Final Psych 201

Variability, Normal Distributions, Hypothesis Testing, Power, Confidence Intervals

Reasons for Variability

Differences in data, differences in procedures, your own mistakes

Descriptive Statistics

Used to summarize and describe sets of data Ex. A GPA summarizes grades

Inferential Statistics

Used to make predictions or inferences about a population based on a sample of data. Ex. hypothesis testing and confidence intervals

Sample

A subset of a population

Random Samples

Samples are selected randomly from a population to minimize bias

Random Assignment

Randomly assigning people you selected into groups to minimize confounding variables

Population

A group that we want to learn more about that shares a common chacteristic

Category Scale

Observations are assigned different categories with no numerical value Ex. Careers

Ordinal Scale

orders different observations but does not tell us distance between points Ex. Class Rank

Equal Interval Scale

A measurement scale where the distance between any two adjacent points is the same. Ex. Temperature in Celsius, a clock

Absolute Zero Scale

A scale that indicates the complete absence of a quantity, where zero represents a true zero point. Ex. Kelvin temperature scale.

Nominal scale

qualitative scale, a form of categorical scale

Interval Scale

Spacing is known, but zero doesn’t matter

Ratio Scale

A quantitative scale that has a true zero point. Ex. height, weight, and temperature in Kelvin.

Characteristics of a positively skewed distribution

In a positively skewed distribution, most data points cluster to the left with a long tail extending to the right. This indicates that the mean is greater than the median which is greater than the mode.

Characteristics of a negatively skewed distribution

In a negatively skewed distribution, most data points cluster to the right with a long tail extending to the left. This indicates that the mean is less than the median which is less than the mode.

Bimodal distribution

A probability distribution with two different modes or peaks.

Characteristics of a normal distribution

A probability distribution that is symmetric about the mean, unimodal, and asymptotic or tails go to infinity. Mean=median=mode

range

largest value - smallest value

Standard deviation

A measure of the amount of variation or dispersion in a set of values, indicating how much individual data points differ from the mean. This is the square root of variance

Indication of population

Greek lettering

Central tendency

mean, median, mode

mean

Average

median

middle most point

mode

Most frequently occurring data point

68% of all data points in a normal distribution are…

within 1 standard deviation of the mean

95% of all data points in a normal distribution…

are within 2 standard deviations of the mean

99.7% of all data points are in a normal distribution…

are within 3 standard deviations of the mean

z-score

How your score compared to others in a normal distribution in terms of standard deviations (this is a standard score)

How to compute a z-score

(raw score - mean)/ standard deviation

mean of a set of z scores

0

standard deviation of a set of z-scores

1

shape of a set of z-scores

normal

Percentile

proportion of people with scores less than or equal to a score. Correlates to z-score Ex. 85th percentile means 85% of scores are below yours

The same person can have different z-scores based on the sample they are a part of

True

To calculate frequency between two z scores

Convert raw scores to z scores and find each value’s z table value. Subtract these values from each other

Probability in terms of statistics

Using frequency to predict what will happen in the future

Why would you do random sampling with replacement

so each observation has an equal chance of being picked every time and the probability doesn’t change

What is a distribution of sample means

All possible samples that could be picked from a population. Samples are different from population because of sampling error

The distribution of sample means is not normal

false. It is normal

Standard deviation of sample means

standard error of sample means (standard deviation/ sqr. root of n) (tells us how well a sample mean estimates the population mean)

what is the z score when the alpha level is .05

1.96

what is the z score when the alpha level is .01

2.567

what is the z score for a 90% confidence interval

1.645

Reject the null

significant evidence to suggest test effected population mean

fail to reject the null

No significant evidence to suggest test effected the population mean

Type 1 error

null is rejected when treatment really doesn’t have an effect (a false positive)

Type 2 error

False reporting that the treatment has no effect (it does) (false negative)

A type 1 error is worse than a type 2

True

How to minimize type 1 error

increase sample size and increase level of significance

power

probability of correctly rejecting null hypothesis

factors that effect power

level of significance, sample size, effect size

small, medium, large effect sizes

.2, .5, .8

What does a larger effect size mean

there is a smaller number of people required to reach desired level of significance

Confidence Interval

Where you’re confident the population mean falls between

Factors that effect width of a confidence interval

Standard error and level of significance

Can you do hypothesis testing if the distribution is skewed

NO

The range is not a particularly useful measure of variability

True because it ignores so much of the data

A positive z score always indicates that the raw score is located above the mean

True

Variability in the sampling distribution of the mean can be decreased by decreasing the sample size

False because sampling error can only be decreased by increasing the sample size

Rejecting a true null hypothesis

a type 1 error

The smaller the alpha level, the lower the risk of…

a type 1 error

The median provides a more representative measure of the central tendency than does the mean in a highly skewed distribution

True

It is impossible for a distribution to have more than one mode

false

The average difference between each score and the mean is a very useful measure of variability

False

A sample standard deviation tends to be ____ the population standard deviation

less than

In a normal distribution, the probability of selecting a score more than 1 SD above the mean is about…

.16

In a skewed distribution, the probability of selecting a score above the mean is

impossible to determine

A one tailed test is better than a two tailed test

false

Failing to reject a false null

type 2 error

Rule of thumb in psych for minimum acceptable probability that a null hypothesis is false

95% (1.96- z score)

Probability is ____ in future tense

frequency

When do you use a t test

when you don’t know a population’s standard deviation and we estimate it

what is the degrees of freedom for a single sample t test

n-1

the smaller the size of the sample, the better s represents sigma, and the better the t distribution approximates a normal distribution

false

s is almost indistinguishable from sigma when N is over 60

false

there are many different t distributions

true

when sigma is not known, we must point estimate its value

true

what do you do if your t statistic falls within the rejection region

reject the null and conclude there was an effect

once you know s, we can compute the sample mean (s_M) by

dividing by the square root of n

what is the main difference between a t distribution and a normal distribution

they have broader tails

if one calculated the effect size using a single sample t test and found an effect size of .5, what would that mean

the mean is half the standard deviation from the population

what does a t distribution depend on

degrees of freedom

what should you avoid if you’re worried about carry over effects

dependent sampling

what is the combined variance of two groups in an independent t test called

pooled variance

what is the degrees of freedom in a dependent t test

n-1 (n is number of pairs)

when computing both independent and dependent t tests, one must estimate the standard error

true

is a dependent t test always non directional

no

what is an advantage of dependent sampling vs independent sampling

it is more powerful

what does D stand for in a dependent t test

the difference between scores from the same subjects from time one and time two

if you suspect individual differences in your sample will be large, use what test

dependent sample t

what are the main sources of carry over effects

practice, fatigue, transparency, subject mortality

what factors effect the estimated standard error in an independent t test

the variability of the scores and the size of the sample

ANOVA can only be used when comparing independent groups

false

a negative f ratio implies that differences were detected, but that they were in the opposite direction of what was predicted

false

what does a significant f ratio tell us in ANOVA

at least one mean differs from one other mean, but not which one

what is the denominator of the f ratio

MS_within

SS_total = ?

SS_between + SS_within

the shape of the f distribution depends on the degrees of freedom

true

when do you use a proteted t test

after you find a significant f ratio