Understanding Research: Results in Inferential Statistics

A series of flashcards for reviewing key concepts and procedures surrounding the independent t test and hypothesis testing in inferential statistics.

What is the independent t test used for?

To determine if means of two independent samples are significantly different.

Can the independent t test be used for any sample size?

Yes, it can be used for any sample size, even if n < 30.

Who invented the t test and what was his pen name?

William Sealy Gosset, known by his pen name, Student.

What does the t score indicate?

It indicates how many standard deviations from the mean of a sampling distribution of mean differences is the mean difference from a study.

What are the steps to conduct a t test?

1. State hypotheses and significance level. 2. Collect data and calculate t statistic. 3. Determine probability by comparing to a sampling distribution of t's. 4. Make decision to accept or reject null hypothesis.

In hypothesis testing, what do Ho and H1 represent?

Ho represents the null hypothesis, while H1 represents the alternative hypothesis.

What is the significance level often denoted as?

Alpha (e.g., α = 0.05).

What does it mean to reject the null hypothesis?

It means that the research hypothesis is accepted, indicating an effect was found.

What type of error occurs when the null hypothesis is falsely rejected?

Type I error.

What is the probability of making a Type I error represented by?

The stated significance level, or alpha (α).

What is a Type II error?

Failing to reject the null hypothesis when the research hypothesis is true.

What does beta represent in hypothesis testing?

The probability of making a Type II error.

What factors affect beta and power in hypothesis testing?

1) Alpha level, 2) Sample size, 3) Effect size.

What is meant by effect size?

It assesses the magnitude of the experimental effect, indicating how large the effect is.

What statistical measure is used for effect size?

Cohen's d.

How do you calculate the degrees of freedom (df) for an independent t test?

df = n1 + n2 - 2.

What is the critical t value used for?

To determine the threshold for rejecting the null hypothesis.

What is the standard normal distribution used for in hypothesis testing?

To standardize scores and calculate probabilities using z scores.

What does the central limit theorem state?

As sample size increases, the sampling distribution of the sample mean approaches a normal distribution.

What is the purpose of the t formula?

To calculate the t statistic based on the mean difference and standard deviations of samples.

What happens when the calculated t falls into the rejection region?

The null hypothesis is rejected.

In the independent t test example on rats, what were the diets tested?

Standard diet and high salt diet.

What was used to assess activity levels in the rats?

The amount of time spent moving in a 10-minute test.

What can cause the probability of correctly rejecting the null hypothesis to increase?

Increasing sample size or effect size.

What does a significant t test indicate about the effect?

It indicates that the effect is reliable, although it does not indicate the size of the effect.

What is the importance of calculating the critical t value?

It helps in making the decision to accept or reject the null hypothesis.

What does it imply if a test is one-tailed?

It tests a directional hypothesis, indicating the expected direction of the effect.

How is the significance of an effect in statistics assessed?

Through statistical tests like t tests to compare means.

What is indicated when calculating the t statistic yields a value that surpasses the critical t value?

There is a statistically significant difference between the sample means.

What represents a low probability of Type I error?

A confidence level of 95%, corresponding to α = 0.05.

What does a Type II error suggest if it occurs?

Concluding that there is no effect when an effect actually exists.

Why is it important to celebrate after hypothesis testing?

It signifies success in the research study, especially if the research hypothesis is accepted.

In a two-tailed test, what are the hypotheses typically framed as?

Ho: µ1 = µ2, H1: µ1 ≠ µ2.