Statistics 15

Power equals _________

1-beta

Maximizing the power of an experiment _________.

minimizes beta

What happens to alpha as effect size increases (all else held constant)?

remains constant

Which term means that chance is not a "good" explanation for your findings?

statistical signficance

"Correct Decision" is defined as _________.

all of these

If H0 is true, then the probability of rejecting H0 is limited by _________. Group of answer choices

alpha

The power of an experiment is affected by _________.

alpha level, sample level and the size of effect of the independent variable

A real effect of the independent variable is defined as _________.

any effect that produces a change in the dependent variable

Which hypothesis states that there will be an effect, difference or association?

the alternative

A Cohen's d of .8 is considered a large effect size.

true

What is another name for a one-tailed hypothesis?

directional

If b = 1, then 1- a=.5

false

Increasing N affects the magnitude of the effect of the independent variable.

false

Most studies in pyschology have adequate power.

false

Power varies from -1 to +1.

false

List one advantage of a one-tailed test.

more power

The higher the power, _________.

the more likely h0 is to be rejected whether h0 is true or false

Which hypothesis is tested when using the hypothesis testing approach to inferential statistics?

the null

The most common alpha level is .05.

true

factors that affect power

Sample Size: To increase power, increase sample size. Significance Level α: A larger value of α increases power. Effect Size: The farther the true value is from the hypothesized value, the larger the power. Data Collection: Using blocking rather than a completely randomized design can increase power.

If H0 is in reality false and it is legitimate to use a directional H1, which of the following will yield a more powerful test?

one-tailed alternative

If the null hypothesis is false, the probability of making a correct decision is given by _________.

power

With the effect of the independent variable and N held constant, as a gets more stringent _________.

power decreases

Cohen's d

reports effect sizes in terms of standard deviations. A cohen's d of 1 would indicate that one group was one full standard deviation apart from a second group (.2, .5, and .8 are considered small medium and large effects).

Which is true of one-tailed tests?

smaller CV

It is impossible to ever prove that H0 is true because _________.

the power to detect very weak but real effects of the independent variable is always low

A correlation of .5 is considered a large effect size.

true

An experiment with N = 18 is more powerful than an experiment with N = 17, all other things being the same.

true

In an experiment where we retain H0, one cannot be certain if it was because H0 was true or that the experiment was not powerful enough to detect an effect by the independent variable.

true

Power = 1- b

true

Power is a measure of the sensitivity of an experiment to detect the real effects of the independent variable, if there are any.

true

Which of the following is equivalent to letting a guilty person go free?

type 2 error

Eta squared

η2 is another measure of effect size and is similar to r2 in that is conveys the amount of variance in one variable that can be accounted for by a second (.01, .09, and .25 are considered small medium and large effects).

power

Power (1-beta) is the ability to find an effect if one exist. Power is the correct rejection of the null. Power is analogous to convicting a guilty man or detecting cancer when the patient actually has cancer.

With other factors held constant, as the effect of the independent variable decreases, power will _________ and the probability of a Type II error will _________.

decrease, increase

If the power of an experiment is 0.7496, the probability of making a Type II error is _________.

0.2504

If H0 is true and the probability of making a Type I error is 0.05, then the probability of making a correct decision is _________.

0.95

Type 2 error

A type 2 error occurs when we fail to reject the null, but we should have. In other words, you failed to find an effect that really does exist. A type 2 error (which equals beta) is the equivalent of letting a guilty man go free or telling telling a pregnant woman that she isn't pregnant.

Type 1 error

A type I error occurs when we reject the null, but we should not have. In other words, you have found an effect that does not exist. A type 1 error (which equals alpha) is the equivalent of convicting an innocent man or telling a woman she pregnant when she isn't.

what is effect size?

Effect size refers to the size/degree of association or the size/degree of differences between two or more variables. In the previous slide, I mentioned that effect size is one of several factors that influences power. Effect sizes are hugely important in statistics because p-values alone can be very misleading. Just because some outcome is statistically significant does not mean it is significant in practice because very large sample sizes will always yield statistically significant results. For example, if I randomly sampled 5000 males and 5000 females and recorded their Iqs, I would likely find a statistically significant difference between the two groups even if the means for the two groups were nearly identical (Mmale=99.95 vs Mfemale=100.20 - this is not real data). As you can see, however, the effect size is quite small—would you buy a supplement to increase you IQ by .25 points?

What is the symbol for the null hypothesis?

H0:

Type 1 and type 2 errors: which is worse?

It depends on the research question. Letting a guilty man go free (type 2 error) is no big deal if we are talking about littering. Let a murder go free, however, is a reason for concern. Convicting an innocent person (type 1 error) is no big deal they get a $25.00 fine for littering. Putting an innocent man to death, however, is a huge mistake. Of course, you want to avoid making either type of error. That's why sample size and effect size are such important issues. Although you want to avoid making either error, you can't actually make a type 1 and a type 2 error at the same time. They are mutually exclusive. If there is no effect to be found (such as examining the relationship between shoe size and IQ), you can only make a type 1 error. If there is actually an effect to be found (such as concluding that sleep duration affects concentration), you can only make a type 2 error. Unfortunately, psychology (most sciences actually) has focused too much on avoiding type 1 errors. As such, much of psychological research has been (and continues to be) underpowered with the typical experiment have power=.5. this means there is only a 50% chance of finding an effect if one exists even though a minimum of .8 is recommended by many experts.

confidence levels

Your confidence level (1-) a is the correct retention of the null. In other words, you don't find anything and there is nothing to be found. Although it appears as if there are four possibilities, there actually on two for any given study. If a person is guilty, you can't make a type 1 error or a good decision called 1-a. If a person is innocent, you can't make a type 2 error or a decision called power.

Which of the following is equivalent to letting an innocent person go free?

confidence level

A type 1 error is always worse than a type 2 error.

false

An experiment with a = 0.05 is more powerful than one where a = 0.01, other factors held constant.

false

Failing to find an effect that does exist is called a type 1 error.

false

If H0 is true, as the power of the experiment increases, the probability of rejecting H0 increases

false

The most common power level is .05.

false

What happens to power as effect size decreases (all else held constant)?

goes down

What happens to power as sample size increases (all else held constant)?

goes up

What happens to the probability of making a type 1 error as alpha increases (all else held constant)?

goes up

If alpha is .05, what is power.

insufficient data

If power is .8, what is your type 1 error?

insufficient data

The Correlation coefficient (r)

is one measure of effect size (.1, .3, and .5 are considered small, medium and large effects).