Chapter 9 - Introduction to the t - Statistic

t distribution

A ________________ is the complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df). The ___________ approximates the shape of a normal distribution, especially for large samples or samples from a normal population.

n = 21

A researcher reports a t statistic with df = 20. How many individuals participated in the study?

The better the sample variance, s^2, represents the population variance, sigma^2, and the better the t statistic approximates the z-score

As the value of df for a sample increases, the better?

Estimated d = mean difference/ sample standard deviation = M - untreated population mean/ sample standard deviation

For Cohen's d, in most situations the population values are not known and you must substitute the corresponding sample values in there place. When this is done, many researchers prefer to identify the calculated value as an ____________

Estimated standard error = square root (sample variance/ sample size)

Formula for estimated standard error?

t = M - population mean/standard error

Formula for t statistic?

Increasing sample size increases the likelihood of rejecting the null hypothesis but has little or no effect on measures of effect size.

How does sample size influence the outcome of a hypothesis test and measures of effect size?

Increasing the sample variance reduces the likelihood of rejecting the null hypothesis and reduces measures of effect size.

How does the standard deviation influence the outcome of a hypothesis test and measures of effect size?

The degrees of freedom. In general, as the sample size (n) increases, the degrees of freedom (n-1) also increase, and the better the t distribution approximates the normal distribution.

How well a t distribution (the t statistic for every sample) approximates a normal distribution is determined by?

True. The smaller sample produces a wider interval

If all other factors are held constant, a confidence interval computed from a sample of n = 25 is wider than a confidence interval computed from a sample of n = 100. True or false?

False. Greater confidence requires a wider interval

If all other factors are held constant, an 80% confidence interval is wider than a 90% confidence interval. True or false?

True

In general, a distribution of t statistic is flatter and more spread out than the standard normal distribution. True or false?

t statistic

The ______________ is used to test hypotheses about an unknown population mean, when the value of population standard deviation is unknown. The formula for the __________________ has the same structure as the z-score formula, except that the ________ uses the estimated standard error in the denominator.

Estimated standard error

The ________________ is used as an estimate of the real standard error, population standard error, when the value of the population standard deviation is unknown. It is computed using the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean, and the population mean.

r^2 = t^2/t^2 + df

The formula for percentage of variance accounted for by the treatment using the t statistic as opposed to using the sum of squares?

Percentage of variance accounted for by the treatment = variability accounted for/ total variability

This value of r^2, and measures the variability accounted for by the treatment effect. This is called what and the formula is?

A t statistic is used instead of a z-score when the population standard deviation and variance are not known

Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?

Confidence interval

_______________ is an interval, or range of values, centred around a sample statistic. The logic behind a ______________ is that a sample statistic, such as a sample mean, should be relatively near to the corresponding population parameter. Therefore, we can confidently estimate that the value of the parameter should be located in the interval.

small effect

r squared = 0.01 means what in the percentage of variance explained?

Medium effect

r squared = 0.09 means what in the percentage of variance explained?

Large effect

r squared = 0.25 means what in the percentage of variance explained?