STAT111: MIDTERM (TERMINOLOGY & DEFINITION)

Inferential Statistics

Is a branch of statistics that focuses on the formulation of conclusion.

Conclusion

Is a statement that is accepted and proven true and valid.

Hypothesis

Tentative answer to the given question about the characteristic of the population or the subject that aimed to analyze.

Hypothesis

Statement which are subjected to testing.

1. Null Hypothesis

2. Alternative Hypothesis

Two (2) Types of Hypothesis

Null Hypothesis

Expressed by Ho.

Null Hypothesis

Idea of neutrality of the variables.

Null Hypothesis

Expressed usually in negative form.

Null Hypothesis

The idea of :

1. There no significant difference

2. There is no significant relationship

3. There is no significant effect

Alternative Hypothesis

Expressed by Ha or Hi.

Alternative Hypothesis

Expressed in affirmative form.

Alternative Hypothesis

The opposite of the Null Hypothesis.

Alternative Hypothesis

The Idea of:

1. There a significant difference

2. There is significant relationship

3. There is significant effect

1. Non-Directional

2. Directional

Two (2) Types of Alternative Hypothesis

Alternative Hypothesis (Non-Directional)

No direction of change.

Alternative Hypothesis (Directional)

Direction of change.

Level of Significance (alpha)

Is the allotted percentage of mistake while making the decision about the hypothesis. Its value ranges from 1% to 10%.

Level of Confidence

Is the contrary of the level of significant. It is the percentage of accuracy and reliability that the decision is valid or correct. In symbol it is expressed as 1- α.

Critical Region or Rejection Region

Is the region located at the very far end of the normal curve.

Critical Region or Rejection Region

This region is very important in the formulating decision about the null hypothesis.

Critical Region or Rejection Region

The area of the critical region is simply the value of the chosen level significance.

Acceptance Region

Is the other portion in the normal curve. Its area is the same with the level of confidence.

Critical Value

Is the number that serves as the boundary line between the acceptance and critical regions.

Testing of Hypothesis

Is the process of evaluation of the hypothesis.

Testing of Hypothesis

Testing of hypothesis is needed to be able to know if the formulated statement is really correct or not.

1. Formulate your null hypothesis

2.Determine the alternative to be used

3.Give the level of significance

4.Choose the appropriate test statistic and the critical value of the test. Draw the normal curve

5.Compute the value of the test statistic

6.Compare the computed value of the test statistic to the normal curve or the p-value and the level of significance and then decide to accept or reject the null hypothesis

Steps in Testing of Hypothesis

1. One-tailed Testing

2. Two-tailed Testing

Two (2) Natures of Testing Hypothesis

One-tailed Testing

Is the nature of the testing process if the alternatie hypothesis (directional) is used.

Two-tailed Testing

is the nature of the testing process if the alternative hypothesis (non-directional) is used.

Test Statistics

It refers to the formulas in the testing of hypothesis.

Test Statistics

It summarizes the characteristics of the sample that are relevant in the testing process.

1. Z-Test

2. T-Test

3. Anova

4. Chi-Square Test

5. Fisher-Exact Test

6. Wilcoxon Rank

7. Mann-U Hay Test

Examples of Test Statistics

1. Parametric Tests

2. Non-Parametric Tests

Types of Test Statistics

Parametric Tests

Normally distributed.

Parametric Tests

Data is interval and ratio.

Parametric Tests

Uses of the values of mean, standard deviation, variance, etc.

Non-Parametric Tests

It is also called "distribution-free methods"

Non-Parametric Tests

Not normally distributed.

Non-Parametric Tests

Nominal or ordinal scale.

Standard Error (SE)

Measures how far is the sample statistics from the population statistics.

Standard Error (SE)

It could be comparison of the mean, median or proportions.

Standard Error (SE)

The most likely is the comparison of the mean.

Confidence Interval Definition

It refers to the estimated possible range values where in the the parameters of the population falls using the sample.

Probability

Measurement of chance of an event to occur.

Probability

Denoted by P or Q.

Probability

Its values ranges 0 ≤ P (E) ≤ 1

or 0 ≤ Q (E) ≤ 1

Experiment

Is the process of obtaining the possible events.

Event

Is the outcome of an experiment.

Sample Space

Is the list of all possible outcomes of an experiment.

Complementary of Event

It refers to the area excluding the possible E event.

1. Mutually Exclusive Events

2. Non-Mutually Exclusive Events

3. Independent Events

4. Dependent Events

Types of Events

Mutually Exclusive Events

Events are not possible to happen simultaneously.

Mutually Exclusive Events

P(A or B) = P(A) + P (B)

Non-Mutually Exclusive Events

Events are possible to happen together.

Non-Mutually Exclusive Events

P (A and B) = P(A) + P (B) - P (A ∩ B)

Independent Events

Are events that are not related at all. It happens the event has no impact on the other.

Independent Events

P(A and B) = P(A) * P(B)

Dependent Events

The outcome of the first event has an impact to the other event.

Dependent Events

P(A and B) = P(A) * P(B|A)