Weekend+Two


 * Weekend Two :: Saturday**

T-Tests - Looks at the differences in the mean. Different types -
 * One sample T-Test
 * Related Sample or Paired T-Test
 * Independent T-Test

Hypothesis - Conjecture about the relationship between two variables. Example: Driving fast and getting a ticket. or Gender vs. Height

Formulate a **Null hypothesis** - Ho - No relationship between x and y. No relationship between gender and height. In the word of education, the Null hypothesis is assumed. The Alternative Hypothesis needs to be proved.


 * Alternative Hypothesis** - State the direction of the relationship of the variables we are testing. Can be positive or negative.

Alternative Hypothesis ( Ha) = positive or negative As you attend school more frequently, you are more apt to do well on the achievement score.

If there is a negative relationship, we say the relationship is y=-x What that means is that is if you increase on x you decrease on y. The more time you spend in jail, the less time you will spend on the job.

Nonlinear relatinpships can also be positive or negative

T-Test - A way to test a relationship between two variables. What is more important is the question that you are asking.


 * One Sample T-Test**

Mean Study of 6th and 7th graders has a mean score of 198 Population Mean of all 6th and 7th graders has a mean score of 240.
 * Example** - Test scores

What is the null hypothesis? There is no relationship (There is no statistical difference) between the mean of the study group and the population.

What is the alternative hypothesis? There is a significant difference between the mean of the study group and the population such that we expect the mean score of the study group is lower than that of the population.

One sample T-Test This is a one sample t-test because we are testing one sample agains the population mean.

Statistically, are we looking at a significance between the two values? We need to look at how the degrees of freedom play out in this situation.

Pfizer comes to you and says we have experimented with two types of drugs - We are looking at which of these two drugs is mot effective in reducing blood pressure. Drug A is 3% reduction, Drug B is 5% reduction - The question to ask is if that 2% is significant? If it is, then market drug B. If not, than it was just by chance that it happened. The probability of what we are seeing is not due to change. We use that 0.05 level of significance - Only taking a chance that 5 times out of a 100, it is a fluke. We are saying that 95 % of the time that it is a
 * Medical - Example**

Null Hypothesis - There is no statistical difference betwen Drug A and Drug for reducing the blood pressure. Alternative Hypothesis - There is a statistica difference between Drug A and Drug B for reducing blood pressure such that Drug B is going to reduce the blood pressure by 2% more than Drug A.


 * Related Sample T Test or Paired T-Test** - Comparing each sample pre- and post- (that is why it is called Related Sample - has to be the same sample that is being compare).

Give five students grades in the first marking period and in the last marking period. 1st / 4th A 40 / 45 B 46 / 50 C 30 / 60 D 35 / 36 E 70 / 80
 * Example** - Teacher gives Grades

The question: is there a significant difference between the 1st marking period grade and the last marking period grade. Null - There is no difference between the first marking period and the fourth marking period.

T-Test Signicance Tables - Page 520 DF - Degrees of Freedom - How many guesses can we make? Simply (typically) n - 1. The total number in the study = n. If the total number in the study was 40, the degrees of freedom would be 39.

Probability that the event will happen by chance - What the probability that the event would happen by chance - that the difference is happening for real.

You do a study and calculate your T value - When you calculate this, you get 2.65 and you calculate this on a sample of 40 students (therefore degrees of freedom is 39. T = 2.65, DF = 39
 * Example**

Look on page 520 - (no 39 for the degrees of freedom, so go up to 40) @ 0.05 and 40, the value is 2.021. Is 2.65 equal to or greater than 2.021? If it is, then reject the null hypothesis that there is no significant difference. Yes - it is - so there the null hypothesis is rejected and the alternative hypothesis is true, showing that there is a significance difference in the study (because the null is based on no relationship).

T Value - Found when you look at he mean differences - and used to determine if the mean differences statistically significant?

Two groups, separate sources.
 * Independent Sample T-Test**


 * Example** - Are the reading scores for boys greater than that of girls?

Variable View - For this activity, we have eight variables. Enter each variable and assign the properties of each in the name column.
 * SPSS**

Analyze is where all analysis functions are - If you want to find out how many males and females: Menu Bar -> Analyze-> Descriptive Statistics -> Frequencies, and choose the item that you want to analyze. This will produce a chart analyzing the results -

Want to look at the valid percent - always use this data when moving forward from this chart. Is the mean for the students in the study is the mean attitude greater than 4? Menu Bar-> Analyze -> Compare Means -> One Sample T-Test, Asks what the test value is? Set the test value @ 4, and move Att1 over into this chart. Resulting chart gives you the sample size, mean, standardized deviation, std. error mean and a second chart gives the One-Sample Test information with t value, DF, Sig (2-Tailed), Mean Difference, Lowerlevel and Upper level for the tails.

Two Tail Test - You can have a positive and negative - don't know if there is a relationship between the two. One-Tailed Test - Aiming toward the Positive or Negative side.

Levene's Test for Equality of Variance The variance between the two groups is the same (null hypothesis). The standard deviation is a follow up indicator - The larger the SD, the greater the variance of the means in the data. When the significance is less than 0.05, one cannot assume the variance is the same in each group. When it is an independent sample T-Test being done, the Levene's test must be used (two samples - must look at the variance in the means to see if the variance between the two groups is the same).

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The Levene's Test was significant because it was less than 0.05, and therefore "something special" (book), or something "good" (Mike) was happening - this means that there is a signifiance in the variance of the means that the variance between the two sets is great. If the significance was greater than 0.05, then the null hypothesis would be accepted (which in the case of the Levene's test, means that there is no significance to the variance of the means). This will determine which way to go on the page below:

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For my own learning - I need to see this from start to finish, and the benefit in what this tells us. Let me try writing this out:

Math Mean Scores for 6th and 7th graders. The mean for 6th grade is 195.79 with a SD of 28.--- and the mean for 7th grade is 198.10 with a SD of 35.--- 1. Look at the SD for each of the grade levels (only for reference). The SD for 6th grade is less than the SD for 7th grade, showing that 6th grade has less variance in their data than 7th grade. 2. Because there are two different groups (independent T-Test), must do a Levene's test to find out if there is significant variance in the means? Need to look at the Levene's Test results from SPSS: F = 25.604, sig = 0.000

3. 0.000 < 0.05, showing that there is significance. We cannot assume the same variance exists in the two means, and therefore must look at the "Ues Equal Variances Not Assumed" from SPSS:

4. Significance is 0.329 - Higher than 0.05, and therefore not significant, which means the difference between the two means is not significant (even though the variance between the two is).

How does this fit into Policy? Does this mean that the changes made in 7th grade (or 6th grade) were not significant?

Day Two - SPSS Notes
 * Weekend Two :: Sunday**