ttest Anova

$59,475 men
t-Test for the difference of means
t
1 2
SX
1 X 2
X1 = mean for Group 1 X2 = mean for Group 2 SX1-X2 = the pooled or combined standard error of difference between means.
Now suppose we Want to find if Mickey Scores better than Minnie. This time we have two independent groups, so we use an “independent samples” test
We can test all three dependent variables (content, teaching and total), make sure you define the groups…
Significance Level
P(Type I Error)=α Alpha= probability to reject a right null hypothesis
Significance Level
Critical probability in choosing between the null hypothesis and the alternative hypothesis Probability Level selected is typically .05 or .01 probability to reject a right null hypothesis The lower significant level, the more confidence we have to reject the null hypothesis
Note that this is a “paired sample” t-test, as each respondent has two relevant data-points being compared
Note that this is a “paired sample” t-test, as each respondent has two relevant data-points being compared
been “fiddled” to make them more
interesting!
1. Overall, this has been an excellent course 2.The course met its stated objectives
Items for content
3.The concepts and skills presented are relevant to our industry 4.There was a good balance of instruction and class discussion 5.The handouts and course material were professional and appropriate
Questions asked are: 1. Is the difference statistically significant? 2. Is the difference large enough to justify a differential treatment strategy?”
$52,100 women
T-tests, ANOVA and Chi-Square test
Statistical Inference
statistical inference : the process of drawing conclusions from data subject to random variation, for example, observational errors or sampling variation.
Standard error: a measure of the variation in the sampling distribution based on what is theoretically believed to occur were we to take a several independent samples from the same population (e.g. variation of X bars, Variation of Xs can be captured as SD) Standard error decreases when the sample size increases
introduced last week… The School ran a series of training
sessions for DHL. We obtained ratings
Example
of the teacher and the course so we could improve our performance. The example is genuine, but the numbers have
Difference of means or Movement of two variables
Mean difference Two
Two Groups? Or Two Vars?
Movement of Variables
Correlation
How many means to compare?
What’s going on here, actually?
Mean “Centralizing tendency”
Bivariate analysis
??
“A bank takes a sample to compare the annual ($) salaries of professional men and women employees. It turns out that men’s average salary is $59,475 while women’s average salary is $52,100.
Sampling Distributions
Sampling Distributions
Sampling Distributions
Sampling Distributions
Standard Error of the Mean
Confidence Interval
Remember our real-life example which was
Regression
More than two
Many Groups? Or Many Vars?
Two Groups
Indep. Sample t-test
Two Variables Paired Sample t-test
Groups
Variables
ANOVA
One way/two way
Repeated Measure
Items for instructor
When we compare the data of two groups of people, or data from one group over two variables, we generally T-tests, have two ways of making the comparison (other than ANOVA univariate differences such as different standard deviation and so on). These two key descriptors are:
1. The Instructor was well-prepared & organized 2. The Instructor demonstrated mastery of the subject matter 3. The Instructor understood the practical issues facing DHL 4. The Instructor was able to maintain interest 5. Ideas and concepts were communicated clearly 6. An appropriate amount of participation was encouraged
Comparing two different contact types onwenku.baidu.comeach construct.
Wait A Minute!
What does the p value mean?
Hypothesis
An unproven proposition or supposition that tentatively explains certain facts or phenomena
Bivariate analysis
Differences or similarity in the absolute value of the Correlation comparison of the movement of the scores between two variables or two groups of the same variable means, and
Highlight two variables you want to compare.
click
This is the output window and, yes, we do have a small, somewhat insignificant difference
How can we apply the paired t test for the on-going project?
Remember? The Sampling Distribution of Samples of 1
In this example, the mean amount of money these people have is $4.50 ($45/10). If we picked 10 different samples of 1 person each, our “estimates” of the mean would range all across the board.
Let’s suppose that we want to know if there is a difference in the mean level for “content” and that of “teaching” (this may indicate either a style or content problem) .

Null hypothesis Alternative hypothesis
Null Hypothesis
Statement about the status quo No difference
Alternative Hypothesis
Statement that indicates the opposite of the null hypothesis
Type I and Type II Errors
Accept null Reject null
Null is true
Correctno error
Type I Error
P(Type I Error)=α
Null is false Type II Error
P(Type I Error)=β
Correctno error