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Chapter 9/10 (t Statistic- used to test hypotheses about an unknown…
Chapter 9/10
t Statistic- used to test hypotheses about an unknown population mean, when o is unknown*
estimated standard error- used as an estimate of the real standard error when the value of the population standard deviation is unknown
Difference between t formula and z-score formula is that the z-score uses the actual population variance, and t formula uses the corresponding sample variance when population value is not known
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t distribution- the complete set of t values computed for every possible random sample for a specific sample size or a specific degrees of freedom. It approximates the shape of a normal distribution
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t = sample mean (from the data) - population mean (hypothesized from null hypothesis) / estimated standard error (computer from the sample data)
Assumptions
- the values in the sample must consist of independent observations
- The population sampled must be normal
Influences
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Larger the variance, the larger the error. Large variance means that you are less likely to obtain a significant treatment effect
Larger the sample, the smaller the error
Larger samples tend to produced bigger t statistics and therefore are more likely to produce significant results
Measuring effect size
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Percentage of variance accounted for by the treatment- A measure of effect size that determines what portion of the variability in the scores can be accounted for by the treatment effect
Confidence interval- an interval, or range of values centered around a sample statistic/ Logic behind a confidence interval is that a sample statistic, such as a sample mean, should be relatively, near to the corresponding population parameter
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Correlation- a statistical technique that is used to measure and describe the relationship between two variables
- The direction of the relationship. The sign of the correlation, positive or negative, describes the direction.
- The form of the relationship.
- The strength or consistency of the relationship.
Positive correlation- two variables tend to change in the same direction: as x variable increases, y variable also increases. Negative correlation- two variables tend to go in opposite directions: as the X variable increases, the Y variable decreases
Perfect correlation- a relationship where the actual data points perfectly fit the specific form being measured
Pearson correlation- measures the degree and the direction of the linear relationship between two variables
Sum of products- A measure of the degree of co-variability between two variables; the degree to which they vary together
- Find the X deviation and the Y deviation for each individual 2. Find the product of the deviations for each individual 3. Add the products
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Spearman correlation- A correlation calculated for ordinal data. Also used to measure consistency of a direction for a relationship