Psyc 241 Exam 2

sampling error

• difference between sample statistic and population parameter

• error of estimation

• samples are variable

sampling distribution

• represent means of samples of people

• conveinent and efficient (hard to measure every person)

mean of distr. of sample means

• population mean

inc size of sample

• closer to population mean

• standard deviation gets smaller because mean excludes outliers

central limit theorem

• distribution of means is less variable then distribution of individual scores

• the assertion that a distribution of sample means approaches a normal curve as sample size increases, regardless of the shape of the population from which the sample is drawn

sampling distribution

• approximately normal if population = normal or n is greater than/equal to 30

• sampling distribution mean = population mean

• sampling distribution standard deviation < the population standard deviation

Standard Error

• measuring average distance expected between sample mean and and mean

• dec as sample size inc (curve gets skinnier)

Z scores

• standardized raw scores

• find probability of selecting sample with specific mean

Unbiased estimator

• sample mean (x bar) is unbiased estimator of the mean (mew)

• s² is unbiased estimator of σ²

• sample proportion is unbiased estimator of population proportion

• The sample median is an unbiased estimator of the population median if the distribution of the population is symmetric.

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variability

• high = more error in estimation

unbiased/biased estimator

• biased if it includes the population min and max (most samples don’t include this)

• A sample is biased if it over represents or underrepresents some segment(s) of the population

• it is said to be unbiased if the average value of an estimator equals the population parameter being estimated

Probability sample

• likelihood of selection known (need to know everyone in population) → must be small

• random selection (when p does not equal 1)

• sampling frame known

• enable an analyst to determine the probable errors that an estimator might generate

simple random sampling

• people selected by chance

• every possible sample of the same size n has the same probability of being selected

• ex: random generator

systematic sampling

• pick first person at random then go every other person for sample

• set interval

cluster sampling

• chose a few groups and everyone in those groups

stratified sampling

• randomly select from every group

non-probability sample

• likelihood of selection unknown

• convenient sample used to estimate a population parameter in which no statement about the estimate's reliability can be made.

convenience/voluntary

• group of people convenient to researcher

• easily available

• voluntary → occurs when participants volunteer to participate in a study.

snowball

• start w/subset of people and have them keep collecting more people

• used for data that’s hard to get

if the sample mean falls within the interval

• you fail to reject Ho → not sufficient evidence

if alpha is > p

• you reject the null → significant evidence

Hypothesis testing

• allows us to evaluate the probability of different outcomes

• procedure, based on sample evidence, that is used to test a statement or claim about a characteristic of one or more populations.

Null hypothesis significance testing

• method that uses sample data to evaluate a hypothesis about a population

Null

• nothing going on

• often not stated

Alternative hypothesis

• something going on

• stated in hypothesis

• typically non-directional/two-tailed

• sometimes specific

non-directional

• two-tailed test

directional

• one-tailed test

probability

• value meant to imply “very unlikely”

• unlikely to be obtained if Ho is true

Fisher’s P-value

• probability of observing statistic observed if NO effect exists

strong evidence

• p or alpha = 0.01

weak evidence

• p or alpha = 0.2

standard

• p or alpha = 0.05

test statistic

• collect data → after hypotheses are stated and alpha is established

• compute test statistic → Z

• find probability of obtaining that test statistic

determining significance

• depend partially on hypothesis (directional / non-directional)

• compare p to alpha → significant (p < a) and non-significant (p > a)

• compare z to critical z

significant

• reject Ho

• conclude Ha

• restate with significant language

non-significant

• fail to reject Ho

• conclude Ho

• restate with significant language

Find support for hypothesis

• never prove

• never find to be true

“fail to reject null”

• never accept null

“reject null”

• never accept alternative

“non-significant” / “significant”

• not insignificant

“statistically significant”

• does not equal practical significance

Type I error

• say effect when there isn’t one

• convention → p (a-level) = 0.05

• false positive

• reject Ho when Ho was true

Type II error

• say no effect when there is one

• convention → p (b-level) = 0.2

• false negative

• fail to reject Ho when Ho is false

Interval estimate

• range that hopefully contains population parameter

• dependent on confidence interval level (a)

if interval contains Ho value

• no sig difference

• Fail to reject Ho

if interval doesn’t contain Ho

• significant difference

• reject Ho

Effect size

• tells how important it is

• absolute magnitude of an effect (independent of n)

• cohen’s d → mean difference / standard deviation

Power

• ability to detect an effect

• opposite of b → (1-b)

• b=probability of making a type II error

• depends on size of effect

large effect

• more power

inc sample size

• inc power

dec SD

• inc power

inc alpha

• dec power

T score

• similar to z → bell shaped, symmetrical, mean=0

• a little flatter distribution

• large sample size → s approaches σ and t approaches z

t distribution

• when the parameters are not known

• means based on (n) and (df)

• we know the population mean but not the standard deviation

• variance > 1

inc n, dec error, dec variance (t)

• more likely to reject Ho and find significant effect

inc variance, inc error (t)

• less likely to reject Ho and find sig effect

Confidence interval

• alternative to effect size

• assumes sample mean should be near the mean (near → based on standard error)

inc confidence

• inc interval

smaller n

• larger standard error and larger interval

sampling frame

• a list which identifies all members of the population.

sampling distribution of a statistic

• (such as the sample mean or sample proportion)

• is the probability distribution of all values of the statistic when all possible samples of size n are taken from a population.

point estimator

• is a single-valued estimate calculated from the sample data, which is intended to be close to the true population value.

judgement sample

• sample in which the observations are selected by an expert in the field and not picked at random.

P-value

• the probability of observing a value of the test statistic as extreme or more extreme than the observed one

• assuming the null hypothesis is true and all the assumptions related to the hypothesis test are satisfied

how does a distribution of sample means differ from a distribution of raw scores

• the distribution of means has a smaller standard deviation

standard deviation of a sampling distribution

• standard error

predicts that there is no effect for our manipulation/no difference between groups

• null hypothesis

Independent samples

• between participants design

• two groups of people, different people in each group

• more people needed

• greater individual difference error

Independent sample t assumptions

• independent observations

• simple random samples

• normally distributed

• populations with equal variances

homogeneity variance (not tested on this math)

• two samples come from population with equal variances

• if violated adjust df → use a smaller df

hypotheses

• Ho: mew 1 = mew 2

• Ha: mew 1 (doesn’t equal/greater than/less than) mew 2

Confidence interval independent samples

• if equal to zero → not significant

• if it doesn’t contain zero → significant

inc variance (independent samples)

• inc error

• smaller t

• less likely to be significant

dependent samples t

• within participants (repeated measures)

• two groups, same people in each, 2 scores for each person

• samples are dependent on each other → fewer people needed

• reduce individual difference error and variability

• practice effects, manipulate salience (memorizing while drinking ex)

dependent samples t assumptions

• independent observations within each condition

• but full sample data is dependent

• matched pairs randomly sampled from population

• population distribution of differences scores (d) normal → problematic with small samples (n less than 30)

larger sample (n) → dependent samples

• smaller Sd (denominator) → larger t

larger variance (sd²) → dependent samples

• larger Sd (denominator) → smaller t

larger mean difference (X bar d) → dependent samples

• larger numerator → larger t