Week 4- Overview of Inferential Statistics

T-Test

a statistical test used to evaluate the size and significance of the difference between two means - N is generally smaller (<30) and standard deviation is known

Null Hypothesis

a statement or idea that can be falsified, or proved wrong - researchers and statisticians type this, it states that there is no difference and is the opposite of the researcher's hypothesis.

If the researcher rejects the null hypothesis....

they are able to disprove the null hypothesis in favor of the alternative, then their study demonstrates sufficient evidence to disprove the null... so the results are in favor of the alternative hypothesis/ the researcher's hypothesis.

True or False: Researchers should beware of over-generalizations or claims of absolute truth?

True

Parameter

" any measure obtained by having measured a population" - example- mean IQ of all counseling students is a parameter

statistics

" is any measure obtained by having measures a sample"

Z Test: Standard error of the mean

"standard deviation of the sampling distribution"

Confidence Interval

- "An interval of a certain width, which we feel confident will contain the population mean" - Example: if we want to be 95% confident, we want a 95% confidence interval

What is Inferential statistics?

- Smith & Davis (2010), " procedures used to analyze data after an experiment is completed in order to determine whether the IV has a significant effect" - If research methods have been carried out and the research has worked to control confounding variables, then we can conclude with come degree that the outcomes of the study are due to the IV rather than change.

Sampling distribution

- distribution of sample means based on random samples of a fixed sized from a population"

Z-Test: Sampling Distribution

- distribution of sampling means based on random samples of a fixed size from a sampling distribution

What does inferential statistics allow the researcher to do?

- make inferences about the population based on sample - helps us avoid making over generalizations based on one experiences - allow researchers to access a set of tools that provide information about the probability that our conclusions are true

Z and T tests

- population parameters are often unknown,so in many cases, we need inferential statistics - both are parametric inferential statistical tests - both assume normality - assume some knowledge of parameters - For Z: we must known the population mean and std. deviation - For T: we must know the mean of the population

IN order to do a z-test we must know...

- some of population parameters

Sprinthall (2007) card analogy:

- you can bet on the probability that your opponent has an ace. If you have no aces, that is one thing, however, if you hold an ace, then the probability that your opponent has an ace decreases, the more aces you have, the better. - However, it's rare that you hold all four aces. - "in the game of predictive or inferential statistics, the statistician rarely if ever holds all four aces. Therefore every inference mush be couched in terms of probability."

Chi Square goodness of Fit

A nonparametric statistical technique used to compare expected verses observed outcomes. - used with nominal/ categorical or interval data - In SPSS- enter data, use the analyze feature, nonparametic drop down, Chi Square goodness of fit tests

Whenever a decision is made about the outcome in a study, it is communicated with respect to __________?

The null hypotheses

Inferential statistics...

allow up to make inferences about the population or about the many, based on the few/ or the sample.

Researchers should never accept the null hypothesis because...?

if the null hypothesis is true, then the researcher fails to reject it. Dallal (2007)- " null hypothesis are never accepted" We either reject them, or fail to reject them. The distinction between ' acceptance' and 'failure to reject' is best understood in terms of confidence intervals. Failing to reject a hypothesis means confidence internal contains a value of, ' no difference'. However, the data may also be consistent with differences of practical importance. Hence, failing to reject H. does not mean that we have shown that there is no difference."

Researchers often have a hypothesis they would like to prove, however ___________

it is easier to disprove a hypotheses using inferential statistics and very difficult to prove something.

all conclusions for hypotheses testing are said in reference to the ___________

null hypothesis

z-test

statistical test that lets us test the null for a sample when the population mean and variance and both known and provide evidence as to whether the sample represents the population - not used as frequently in the counseling literature as the t test.

Central Limit Theorem

the distribution of sample averages tends to be normal regardless of the shape of the process distribution - when a series of random samples are selected from a population, then those samples assume the shape of a normal curve.

Generalizability

the extent to which we can claim our findings inform us about a group larger than the one we studied

standard error of the mean

the standard deviation of a sampling distribution