Inferential Statistics

Inferential Statistics

have the purpose of determining the probability of the occurrence of an experimental result observed from a sample given a specified set of conditions in the populations(s) from which the sample was taken

Steps to specify nature of occurrence in the population

Step 1: first we specify some conditions in the population

Step 2: then we do the study with a sample and obtain our sample result

Step 3: then we calculate the probability of getting this result from the sample if the conditions specified in the population are accurate

Hypothesis testing

• testing the probability of obtaining the observed sample result if the population characteristics of the variables are “such-and-so”

• hypothesis = a statement of expectation about the characteristics of, or the relationships between the variables in the population OR a formal statement of the expected relationship(s) between variables under specified conditions of observation

2 kinds of hypotheses

1. Null hypothesis

2. research hypothesis (alternative hypothesis)

these are mutually exclusive! if one is true, the other cannot be true

1. Null Hypothesis

• a formal statement of no relationship between the variables of interest in the population

2. Research hypothesis

• a formal statement that there is a relationship between the variables of interest in the population

• typically, this includes a description of the type of relationship also.

P-value

LEXICON: the probability of the occurrence of the observed data generated from a random sample taken from a population, given some specified relationship between the IV and the DV in the population from which the sample was taken.

TYPICALLY:

p-value = the probability of occurrence given that there is no relationship between the variables of interest (IV/DV) in the populations from which the samples were drawn (presumably, randomly)

p-values allow us to engage in hypothesis testing

Purpose of hypothesis testing

• to determine when to reject the assumption (hypothesis) that there is no relationship between the IV and DV in the population (when to reject the null)

• employs a set of guidelines to determine when to reject and when not to reject the null hypothesis

when do we reject the null?

• when the p-value is less than a pre-specified signified level

ALPHA

• pre-specified level of importance

• the value of alpha depends on the research context and on the particular type of inferential statistic you are using (mainly between 0.05 or .01

S

Statistically Significant

• we are referring to the p-value associated with the inferential statistic we have calculated for our data

LEXICON:

a statistically significant result is on that has a probability of less than alpha of occurring if the null hypothesis is true.

if the result is significant we reject the null hypothesis

Two types of mistakes when we engage in hypothesis testing

1. type I error

2. type II error

1. Type I error

an error made when you incorrectly reject the Null hypothesis. That is, you have rejected the Null when the Null is actually true. Alpha represents the probability of making a type I error

What does it mean to reject the null?

you are making the claim that the sample results you have observes are not likely to have come from a population in which the null hypothesis is true

T

Type II error

an error is made when you incorrectly accept the Null hypothesis. That is, you fail to reject the Null when the Null is actually false. Beta represents the probability of making a type II error.

what does fail to reject the null mean

• you are making the claim that the sample results you have observed are likely to have come from a population in which the Null hypothesis is true.

Type I error = alpha

• alpha is commonly chosen to be .05 or .01

type II error = beta

• inversely related to Type I error. The higher you set the alpha, the lower the beta will be

setting an alpha

Setting α = .05 as the dividing line between "significant" and "not significant" means that in the long run, over repeated analysis with independent samples, 5% of the time, a Type I error will be made. 

 

That is, in 5% of the times that you have rejected the null hypothesis when the null hypothesis was actually true.

 

Being conservative:

• you are reducing the risk of making a type I error, which in turn then leads to an increase in the risk of type II errors

Being liberal

• you would be increasing the risk of Type I error, which would decrease the risk of type II errors

level of significance

• the only factor that influences the risk of Type I errors

• type II errors are influenced by the level of significance and the sensitivity of the experiment

t-test

statistic used when we are interested in determining whether 2 groups or conditions (levels of IV) are significantly different from each other with respect to a specific variable (namely the DV)

Research results can be

1. significant

2. not significant

do not use any other words!! it is one of these two

Statistically significant

if the p-value associated with the ‘t’ that you have calculated from your sample data is less than or equal to alpha, you reject the Null hypothesis

Insignificant findings

1. there may be no “real” relationship between the variables in the population

2. there may be a “real” relationship between the variables in the population but our sample only weakly represents it and our statistical tools fail to detect it

3. there may be a “real” relationship between the variables in the population but our sample is not representative of the population and therefore has failed to yield evidence of it.