Chapter 5 - Sampling, The Central Limit, Theorem and Hypothesis Testing

Sampling error

the difference between the characteristics of the entire population and the characteristics of any sample used to estimate the population

Representative sample

A sample with approximately the same mean and standard deviation as the underlying population 

Sampling bias

When a sample is consistently skewed by the manner in which a study is performed 

Distribution of mean

the distribution of the means for all the other samples of the same size that could have been collected 

Standard error

the amount of variability in the distribution of sample means

Convenience sample

sampling people who live near them or who are easily accessible to them - who is most convenient to them

WEIRD = WHAT

WEIRD = White, educated, industrialized, rich and democratic 

WEIRD posses WHAT because it is the most common sample used in social science research 

WEIRD posses SAMPLING BIAS because it is the most common sample used in social science research 

Population mean is represented by WHAT

Population mean is represented by µ 

Distribution of sample means

distribution of all the possible means of all possible samples of a given sample size.

The distribution of sample mean is theoretical because its impossible to collect all the WHAT samples in a given sample size from a WHAT

The distribution of sample mean is theoretical because its impossible to collect all the POSSIBLE samples in a given sample size from a POPULATION

sigma (σ) to represent the WHAT

sigma (σ) to represent the population standard deviation

The variability among all samples WHAT as the sample size WHAT because you are gathering more data from the population.

The variability among all samples DECREASES as the sample size INCREASES because you are gathering more data from the population.

Formula of standard error = WHAT

Formula of standard error = sigma / square root of n

(sigma = standard deviation from the population, n = sample size selected 

Theorem

mathematical fact that has been demonstrated over and over again by a formal “proof”

Central limit theorem

the distribution of sample means is roughly normally distributed as long as the sample sizes are sufficiently large and the data don’t have dramatic skew or outliers.

A minimum of WHAT participants is required for a study 

A minimum of THRITY participants is required for a study 

Null hypothesis significance testing (NHST)

determine if your data supports or do not support your research hypothesis 

To determine if your data supports or do not support your research hypothesis there are four steps 

1. WHAT

2. WHAT

3. WHAT

4. WHAT

To determine if your data supports or do not support your research hypothesis there are four steps 

1. Define the null hypothesis and alternative hypothesis.

2. Define the threshold for significance.

3. Perform the inferential statistical test.

4. Make a decision about the null hypothesis.

You need a probability of WHAT% or less to declare statistical significance 

You need a probability of 5% or less to declare statistical significance 

p value

the probability of finding a sample of experimental participants acting the way that they are acting, while the null is really true, is 5% or less

The NHST only tells you how WHAT your experimental group is compared to the control group 

The NHST only tells you how UNUSUAL your experimental group is compared to the control group 

Null hypothesis (Ho)

the way you expect your data to look if your control and experimental samples are acting about the same at  the end of your experiment 

Alternative hypothesis (HA)

The way you expect your data to look if your manipulation of the independent variable seems to have changed the experimental participant 

Alternative hypothesis is directional

the experimental group will be higher or lower in the dependent variable at the end of the experiment 

Alternative hypothesis is nondirectional

you state that the two groups will simply be different at the end of the experiment 

Always say WHAT null hypothesis, WHAT to reject null hypothesis or WHAT null hypothesis since this is the null hypothesis significance test 

Always say RETAIN null hypothesis, FAIL to reject null hypothesis or REJECT null hypothesis since this is the null hypothesis significance test 

Use WHAT to determine the cutoff points in the normal curve beyond which the outermost 5% of the data lie 

Use z scores to determine the cutoff points in the normal curve beyond which the outermost 5% of the data lie 

If performing nondirectional tests or two-tailed test the significance will be established at WHAT of the distribution 

If performing nondirectional tests or two-tailed test the significance will be established at EITHER TAIL of the distribution 

This will then be any data that exists at either side of the curve or 2.5% on either side z = WHAT

This will then be any data that exists at either side of the curve or 2.5% on either side z = 1.96 

This 5% is also called the WHAT because we reject the null hypothesis if data falls here 

This 5% is also called the REJECTION REGION because we reject the null hypothesis if data falls here 

If performing directional or one-tailed test its either in the WHAT or WHAT

If performing directional or one-tailed test its either in the HIGHER or LOWER TAIL  

The cut off for z = WHAT because the upper and lower or not evenly split so we put all the data in one tail 

The cut off for z = 1.645 because the upper and lower or not evenly split so we put all the data in one tail 

One-tailed test gives us two test

1. WHAT

2. WHAT

One-tailed test gives us two test

1. Right-tailed test

2. Left-tailed test 

Right-tailed test

the experimental group will be to the right of the distribution or have a larger mean score on the dependent variable 

Left-tailed test

the experimental group will be to the left of the distribution or have a lower mean score on the dependent variable

Statistical significance

the chances of obtaining the results that were obtained, if the null is true, are equal to or less than 5%

For us to reject the null hypothesis, the mean of our experimental data must lie in the outermost WHAT% of a curve that represents the distribution of control-group means

For us to reject the null hypothesis, the mean of our experimental data must lie in the outermost 5% of a curve that represents the distribution of control-group means

One-sample z test

evaluates whether a value for a variable collected from a population and a preexisting value for the same variable are different from each other 

The equation for test statistic = WHAT

The equation for test statistic = claim value - Mpopulation / SEpopulation 

Where

• claim value = value you want to test to see if its true,

• Mpopulation = mean of the experimental population,

• SEpopulation = standard error of the experimental population

If the data falls in the z = 1.96 we WHAT the null hypothesis

If the data falls in the z = 1.96 we REJECT the null hypothesis