Statistical Methods Final-Homan

Hypotheses for hypothesis testing

-is a statement about a population not a sample -must be all inclusive-they cover all possible outcomes -must be mutually exclusive-only one hypothesis at a time can be true -the null hypothesis is a negative statement that makes a specific prediction (can't prove a negative statement only disprove it)

Central Limit Theorem

1. If N is large, then the sampling distribution of the mean will be normally distributed 2. If N is large, then the mean of the sampling distribution is the same as the mean of the population from which the samples were selected 3. If N is large, then a statistician can compute the standard error of the mean

6 Steps of Hypothesis Testing

1. Test 2. Assumptions 3. Hypothesis 4. Decision Rule 5.Calculation 6. Interpretation

What does a z score indicate?

A location. It is a raw score expressed in terms of how many standard deviations it is away from the mean

A scientist has conducted a one-sample experiment. What two parametric procedures are available to her? What is the deciding factor for selecting between them?

A single sample z-test and single sample t-test. The deciding factor is whether or not she knows the population standard deviation.

What does a measure of central tendency indicate?

A single value used to represent a typical score in a set of scores

Why is it better to perform a one-way ANOVA instead of multiple t-tests

ANOVA is needed to keep Type I error at a reasonable level. Error greatly increases with multiple t-tests.

Random Sample

All the cases in the population have an equal chance of being selected

If a significant F ratio is obtained, why is it necessary to do post hoc comparisons?

Because we don't know WHERE it is significant, only that it is

Why should F=1 if the data represent the null hypothesis?

If there is no treatment effect, then there is no variability due to treatment, there is only variability due to individual differences OVER variability due to individual differences which would equal 1. Same denominator and numerator

Why is effect size important?

It tells us how large the impact of the explanatory variable is on the outcome variable. Tells us if it is a real effect in the population

Type II Error

Occurs when the null hypothesis should be rejected, but isn't (something happened) probability is known as beta, commonly set at .20

What are the assumptions for the independent samples t-test?

Random samples, Independence of Observations, Normality, Homogeneity of variance

One-tailed test

Researcher has an expectation about the direction of the impact of the explanatory variable-predict the results will turn out in a certain direction-easier to reject the null hypothesis

When would you use a paired samples t test?

The cases selected for one sample are connected to/depend on the cases selected for another

Look at the formula for the one-sample t-test. In words, what is this statistic telling us?

The t-statistic forms a ratio.The top of the ratio contains the obtained difference between the sample mean and the hypothesized population mean. The bottom of the ratio is the standard error which measures how much difference is expected by chance. With a large sample, you can say that the t-statistic is an 'estimated z score'

Look at the formula for the independent-samples t test. In words, what is this statistic telling us?

The top of the ratio contains the obtained difference between the sample statistic and the hypothesized population parameter. The bottom of the ratio is the standard error which measures how much difference is expected by chance.

What is the mathematical definition of the variance? Mathematically, how is a sample's variance related to its standard deviation and vice versa?

The variance is the mean squared deviation score. Deviation scores represent the amount of distance a score falls from the mean. The sample standard deviation is the square root of the sample variance. The formula for sample variance includes the sum of the squared deviation scores.

When would you use an independent samples t-test?

Used to see if the average score in one population is better or worse than the average score in another population

When should you use a repeated measures ANOVA?

Used when comparing two or more dependent samples

Type I Error

When the researcher rejects the null hypothesis but shouldn't have (nothing happened) Routinely probability is set at .05 (alpha)

When would you use a one-way ANOVA?

When you have more than two groups to compare

Sampling Distribution

a frequency distribution generated by taking repeated, random samples from a population and generating some value, like a mean-used when population distribution looks flat, if sample size is large, a sampling distribution will create a normal distribution and z scores can then be used

Normal Distribution

a specific symmetrical distribution whose highest point occurs in the middle and whose frequencies decrease as the values on the x-axis move away from the midpoint

Mean

average-sum of all values in a data set divided by the number of cases-used with interval or ratio data

Why is the mean called the 'balance point of a distribution?'

because the sum of a set of deviation scores always equals zero. The mean balances the negative deviation scores on one side and the positive deviation scores on the other

hypothesis testing

data from a sample are used to evaluate a hypothesis about a population

Sampling Error

discrepancies, due to random factors, between sample statistic and a population parameter

Two-tailed test

doesn't indicate direction, only that there is an impact-allows researcher to test for an effect in either direction-typically the norm used more often than one tailed tests

Main effect

examine the overall impact of an explanatory variable by itself

Explain the logic of the F ratio. What are the sources of error in the numerator and the denominator?

f=( Variability due to treatment effect+ variability due to individual differences) OVER (variability due to individual differences) one way ANOVA calculates the ratio of between group variability to within group variability If there is no effect the F ratio will equal 1 As the effect of treatment grows, the numerator becomes larger than the denominator and the F ratio climbs above 1 As the F ratio increases, as it climbs higher than 1, the results are more likely to be statistically significant

What two aspects of the data determine which measure of central tendency to use?

level of measurement (nominal, ordinal, interval, or ratio) shape of the data (consider outliers, if data is skewed, or bimodal or multimodal)

Median

middle score-used with ordinal data-or when there is an outlier or data is skewed

Mode

most frequent score-used with nominal data and report multiple modes in bimodal data

Interaction

occurs if the impact of one explanatory variable on the dependent variable depends on the level of the other explanatory variable

Power

refers to the probability of rejecting the null hypothesis when it should be rejected. Want power to be as high as possible

On what two factors does the size of a z score depend?

standard deviation and raw score

Variability

summarizes how much variety exists in a set of scores

What is the advantage of a paired samples t test?

this design controls for individual differences-researcher can be more confident that any observed difference between the groups on the outcome variable is due to the explanatory variable and not a confounding variable.