Kilianski Exam 1 Quantitative Methods conceptual

Inferential statistics

Making inferences based on probability about an entire population using data from a sample

descriptive statistics

provide a "picture" of the characteristics of a sample or populations with respect to a variable

-can never draw conclusions from this alone

-doesn't apply to nominal or ordinal data

Validity

if the measures we're using are measuring the thing we're supposed to be measuring(e.g. if a scale gives the same but incorrect measure every time then it is INvalid)

Reliability

the consistency of a measurement, that every time you measure something it comes back the same(regardless of its validity, example: if a scale gives the SAME but incorrect measure every time than it IS RELIABLE)

Nominal Data

-categorical

-dichotomous, categories are mutually exclusive

-refers to naming

-no math operations apply

-ex. gender, favorite color/flavor

-counts and percentages only

-can be numbers but must be from a choice not infinite or decimal points

Ordinal Data

-elements can be arranged in hierarchical order/rank

-data does not tell you the distance between values

-who finished first in a race

-position or rank in a distribution, first, second, third, fourth, fifth, etc.

Interval Ratio Data

-scale/continuous variables

-ex. weight, height, GPA, annual income

-intervals between each value are equal

-math operations can be carried out

-can be measured

-ratio variables have true 0 value, not celsius or Fahrenheit,

-interval variables have arbitrary 0 values.

Independent Variable

Determiner

Dependent Variable

What gets determined or undetermined

Experimental Research

Experiments where the Independent variable(not the sample we're studying) is manipulated and the subject isn't manipulated. Cause can be determined.

Post-Facto/Non-Experimental Research

Research where you can't draw causal conclusions. Variables cannot be controlled only measured.

Frequency Distribution

Where all the variables plot out and how often, the y-axis is ALWAYS the frequency and the x-axis is ALWAYS the variable in question

Mean

The average(measure of central tendency)

Mode

Most frequently occuring value (measure of central tendency)

Median

Center score, equal number below or above of scores (measure of central tendency)

Distributional Skew

Which side of the chart the data clusters at(not where the mode is at)

What's a negative skew?

-If the mean(average) is less than the median.

-When the tail is skewed to the left/low side

-goes from mean, median, mode

What's a positive skew?

-If the mean is greater than the median

-When the tail is skewed to the right/high side

-goes from mode, median, mean

Standard Deviation (SD)

-average distance from the mean in a set of scores

-it is the square root of the sum of x minus m squared divided by N

-Interval Ratio data only

-if the average distance from the mean is small, you have small variability and vice versa

-can never be > 1/2 range

-a big range does not always indicate a big SD

Leptokurtic

If SD<1/6 of the range (tall)

Mesokurtic

If SD=1/6 of the range (normal)

Platykurtic

If SD>1/6 of the range (flat)

Variability

How much random variation is there in the data that is not due to the independent variable

Range

Maximum-the minimum (1-5million dollars a year)

Variance

SD squared, interval ratio data only

Normal Distribution

Symmetrical,

Mean Median and Mode are all equal

Only ONE mode

No skewness

No kurtosis

Areas under curve are invariant(unchanging) and we ALWAYS KNOW what percentage of the scores lie above or below a given SD (in frequency distribution its a percent)

Parameter

numbers that summarize data for an entire population

Statistic

numbers that summarize data from a sample

Alpha level 0.5

+/- 1.96; 95%

Alpha level 0.1

+/- 2.58; 99%

When we reject the null hypothesis

we determine that the null hypothesis is unlikely to be true

Type 1 error

recurs when we reject the null hypothesis when it was in fact true, at alpha .05 the probability we were wrong is 5% and alpha .01 is 1%

When alpha is .05, we have a 5% probability of incorrectly rejecting H0:

i.e., saying there is an effect when in fact there is not . In statistical notation that μ sample = μ .

Type 2 error

recurs when we fail to reject the null hypothesis when in fact we should've rejected the null

When alpha is .05, we have a 95% probability of incorrectly failing to reject H0:

i.e., saying there is NO effect when in fact there is one . In statistical notation that μ sample ≠ μ .

SAMPLING DISTRIBUTION OF THE MEAN

A frequency distribution of an infinite number of sample means of size N taken at random (sampling with replacement) from a population.

-It is a normal distribution (even when the population from which these means are drawn is NOT normal)

-Its mean is equal to µ (the population mean) from which these samples were drawn

-It has a standard deviation, known as the STANDARD ERROR OF THE MEAN, which is equal to σ (the population standard deviation) divided by √N

-The SAMPLING DISTRIBUTION OF THE MEAN is the basis for the Z-test and the Single-Sample t-test.

SAMPLING DISTRIBUTION OF THE DIFFERENCE

A frequency distribution of an infinite number of differences between pairs of sample means taken at random (sampling with replacement) from the same population.

-It is a normal distribution

-Its mean is equal to 0

-It has a standard deviation, known as the STANDARD ERROR OF THE DIFFERENCE, which we must estimate because we would need σM (the standard deviation of all the sample means taken from the population) to calculate its actual value.

-The SAMPLING DISTRIBUTION OF THE DIFFERENCE is the basis for the INDEPENDENT SAMPLES t-test.

z score

how far you are from the mean

-based on the sampling distribution of the mean

-use when you have the population SD and mean

Standard error of the mean

the standard deviation of the sampling distribution of the mean

-SD will grow/shrink depending on your sample size

t statistic

estimate of the standard error of the mean

Population mean=

μ

Sample mean=

M

Sample size=

N

Standards deviation of the entire population=

σ

Standard deviation of sample

SD

Null Hypothesis

Ho

degrees of freedom

how many values in the set are free to vary

Which of the following, if any, are characteristics of the normal distribution?

-Its mean, median, and mode are all equal

-Its form is mesokurtic (the SD = 1/6 of the range)

-The areas under the curve are fixed (e.g., 68.26% of the area lies between +1 and -1 SD of the mean)

The average variation from the mean in a set of measurements in a sample is the conceptual definition of the

standard deviation

Given a data set with a standard deviation of 7 and a range of 60, you should conclude that the distribution is

leptokurtic

Which of the following is FALSE with respect to the standard deviation?

It can never be 0

In a sample of high school runners' times in the 1600 meters, the mode was 4:50, the mean was 4:35, and the median was 4:42. What can we say about the distribution?

It's negatively skewed

In estimating the standard error of the mean, we use the sample SD, but then divide it by the square root of N-1 instead of N. Why?

The sample SD is a biased estimate, consistently underestimating the population SD

With respect to z-scores, for any sample the mean is always ___ and the SD is always

0; 1

With respect to the "sampling distribution of the mean,"

-the mean, median, and mode must all be equal to the population mean

-the distribution of the means must be normal, even if the actual population distribution from which the samples are taken is not

The sampling distribution of the mean has a standard deviation referred to as the

the standard error of the mean

When you know the population mean, but the population standard deviation is unknown, and you want to determine if a sample mean is "significantly different" from the population mean, you should use a(n)

single-sample t-test

Inferential statistics are referred to as 'inferential' because they are used to draw conclusions about ___ from ___.

populations; samples

When doing a t-test, our obtained t-value must ________ the critical value in the table (for the designated degrees of freedom) in order to _________ the null hypothesis.

be equal to or greater than; reject

The null hypothesis for the single-sample t-test is that any difference between the sample mean and the population mean is due to

-chance

-random variation

-sampling error

The t-test or the z-test can be used if the dependent variable is nominal.

false

If a researcher asks subjects to identify their sexual orientation as either heterosexual, homosexual, or bisexual, sexual orientation is being measured on an ordinal level.

false

Only if the researcher manipulates an independent variable can a study be considered an experiment.

true

In experimental research, the dependent variable represents the cause, and the independent variable represents the effect

false

All symmetrical frequency distributions have only one mode.

false

In a single-sample t-test, as the sample SD increases, the size of the obtained t-value ____, making it ______ likely to reject the null hypothesis.

decreases; less

If we were to create a frequency distribution of differences between pairs of sample means taken from the same population, which of the following would be FALSE about that distribution

the mean of the distribution would be equal to the population mean

In an independent samples t-test, the obtained (i.e., the calculated) value of t represents

how far the mean difference is from 0 in standard errors of the difference

If we wanted to determine whether a sample of male and female voters differed in their preference for a particular candidate (i.e., for which one would they vote), we would use the

chi-square test

In an independent samples t-test, the difference between the two sample means can be due to

the independent variable

sampling error

The size of the chi-square statistic depends on

the differences between frequency observed and frequency expected by chance in each cell

Using an alpha of .01 instead of .05

will decrease the effect size statistic

In any t-test what influences whether or not we reject the null?

the size of the difference between means

the sample size

the sample SD

Degrees of freedom in a chi-square test is determined by

the number of rows and columns in the design

The obtained value of any inferential statistic must be ____________ the critical value in order to __________.

greater than; reject the null

Why can we never base conclusions solely on the size of a mean difference or differences in frequences?

because such differences can come about by sampling error no matter how large they are

The phrase "statistically significant" means that

.the obtained result is unlikely to have come about by chance

We can only use the z-test when we are comparing a sample mean to a known population mean and

.we have the population standard deviation

In any t-test, if the SD ________ our probability of rejecting the null hypothesis _________

.decreases; increases

When we ______ the null hypothesis we are concluding that any difference between mean or between frequencies__________

.fail to reject; is probably due to sampling error

When an independent variable is actively manipulated, the research method must be experimental.

true

If a researcher uses the post-facto method and establishes a significant relationship, the possibility of a cause and effect relationship must be ruled out.

False. as in the post facto method the independent variables are assigned first or depending on it the categories are made with causes the records to depend on the category to which a result is assigned and hence be the results are dependent on the "cause" that is the independent variable or the category.

If a researcher establishes a unidirectional relationship, the research method used must have been experimental.

True

if a researcher establishes a significant correlation in order to predict college grades on the basis of high school grades, the high school grades are the independent variable.

True

The main purpose of the various experimental designs is to establish equivalent groups of subjects.

True

In experimental research, the independent variable always defines the differences in the conditions to which the subjects are exposed.

true

A study designed to test the effect of economic inflation on personal income should establish personal income as the dependent variable.

true, as in the experiment income is the dependent variable since it depends on economic inflation at that situation and changes with change in economic inflation.

In correlational research, the independent variable is always manipulated.

FALSE since in correlation research we are usually concerned with linear correlation where the independent variable cannot be actively manipulated since then it would include different situations due to change in independent variable.

Correlational research must always be post-facto research.

True

Meta-analysis attempts to combine many research studies and establish an overall effect size for the entire group of studies.

true

A one group, repeated measures design often runs the risk of falling prey to the hawthorne effect.

true

determining whether the IV is manipulated or assigned indicates where the research is experimental or post facto.

true

In the quasi experiment, the IV is always an actively manipulated variable.

true

Indicate which scale of measurement- nominal, ordinal, or interval: the phone company announces that area code 617 serves 2 million customers.

Nominal

Indicate which scale of measurement- nominal, ordinal, or interval: Insurance company statistics indicate that the average weight for adult males in the United States is 168 pounds.

Interval/ratio

Indicate which scale of measurement- nominal, ordinal, or interval: post office records show that 2201 persons have the zip code 01118.

Nominal

Indicate which scale of measurement- nominal, ordinal, or interval: The boston marathon committee announces individual names with their order of finish for the first 300 runners to cross the finish line.

Ordinal

Indicate which scale of measurement- nominal, ordinal, or interval: Central high school publishes the names and SAT scores for the students selected as National Merit Scholars.

Interval/ratio

Indicate which scale of measurement- nominal, ordinal, or interval: In one county correctional facility, it was found that of the 3500 inmates released three years previously, a total of 1500 had recidivated, where as 2000 had not.

Nominal

when finding the median, it makes no difference whether one starts counting from the top or the bottom of the distribution scores

true

the mean is influenced more than the median by a few extreme scores at one end of the distribution

true

In a positively skewed distribution, the mean lies to the left of the median

false