Research Class 10 Part 1

what kind of errors can you make

alpha, beta, power

the smaller the probability of a type 1 error, the larger the probability of type II error, and the smaller the ___

power

when a researcher rejects (fails to accept) the null hypothesis that is true in the population

type I error

in type I error, the researcher states there was a treatment effect when in fact there was ___ effect

no

when a researcher fails to reject the null hypothesis when it is false in the population

type II error

in type II error, there really is a treatment effect, but the research process is ___ to detect it

insufficient

What steps can a researcher take to try to reduce or at least predict the possibility of error?

determining power and level of significance

what are the types of power analyses can you do

alpha and beta

___ is the probability of a Type I Error, also called the level of significance

alpha

___ is the probability of a Type II Error, also called power

beta

there are ___ components in a power analysis

4

3 of these components must be known or estimated, and the 4th can then be ___ by the power analysis

determined

A ___ is used to reduce the risk of Type II Error

power analysis

most often, a power analysis is done prior to the research to determine the ___ needed to support a significant result

sample size

the 4 components are…

• alpha (the desired significance)

• sample size

• effect size (often estimated from prior research)

• power (1-beta), probability of rejecting null

Plug all these 4 parts into a ___ and then it will tell you what sample size you need

formula

this power analysis is the first step to ___

hypothesis testing

Before we determine the level of significance, we decide on the test statistic from the ___ hypothesis

research

To demonstrate the concepts of level of significance we will use the ___

Z test

the term test statistic simply indicates that the ___ is converted to a single specific statistic that is used to test hypotheses

sample data

conducting a power analysis is good research planning because rather than collecting as many people as possible, you need a ___ sample necessary to produce a reliable result

minimum

A ___ is a standardized measure of how far a particular data value is from the mean of a normally distributed data set

z-score

By providing a uniform scale to express how extreme a given data point is relative to the mean, z-scores are helpful in identifying ___ as well as comparing data from different distributions.

outliers

the z-score formula can be seen as the ___ difference and the difference due to chance

obtained

the purpose of a test statistic (z score as a statistic) is to determine whether the result of the research (obtained difference) is more than would be expected by ___ alone

chance

what does an alpha score of 5% mean in a two tailed test (non directional hypothesis)

You are willing to take risk of 2.5% for each side that you are going to make a mistake

one tailed means you are predicting the direction and therefore a ___ hypothesis

directional

after step 1 which is stating the hypothesis (null and research), next you state the level of ___

significance

the distribution of the sample means is divided into two areas

the body (the middle area under the curve) and the tail (the critical region under the curve)

If the obtained sample means falls in the ___ under the curve, that would support the null hypothesis--no real significant difference, any difference is due to chance alone

body

If the obtained sample means falls in the ___ under the curve, that would reject or refute the null hypothesis

tails

Tail ends is where you want to be for statistical ___

significance

Non directional = 2.5% on each side, directional 5% risk on ___ side

one

the ___ part or body is not significant, the white part

middle

the ___ region is the region of significance and is the criteria for a decision or the level of significance

critical

the mean of any random sample will almost always be ___ than the population mean (all samples have error), there is usually some difference between samples

different

however, the difference is significant if the sample mean is in the ___ region (tails)

critical

The boundaries for the critical region are determined by convention as ___ of the area under the outer extremes of the curve

5%, 1%, or 0.1% (0.05, 0.01, 0.001)

if the hypothesis is non-directional, then the alpha probability must be divided into the ___ tails

two

the third step of hypothesis testing is to choose a ___ test

one tailed or two tailed

Depending on the direction of the hypothesis, if theoretically the result could possibly go in the opposite direction, then the most rigorous decision is the ___ test

two tailed

some authors may still do a one-tailed test, but this could produce a ___ error

Type I

___ tests test hypotheses where specific population parameters are used such as t test, ANOVA, etc, this is more powerful than non parametric tests, and must meet the 4 assumptions

parametric

recap, what is power analysis

power is the probability of finding a significant result if it exists (i.e. Power is the probability of not making a Type II Error)

therefore, the Power probability is the complement of ___ as Power is (1 - beta)

beta

Type II Error occurs when a false null hypothesis is ___ (i.e. there really is a significant difference or relationship in the population, but the research methods are not sufficient to find it)

accepted

a common scenario is this:

given the desired alpha of .05, (95 % significance level by convention) and the desired power of .80 (by convention), ___ other component is needed before finding the necessary sample size

one

some estimate of the sample means, and an SD is needed (from prior research) in order to calculate an ___

effect size

what is effect size

how large a sample size you need to detect a small but significant difference or a large difference

If you anticipate that the differences between groups will be large, then a ___ sample size is required

small

If you anticipate that the differences will be ___, then a large sample size will be needed to detect this

small

with three components determined, it is now possible to go to a Power Analysis ___

table

for an alpha of .05, Part ___ of the table (Cohen’s d table) is used

A

find the estimated effect (.40) along the top and the desired power down the side

the ___ will provide the sample size required

table

e.g. alpha .05, power .80, effect .40

looking at the table, we can see 98 subjects are ___ to avoid a Type II error caused by too small a sample

needed

___ of what we have done so far:

1. Types of hypothesis errors

2. Setting alpha to determine risk of Type I error

3. Setting beta to determine sample size (power) to avoid risk of Type II error

review

Now we are ready to conduct the ___ (hypothesis) test

inferential

what are examples of parametric tests

t test or ANOVA, pearson R

parametric tests are more ___ than non-parametric tests

powerful

you must meet 4 ___ of the parametric tests

assumptions

The three inferential statistics we have disused so far (t-tests & ANOVA, pearson r ) are ___ tests.

parametric

Parametric statistics test hypotheses about specific population ___ (e.g. the mean)

parameters

what are the parametric test assumptions

1) Normal distribution

2) Homogeneity of variance

3) Level of measurement is interval or ratio

4) Variables contain a numerical score

when is a t test appropriate?

When we want to make inferences about two populations

the t test strategy is to ___ actual mean difference observed between two groups

compare

the t test asks, is the difference ___ (in either direction) than would be expected by chance alone?

greater

even if the null is true, you would not expect two sample means to be ___, because some differences will always be present

t test wants to know — is this difference due to CHANCE alone (null hypothesis is true) or due to the IV

identical

the t statistic is the same as the ___ statistic except it uses an estimate of variation and not the population standard deviation

z-score

the numerator in the formula for the t statistic reveals the main purpose…

determining the difference between two means (the sample mean & the population mean)

the ___ for the t statistic provides a measure of the variance and the sample size

denominator

The t distribution is a set of distributions depending on ___

degrees of freedom (df)

what is the degrees of freedom

The extent (degree) by which scores are free to vary or be different

what is the formula for df

n-1 = df

Df: recognizes the limits or restrictions on variability (variance) in any data set and controls for it by ___ 1 from the sample size

subtracting

Each inferential test has a distribution table of ___ of scores under the bell curve, just like a unit table for a z score.

all probabilities

Each distribution table for the probability of test statistics will be set ___ on the df.

depending

For the t test it is the ___ table

t distribution

for df > 100 the t distribution is ___ to the normal distribution

equivalent

there are two types of t tests

independent (unrelated) and dependent (related)

Independent (unrelated) samples looks at…

two distinctly different groups

dependent (related) samples looks at the ___ group on two different occasions

same

t tests are to compare two sets of data where the IV is nominal or ordinal and the DV is ___

interval or ratio

the independent or unrelated samples t test comes from two different, independent samples, such as…

one treatment and one control

the second type of t test is for two dependent samples, they come from a same sample at two different times, ___ measures within subjects

repeated

No logical relationship exists between persons in one group and persons in another group

independent samples t test

what question does independent samples t test ask

Is the difference in means between the 2 groups greater than what would happen by chance alone?

what are the 3 assumptions for independent samples t test

1. IV is categorical

2. DV is continuous, normally distributed

3. homogeneity of variance

what does homogeneity of variance mean

similar variance of the dependent variable for the two groups

When all three assumptions are met, the ___ for similar variances is used

pooled formula

Used to compare means of two groups when the individual scores in one group are paired with particular scores in the other group

dependent samples t test

what are the 3 ways to match or pair samples

1. single group of people measured twice

2. match persons in first and second group

3. separating biological twins into separate groups

what are the assumptions for dependent samples t test

1. sample data consist of matched pairs

2. samples are simple random samples

3. sample size n = 30, or the pairs of values in a population have a normal distribution

the t statistic for dependent (related) samples: within-subjects or repeated- measures studies and involve taking data ___ a treatment using the same sample

before and after

what is the advantage of repeated-measures designs

increased control since the subjects are exactly the same individuals for each measure

how do you report t test results?

1. type of rest conducted

2. calculate t value from sample data

3. df

4. p value, whether it was significant

5. mean, SD, and N for each group

if t statistic falls in the critical region we reject the ___

null

what does this mean?

The difference was greater than by chance alone

the 2nd parametric test is the ___

ANOVA

what does ANOVA stand for

analysis of variance

ANOVA is similar to a t test except there are ___ groups or more

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