SOC212 - Application Question #2

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Chapter 9  

Significantly Significant:

What It Means for You and Me

Part IV Significantly Different: Using Inferential Statistics

What significance is and why it is important

Significance versus meaningfulness

Type I errors

Type II errors

Importance and differences between Type I and Type II errors

How inferential statistics works

How to determine the right statistical test

What You Will Learn in Chapter 9

Any difference between groups that is due to a systematic influence rather than chance

Must assume that all other factors that might contribute to differences are controlled

The Concept of Significance

Significance level

The risk associated with not being 100% positive that what occurred in the experiment is a result of what you did or what is being tested

The goal is to eliminate competing reasons for differences as much as possible

If Only We Were Perfect…

Statistical significance

The degree of risk you are willing to take that you will reject a null hypothesis when it is actually true

The Null Hypothesis and Your Action

The probability of rejecting a null hypothesis when it is true

Conventional levels are set between .01 and .05

Usually represented in a report as p < .05

Type I Errors (Level of Significance)

The probability of rejecting a null hypothesis when it is false

As your sample characteristics become closer to the population, the probability that you will accept a false null hypothesis decreases

Type II Errors

Different Types of Errors

A study can be statistically significant but not very meaningful

Statistical significance can be interpreted only in terms of the context in which it occurred

Statistical significance should not be the only goal of scientific research

Significance is influenced by sample size…we’ll talk more about this later

Significance Vs. Meaningfulness

Descriptive Statistics

Describes a sample’s characteristics

Inferential Statistics

Used to infer something about the population based on the sample’s characteristics

Inferential Statistics

A representative sample of the population is chosen

A test is given, and means are computed and compared

A conclusion is reached as to whether the scores are statistically significant

Based on the results of the sample, an inference is made about the population

How Inference Works

Deciding Which Test to Use

A statement of null hypothesis

Set the level of risk associated with the null hypothesis

Select the appropriate test statistic

Compute the test statistic (obtained) value

Test of Significance: The Plan

Determine the value needed to reject the null hypothesis using appropriate table of critical values

Compare the obtained value to the critical value

If obtained value is more extreme, reject null hypothesis

If obtained value is not more extreme, accept the null

Test of Significance: The Plan

The Picture Worth a 1,000 Words

Entire curve

Represents all the possible outcomes based on a specific null hypothesis.

Critical value

The point beyond which the obtained outcomes are judged to be so rare that we conclude the outcome is not due to chance

Looking at the Test of Significance and The Bell Curve

Left of the critical value

We conclude the null hypothesis is the most attractive explanation for any differences observed

Right of the critical value

The conclusion is that the research hypothesis is the most attractive explanation for any differences observed

Looking at the Test of Significance and The Bell Curve

The best estimate of the range of a population value

How confident you are that the population mean falls between two scores

We use the positive or negative raw scores equivalent to the z scores of our confidence interval.

Confidence Interval	Significance Level	z scores
99%	1%	±2.56
95%	5%	±1.96

Confidence Intervals

The confidence interval is determined by showing the mean and the appropriate positive and negative z scores equal to our significance level as well as the standard deviation

If we have a mean of 64 and a standard deviation of 5 on a test and what would be the 95% confidence interval

64±1.96(5)

Confidence Intervals