
If there is a big discrepency between the data and the hypothesis, we will conclude the hypothesis is wrong.
1. Sample means that are likely to be obtained if Ho is true; that is, sample means that are close to the null hypothesis.
2. Sample means that ar
The alpha level
Selecting a specific probability value, level of significance or alpha level, for the hypothesis test.
The alpha ? value is a small probability that is used to identify the low-probability samples.
? = .05 (5%), ? = .01 (1%), ? = = .001 (0.1%)
Ex. With ?
alpha level or level of significance
The alpha level, or the level of significance, is a probability value that is used to define the concept of "very likely" in a hypothesis test.
Critical Region
The critical region is composed of extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. If the sample data fal