Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 9 and 10 - Coggle Diagram
Chapter 9 and 10
The t-statistic is used to test a hypothesis about an unknown population mean. The t-statistic is used like a z-score, but uses the standard error as the denominator.
The estimated standard error is used to estimate the actual standard error when the standard deviation is unknown. It is computed from the sample standard deviation and provides an estimate of the standard distance between a sample mean and the population mean.
As the sample size increases, the sample variance becomes a better estimate of the population variance. For a t statistic, the relationship is expressed using degrees of freedom. As the sample size increases, so do the degrees of freedom, and the t statistic becomes a better approximation of the z-score.
The complete set of t values forms a t distribution. As the degrees of freedom become larger, the t distribution becomes more similar to a normal z distribution.
The t distribution has more variability than a normal z distribution, especially when the degrees of freedom are small.
In a t statistic, both the numerator and the denominator used to compute the standard error can change from sample to sample.
Interpreting the t statistic: when the obtained difference between the data and the hypothesis is much greater than expected relative to the standard error, we obtain a large positive or negative t statistic. The data are then not consistent with the hypothesis, so we reject the null hypothesis. When the difference is small, we fail to reject the null hypothesis.
A single-sample t-test. The t-test requires a null hypothesis and a sample from the unknown population.
The sample must consist of independent observations. Two observations are independent when there is no consistent, predictable relationship between them. The population sample must also be normal.
The estimated standard error is directly related to the sample variance. Larger variance produces a larger standard error.
-
-
Cohen's d is a measure of effect size. When population values are unknown, corresponding sample values are substituted. An estimated d of 1.00 indicates that the treatment effect is equivalent to one standard deviation
A confidence interval is used to estimate an unknown population mean. A sample mean tends to provide a reasonably accurate estimate of the population mean.
Increasing the sample size makes the confidence interval smaller. A larger sample provides more information and produces a more precise estimate.
Independent measures research design, also called a between-subjects design, uses separate and independent samples to compare groups of individuals.
Repeated measures research design, also called within-subject design, obtains two sets of data from the same group of participants.
The goal of an independent measures research study is to evaluate the mean difference between two populations under two treatment conditions.
Standard error for the independent measures t statistic measures the amount of error expected between a sample mean difference and the population mean difference.
Three assumptions of an independent-samples t-test : observations within each sample must be independent, the two populations must be normal, and the two populations must have equal variances.
The independent-samples t-test allows researchers to measure effect size using Cohen's d. Typically reported as a positive value and describes the magnitude of the treatment effect.
-
Large sample variance can obscure a mean difference between samples and lower the likelihood of rejecting the null hypothesis.
Random assignment in an independent-measures t-test involves two separate groups of participants. A random sample is selected, and participants are randomly assigned to treatment groups. This helps ensure this no bias between the groups due to individual difference.
Pooled variance combines the two sample variances into a single value. This allows the larger sample to carry more weight when determining the final value.
-
The F-max test is based on the principle that a sample variance provides an unbiased estimate of the population variance