week 13

In an experiment, the t value is 4 and the degrees of freedom is 12. Calculate the effect size.

0.75

Instead of inferring population values on the basis of a single investigation, scientists look at the results of several studies that reproduce previous investigations. This describes the importance of ______ in scientific study.

replication

Researchers traditionally have used either a _____ significance level in the decision to reject a null hypothesis.

.05 or a .01

A Type I error is made when the

null hypothesis is rejected but the null hypothesis is actually true

How can one change the probability of making a Type I error in research? (Check all that apply.)

By increasing the alpha level By decreasing the sample size

Identify an accurate statement about interpreting nonsignificant results.

Nonsignificant results are highly likely to be found if the alpha level is very low.

is the likelihood of the occurrence of some event or outcome.

Probability

indicates that there is a low probability that the difference between the obtained sample means was due to random error.

Statistical significance

A decision matrix shows that there are

two kinds of correct decisions and two kinds of errors

In the context of the F test, when a study has only one independent variable with two groups, F and t are

virtually identical

Identify the scenarios in which a correct decision occurs. (Check all that apply.)

A null hypothesis is accepted and the null hypothesis is true in a population. A null hypothesis is rejected and the research hypothesis is true in a population.

Identify the factors that are related to the probability of making a Type II error. (Check all that apply.)

A significance (alpha) level Sample size Effect size

In an experiment with two groups X1 and X2, both groups have ten participants. XX1 is 4, and XX2 is 2; s12 is 1.5, and s22 is 1.6. Calculate the t value.

3.59

From the given image, identify the number that indicates a Type II error.

4

True or false: Even when all of the principles of experimental design are rigorously followed, there will be some difference in the sample means of two groups.

True

Which of the following need to be specified to use a statistical test? (Check all that apply.)

The alpha level The null hypothesis that is being evaluated The research hypothesis that is being evaluated

Which of the following determines the probability of making a Type I error in research?

The choice of alpha level

A general principle is that the larger the sample size in a research study, the

greater the likelihood of obtaining a significant result

Calculate the degrees of freedom for an experiment that involves three groups with ten participants each.

27

Which of the following situations indicates the highest probability of a given outcome?

Chances of a particular team winning a match given that it has won all the matches it has ever played

The t test The F test

Commonly used to examine whether two groups are significantly different from each other Most likely used to ask whether there is a difference among three or more groups or to evaluate the results of factorial designs

Identify the types of variance of which an F statistic is a ratio. (Check all that apply.)

Error variance Systematic variance

Type I error Type II error

Finding the defendant guilty when the person actually is innocent Finding the defendant innocent when the person actually is guilty

Identify the accurate statement regarding a null hypothesis.

If one can determine that the null hypothesis is incorrect, then the research hypothesis is accepted as correct.

A very low significance level A large sample size A large effect size

Increases the chances of a Type II error Increases the chances of detecting true differences Decreases the chances of a Type II error

Identify a true statement about sampling distribution.

It is based on the assumption that the null hypothesis is true.

Identify the formula used to calculate the power of a statistical test. The p in the formula refers to probability.

Power = 1 - p (Type II error)

The null hypothesis (states) The research hypothesis (states)

States that an independent variable has no effect States that an independent variable does have an effect

Group difference Within-group variability

The difference between the obtained means The amount of random error in the sample

Which of the following is a reason for a Type II error?

The procedures used in the experiment

Identify the probable reasons for a Type II error in research. (Check all that apply.)

The sample size is too small to detect a real relationship between variables. The effect size is small.

In t tests, the t value is a ratio of two aspects of the data. Identify these aspects. (Check all that apply.)

The variability within groups The difference between the group means

Identify an accurate statement about inferential statistics.

They allow one to arrive at conclusions on the basis of sample data.

Which of the following is a true statement about statistical tests?

They are MOST likely to produce significant results when the effect size is large.

Mathew is making a decision about whether or not to buy a cell phone from the brand DG. The null hypothesis is that the DG phone does not have an extended battery life. In reality, the DG cell phone has an extended battery life, but Mathew decides not to buy the cell phone because he accepts the null hypothesis as true. In this scenario, Mathew is making

a Type II error

Whether to specify a one-tailed or two-tailed test will depend on whether

a study was originally designed to test a directional hypothesis

An interval of values defines the most likely range of actual population values. The interval has an associated

confidence interval

Identify the formula that is used to calculate the value of Cohen's d, which is an effect size estimate used when comparing two means.

d = M1-M2√(SD21+SD22)2

The _____ are the number of scores free to vary once the means are known in statistical tests.

degrees of freedom

Identify the formula that is used to calculate the degrees of freedom when there are two groups.

df = n1 + n2 - 2

In the context of an F statistic, _____ is the deviation of the individual scores in each group from their respective group means.

error variance

In the context of probability, a significant result is one that is very unlikely if the

null hypothesis is correct

The total number of observations that impact the determination of statistical significance is known as the

sample size

All statistical tests rely on _____ to determine the probability that the results are consistent with the null hypothesis.

sampling distributions

All statistically significant decisions are based on probability distributions called

sampling distributions

Examining confidence intervals is an alternative way of thinking about

statistical significance

A statistically significant result is one that has a low probability of occurring if

the population means are equal

A one-tailed test A two-tailed test

A situation in which research hypothesis specifies a direction of difference between the groups A situation in which research hypothesis does not specify a predicted direction of difference between the groups

Which of the following factors increase the acceptability of a null hypothesis when the results obtained are nonsignificant? (Check all that apply.)

Evidence that shows the variables are not related come from multiple studies. The study was well-designed and the dependent measures were sensitive.

True or false: A meaningful result is more likely to be overlooked when a significance level is very high.

False

True or false: If the result of a study is significant, there is no need for other studies to repeat it.

False

True or false: Nonsignificant results always indicate that the null hypothesis is correct.

False

True or false: The F test is only appropriate for the simplest experimental design.

False

True or false: The Pearson r correlation coefficient is always statistically significant.

False

True or false: The outcome of a study is considered significant when there is a .20 or more probability of obtaining the results.

False

statistics are used to determine whether the results of an experiment match the outcome if one were to conduct the experiment repeatedly with multiple samples.

Inferential

Identify the accurate statements about the significance level chosen by researchers. (Check all that apply.)

It merely specifies the probability of a Type I error if a null hypothesis is rejected. It usually is dependent on the consequences of making a Type I versus a Type II error.

In a research study, the independent variable is measured on an interval scale and the dependent variable is measured on a ratio scale. Which of the following statistical tests will be best suited to determine the relationship between these two variables?

The Pearson correlation coefficient procedure

In a research study, there are two or more independent variables that are measured on a nominal scale and their corresponding dependent variables are measured on a ratio scale. Which of the following statistical tests will most appropriately determine the relationship between the variables?

The analysis of variance procedure

Identify the accurate statements related to a statistical test. (Check all that apply.)

The goal of the test is to allow one to make a decision about whether the obtained results are reliable. The significance level (alpha level) chosen indicates how confident one is when making a decision.

What does the acceptance of a research hypothesis imply?

The independent variable had an effect on the dependent variable.

In the context of a decision matrix, identify the possible truths about a population. (Check all that apply.)

The null hypothesis is true. The null hypothesis is false.

The null hypothesis The research hypothesis

The population means are equal. The population means are not equal.

Which of the following is a true statement about sophisticated statistical analysis software packages?

They provide descriptive and inferential statistics quite quickly.

Identify the accurate statements about sophisticated statistical analysis software packages. (Check all that apply.)

They provide information on statistical significance in the output. They facilitate graphic displays of data.

The logic of inferential statistics is that if the groups of a research experiment are equivalent, it is assumed that any difference in the dependent variable must be due to the

effect of an independent variable

In which of the following scenarios is a researcher most likely to decide to reject the null hypothesis?

When the obtained data have a probability of 0.02 according to null hypothesis expectations

If it is very unlikely that a random error is responsible for the obtained results, then the

null hypothesis is rejected

Inferential statistics are necessary because the results of a given study are based

only on data obtained from a single sample of research participants

In the context of statistical significance, as the size of one's sample increases, one is more confident that the

outcome is different from the null hypothesis expectation

A desired probability of correctly rejecting the null hypothesis in a research study is called the _____ of a statistical test.

power

The decision to reject the null hypothesis is based on

probabilities rather than on certainties

In the context of an F statistic, _____ is the deviation of the group means from the grand mean, or the mean score of all individuals in all groups.

systematic variance

The null hypothesis is rejected when it is found that there is a very low probability that

the obtained results could be due to random error

is used to describe the strength of the relationship between two variables when both variables have interval or ratio scale properties.

The Pearson r correlation coefficient

A _____ occurs when the null hypothesis is accepted although in the population the research hypothesis is true.

Type II error

In the formula for the t test for two groups with equal number of participants in each group, what does s2s2 stand for?

Variance of each group

The probability of obtaining results required for deeming a a result significant is called the

alpha level

The denominator of the t formula in t tests is essentially an indicator of the

amount of random error in the sample

An accurate statement about inferential statistics is that they give the probability that the

difference between sample means reflects random error rather than a real difference

Which of the following is the formula for the t test for two groups with equal numbers of participants in each group?

t = X1-X2S21n1+S22n2

Error variance is also referred to as

within-group variance