T-Statistics
Estimated Standard Error- estimate of the real standard error when the value is unknown.
2 Reasons for T-scores over Zscores
Sample Variance is more accurate and unbiased
Will encounter other versions of t statistics that require Variance (instead of standard deviation)
The square root of the sample variance divided by the sample size
Formula for T Statistic is used to test the hypotheses about an unknown population mean, u, when value is unknown.
Degrees of freedom (df) df=n-1 describes the number of scores in a sample that are independent and free to vary.
Assumptions to test
- Must consist of independent observation
- Population sampled must be normal.
Due to Estimated Standard Error located in the denominator of a t-statistic a larger value for Estimated Standard Error produces a smaller value (closer to zero)
High variance reduces the likelihood of rejecting the null hypothesis. The larger the sample size the smaller the error.
Estimated Cohens'd -Mean difference divided by the standard deviation.
Names the value after one of the statisticians who first substituted sample statistics into Cohen's formula.
Percentage of Variance accounted for by treatment.
A measure of effect size that determines what portion of the variability in the scores can be accounted for by treatment effect.
Removing treatment effect reduces the variability
Measuring the percentage of variance.
r2 = Variability accounted for divided by total variability.
Cohens are not influenced at all by sample size and measures of r2 are only slightly affected by changes in the sample size (n)
Criteria for interpreting the value of r2 as proposed by Cohens
r2=0.01 Small effect
r2=0.09 Medium effect
r2=0.25 Large effect
Confidence interval- an interval or range of values centered around a sample statistic
Correlations
Correlation is a statistical technique that is used to measure and describe the relationship between two variables.
Positive Correlation- the two variables tend to change in the same direction: as the value of the X variable increases from one individual to another, the Y variable also tends to increase; when the X variable decreases, the Y variable also decreases.
Ex. 
Negative Correlation- the two variables tend to go in opposite directions. As the X variable increases, the Y variable decreases. That is, it is an inverse relationship.
Ex:
The Direction of the Relationship The sign of the correlation, positive or negative, describes the direction of the relationship.
A correlation of 1.00 indicates a perfectly consistent relationship.
A correlation of -1.00 indicates a perfectly consistent relationship
Pearson correlation- measures the degree and the direction of the linear relationship between two variables.
The Pearson correlation for a sample is identified by the letter r.
r= the degree to which X and Y vary together divided by the degree to which X and Y vary separately.
Definitional Formula for the sum of products is where Mx is the mean for x scores and My is the mean for y scores.
Sum of products of deviation- A measure of the degree of covariability between two variables; the degree to which they vary together.
Find the X deviation and the Y deviation for each individual
Find the product of the deviations for each individual.
Add the products.
SP-Uses products and SS uses squares
A positive correlation means that individuals who score high on X also tend to score high on Y.
A negative correlation indicates that individuals with high X scores tend to have low Y scores
Why are Correlations used???
1. Prediction
2. Validity
3. Reliability
4. Theory Verification
Spearman Correlation- A correlation calculated for ordinal data. Also used to measure the consistency of direction for a relationship.
Spearman correlation is used to measure the relationship between X and Y when both variables are measured on ordinal scales