Test for Goodness of fit- Sept. 12/ 2012

Chi square goodness of fit...
-used in testing to see whether a frequency distribution fits a specific pattern
- Hypotheses:
       H_o: .... show no preference ....

       H₁: .... show preference....

- Degree of Freedom

       n-1

-Formula for the Chi-Square Goodness of Fit Test

-Assumptions for Chi Square Goodness of Fit

      1. The data that  are obtained from a random sample.

      2. The expected frequency for each category must be 5 or more.

-Procedure

      1. State the null hypothesis and identify the claim.
      2. Find the critical value.
      3. Compute the test value. (sum of the values)
      4. Make the decision.
      5. Summarize the results.

Oh well, that's all that I can remember...

By: Carl Joel E. Palma III-Gold 

Testing the Difference Between Two Means (Small Samples) and Proportion- Sept. 10, 2012

Testing the difference between two means: small independent samples
Formulas:

Testing the difference between two means: small independent samples
Formula:

Testing the difference between proportions:

That's all... 

By: Carl Joel E. Palma III-Gold

Correlation and Regression- Sept. 28, 2012

According to our teacher:

Terms...... In correlation and Regression

Correlation: Is a statistical method used to describe whether a relationship between variables exist.
Regression: A statistical method used to describe the nature of relationship between variables.
Scatter Plot: The graph of the ordered pairs (x,y) of numbers consisting of the independent variable x, and dependent variable y.
Correlation Coefficient: Use to determine the strength of the relationship between two variables.

Types of Relationships
1. Simple relationships- there are only two variables under study.
     a. Positive relationship- exist when both variables increase or decrease at the same time.
     b. Negative relationship- as one variable increases, the other variable decreases.
2. Multiple relationships- many variables are under study

Independent variable- is the variable in regression that can be controlled or manipulated
Dependent variable- is the variable in regression that cannot be controlled or manipulated

That's all...
By: Carl Joel E. Palma III- Gold

Test for Homogeneity of Proportions- Oct. 2, 2012

Test for Homogeneity of proportions
- it is used to determine whether the proportions for a variable are equal when several samples are selected from different populations

Hypotheses:

H_o: p₁=p₂=p₃

H₁: at least one proportion is different from the others

Possible decisions:

Do not reject H_{o, it can be assumed that the proportions are equal and the differences in them are due to chance.}

Reject H_{o, it can be assumed that the proportions are not equal.}

_{By: Carl Joel E. Palma III- Gold}

Contingency Tables- Oct. 1, 2012

Our lesson in Contingency tables:

This lesson is pretty hard though...

As what I've learned...

- Test for independence of variables is used to determine whether two variables are independent or related to each other when a sample is selected

First-   State the hypotheses
ex.

H_o: The opinion about the procedure is independent...

H₁: The opinion about the procedure is dependent...

Second-   To get the degree freedom:
(R-1)(C-1)
ex.
If there are three rows and two columns
(3-1)(2-1)= 2

Third- Find the expected value
Fourth- Find the Test value
using this formula

Fifth- Find Critical Value
using d.f. = 2 a= o.o5 CV= 5. 991

Sixth- Make the decision.
Seventh- Make the summary.

By: Carl Joel E. Palma III- Gold

Scheffe and Tukey Tests- Oct. 12, 2012

Scheffe Test

-Used when the decision is to reject the null hypothesis

-You need to compare the means two at a time using all possible combinations

Formula:

Tukey Test

- According to our teacher, this test can be used after the ANOVA has been completed to make pairwise comparisons between means when the "groups have the same sample size.

Formula: 

That's all...

By: Carl Joel E. Palma III- Gold

October 9,2012-Lesson about ANOVA (Analysis of Variance)

Next week will be the schedule for our second departmental test, so we are now going fast with our lessons so that we will be able to take the whole coverage of Advanced Statistics.

Now we’re having the lesson about Analysis of Variance (ANOVA). This lesson will be useful for our Advanced Research next school year so we should understand the lesson well. Here are some key points for this lesson:

*The z-test and t-tests should not be used when three or more means are compared, instead, F-test can be used to compare three or more means. (ANOVA)

*The most commonly used tests are the Scheffe test and Tukey test.

*Between-Group variance (S_B²)– one of the first estimates, involves finding the variance of means.

*Mean Square of the Between Group (MS_B) – one of the first estimates, made by computing the variane using all the data and is not affected by differences in the means.

*Within-Group Variance (S_W²) or Mean Square of the Within-Group (MS_W) – the second estimates, is made by computing the variance using all the data and is not affected by differences in the means.

*Analysis of variance used to compare three or more means which contains only one variable. (One-Way Analysis of Variance)

*ANOVA that involve two variables. (Two Way Analysis of Variance)

*No difference in the means: the between group variance estimate will approximately equal to the within group variance estimate; F test value will be approximately equal to one; Null hypothesis will not be rejected.

*Means differ significantly: the between-group variance will be much larger than the within-group variance; F test value will be significantly greater than 1; the Null hypothesis will be rejected.

*k=number of groups

*N=sum of the sample sizes for groups

*SS_B =sum of squares between groups

*SS_w=sum of squares within groups/ (sum of squares for the error)

*MS_B =Between group variance (S_B²)=SS_B/k-1)

*MS_W =Error variance

*Scheffe Test = one must compare the means two at a time, using all possible combination of means.

*Tukey Test can also be used after the analysis has been completed to make pairwise comparisons between means when the groups have the same sample size. The symbol for the Tukey test is q.

Analysis of Variance includes a wide range of symbols, ideas and needs a lot of understanding. Our knowledge of ANOVA will be used for our studies when we are already in 4^th year.

Posted by: Kent Spencer Manalo Mendez