Please enable JavaScript.
Coggle requires JavaScript to display documents.
chapter ,9 t Statistics (chapter 15, (Pearson Correlation and z zone,…
chapter ,9 t Statistics
chapter 15,
-
-
Correlation and the Pattern;Thus, the value of the correlation describes the relationship that exists in the data.
Because the Pearson correlation describes the pattern formed by the data points, any factor that does not change the pattern also does not change the correlation.
Introduction of . Usually the two variables are simply observed as they exist naturally in the environment—there is no attempt to control or manipulate the variables.
The t Statistic ; An Alternative to z:The goal of the hypothesis test is to determine whether the obtained difference between the data and the hypothesis is significantly greater than would be expected by chance
Problem with z score: however, the standard deviation for the population is not known. In fact, the whole reason for conducting a hypothesis test is to gain knowledge about an unknown population.
Introducing the t Statistic : The value n − 1 is called the degrees of freedom (or df) for the sample variance.
Degree of freedom and=d the t Statistic : Degrees of freedom of an estimate is the number of independent pieces of information that went into calculating the estimate
The t Distribution :the distribution of z-scores for sample means tends to be a normal distribution. Specifically, if the sample size is large (around or more) or if the sample is selected from a normal population,
-
Shape of the t Distributions :The exact shape of a t distribution changes with degrees of freedom. As of gets very large, the t distribution gets closer in shape to a normal z-score distribution.
:Determine proportions and Probabilities for t Distributions : In the hypothesis-testing situation, we begin with a population with an unknown mean and an unknown variance, often a population that has received some treatment
Estimate Cohen's d :Calculate Cohen’s d or the percentage of variance accounted for to measure effect size for a hypothesis test with a t statistic.
influences of shape e size and sample Variance : In particular, the number of scores in the sample and the magnitude of the sample variance both have a large effect on the t statistic and thereby influence the statistical decision. The structure of the t formula makes these factors easier to understand.
Measure Effect size for the t Statistic : The concept behind this measure is that the treatment causes the scores to increase (or decrease), which means that the treatment is causing the scores to vary.
Critical Region for a One -Tail Test : The first stage in this process is simply to determine whether the sample mean is in the direction predicted by the original research question.
Directional Hypotheses and One - Trial Test On the other hand, a directional test may be used in some research situations, such as exploratory investigations or pilot studies or when there is a prior justification
Hypotheses Test with the t Statistic You can that this is another example of a null hypothesis that is founded in logic rather than prior knowledge of a population mean., All three factors are in the problem to solve the solution ,State the Hypotheses and Select an Alpha Level. Locate the Critical Region.
:
Assumption of he t Test: More precisely, two events (or observations) are independent if the occurrence of the first event has no effect on the probability of the second event
Confident Interval for Estimate u : The distribution of t statistics for . The t values pile up around and 80% of all the possible values are located between and .
Constructing a Confidence Interval : The distribution of t statistics for . The t values pile up around and 80% of all the possible values are located between and .
o gain more confidence in your estimate, you must increase the width of the interval. Conversely, to have a smaller, more precise interval, you must give up confidence.
Sumo of Product of Divination :To calculate the Pearson correlation, it is necessary to introduce one new concept: the sum of products of deviations, or SP
Once you have chosen the first two numbers in the set, the third is fixed. In other words, you can’t choose the third item in the set. T