Lecture Notes 2 - Descriptive Statistics, Inferential Statistics, Hypothesis PDF

Preview

Summary

Descriptive Statistics, Inferential Statistics, Hypothesis...

Description

Chapter 7 & 9 (4.1): Descriptive Statistics ❖ Describes a sample’s characteristics ❖ Descriptive statistics describe the data, but can not make any conclusions

Inferential Statistics ❖ Used to infer something about the population based on the sample’s characteristics. ❖ Inferential statistics draw conclusions about the data. Can determine whether or not one variable causes an effect in another.

How Inferences Work 1. 2. 3. 4.

A claim is made (hypothesis) A sample representative of the population is chosen A test is given, and results are computed and compared A conclusion is reached as to whether the scores are statistically significant 5. Based on the results of the sample, an inference is made about the population

Hypothesis ❖ A hypothesis is a statement about the value of a populationparameter or a population model ❖ We want to decide whether the hypothesis is true or false ❖ It's an educated guess ❖ Translates the problem or research statement into a form that can be tested ❖ There are two different types of hypothesis ➢ Null Hypothesis ➢ Research (Alternative) Hypothesis ❖ Cations: ➢ Before you make a hypothesis, you have to clearly identify the question that you are interested in studying ➢ A hypothesis is not the scientific question ➢ It is an educated testable prediction about what will happen

➢ It predicts cause and effect ➢ Answering some research questions may require multiple hypothesis and/or multiple experiments ❖ Creating a hypothesis: 1. Brief and to the point 2. Stated in declarative form rather than a question 3. Defines expected relationship between variables 4. Reflects theory or literature on which it is based (consistent with data) 5. Testable includes variables that can be measured

Null Hypothesis ❖ Two or more variables are equal to one another ➢ No effect on the experiment ❖ Written as H 0 ❖ Starting point for research ❖ Status quo ❖ Assume it to be true ❖ Benchmark to compare the actual outcomes

Research Hypothesis ❖ Known as alternative or alternate hypothesis ❖ A relationship between two variables ➢ There will be an effect on the experiment ❖ Can be written as Hₐ or H₁ ❖ Can be … Directional ■ Direction of difference is specific ■ One-tailed test ■ Includes a < or > in the numeric statement ➢ Non-Directional ■ Reflects differences, not direction specific ■ Two-tailed test ■ includes a ≠ in the numeric statement

❖ 3 types of equations ➢ H 1 : μ 1 =/ μ 2 (not equal) ➢ H 1 : μ 1 > μ 2 (greater than) ➢ H 1 : μ 1 < μ 2 (less than)

Rejection Regions Region of rejection ➢ Represents the values of a statistic whose combined probability is low enough that we could reject H 0 Region of non-rejection ➢ Represents the values whose probability is not low enough to allow us to reject H 0

Notes ❖ Significance level is represented by ➢ Alpha = α ❖ Entire Curve - represents all possible outcomes from a null hypothesis ❖ Low probability ➢ Critical Value(cv) - The point beyond which the obtained outcomes are judged to be so rare that we conclude the outcome is not due to chance ■ If the obtained value is more extreme than critical value, we reject the null hypothesis ■ If the obtained value is less extreme than the critical value, we fail to reject the null hypothesis ➢ P-Value - Probability of obtaining an effect as extreme as your test statistic, if the null hypothesis is true (p < 0.05 (%5)) ■ If the p-value is less than the level of significance, we reject the null hypothesis ■ If the p-value is greater than the level of significance, we fail to reject the null hypothesis ■ If p is low, the null most go!

➢ When making conclusions we’ll only reject or fail to reject the null hypothesis, we’ll never  accept the null ➢ If the p-value is greater than the level of significance, we will fail to reject the null hypothesis ➢ If the p-value is less than or equal to the level of significance, then we reject the null hypothesis and conclude that the test is statistically significant at that level of significance ➢

Significance Test ❖ Comparing p-value to significance level ❖ Comparing test statistic to significance level

Statistical Significance ❖ ❖ ❖ ❖

Comparing significance level (alpha) to p-value Comparing test statistic to critical level Gives you evidence to reject the null hypothesis Probability that our findings would occur if the null hypothesis is true

Clinical Significance ❖ Known also as clinical importance, practical significance, or meaningful ❖ Is concerned with whether or not the effect seen is enough to alter practice ❖ This is a matter of judgment ❖ Large effect sizes may indicate clinical significance

Statistical Vs. Clinical Significance ❖ 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 ❖ Statistical significance is influenced by sample size

➢ The larger the sample, the more likely you will find a significant result of some kind

Factors: ❖ Sample size ➢ Larger samples make it more likely that we can reject H 0 ❖ Alpha ➢ The smaller the value of,the more difficult it is to reject H 0

❖ Nondirectional hypotheses have regions of rejection inboth extremes of the distribution, and are called two-tailed

❖ Directional hypotheses have a region of rejection only one extreme of the distribution, and are called one-tailed...