Stats 4

Statistical Hypothesis Testing

A procedure that allows us to evaluate hypotheses about
population parameters based on sample statistics

Alpha

The level of probability at which the null hypothesis is rejected. It is customary to
set alpha at the .05, .01, or .001 level.

P-value

he probability associated with the obtained value of Z.

Steps in Hypothesis testing

(1) Making assumptions
(2) Stating the research and null hypotheses and selecting alpha
(3) Selecting the sampling distribution and specifying the test statistic
(4) Computing the test statistic
(5) Making a decision and interpreting the results

T statistic: definition- T statistic (obtained) -

The test statistic computed to test the null
hypothesis about a population mean when the population standard deviation is unknown
and is estimated using the sample standard deviation.. that we can obtain the Z statistics* when we know the population stand

T-Distribution

A family of curves, each determined by its degrees of freedom (df). It is
used when the population standard deviation is unknown and the standard error is
estimated from the sample standard deviation.

Degrees of Freedom

The number of scores that are free to vary in calculating a statistic.

5 STeps of t statistic testing

1) Making Assumptions 2) Stating the Research and the Null Hypotheses and Selecting Alpha 3) Selecting the Sampling Distribution and specifying the Test Statistic 4) Computing the Test Statistic 5) Making a Decision and Interpreting the Results

Assumptions of T statistic testing

1) A random sample is selected. 2) Because N>50, the assumption of normal population is not required. 3) The level of measurement of the variable income is interval ratio.
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One sample t-test

hypothesis testing with two sample follows the same structure as for one sample tests: the assumptions of the test are state, the research and null hypo are formulated and the alpha level selected, the sampling distribution and the test statistic are spec

Two sample t-test

The difference between one- and two- sample hypothesis test is the form taken by the research hypothesis and null hypothesis and also the sampling procedure. With a two sample case, we assume that the samples are independent of each other, the choice of s

Research hypothesis for one and two sample t test

look above! but one sample t test compares one signle population parameter and two compares two pop parameter. Research hypo (H1) is that the avg years of education for blacks is not equal to the avg years of eduation for Hispanic respondents.

Null hypothesis for one and two sample t-test

H0 for both sample t tests the, null hypo states that there are no differences between the two population means.

The sampling distribution of the difference between means

A theoretical probability
distribution that would be obtained by calculating all the possible mean differences
(Mean Sample 1 - Mean Sample 2) that would be obtained by drawing all the possible
independent random sample of size N1 and N2 from two populati

Chi Square test defintion and example

an inferential statistics technique designed to test
for significant relationships between two variables organized in a bivariate table. EX: the relationship betwen two variables (gender, man and woman, and first generation attending college)

statistical independence

the absence of association between two cross-tabulated
variables. The percentage distributions of the dependent variable within each category of
the independent variable are identical. When two variables are not associated, that is, an individual's score

expected frequencies

the absence of association between two cross-tabulated
variables. The percentage distributions of the dependent variable within each category of
the independent variable are identical.

observed frequencies

the cell frequencies actually observed in a bivariate table.

chi square obtained

the test statistic that summarizes the differences between the
observed (fo) and the expected (fe) frequencies in a bivariate table.
The chi-square statistic will tell us whether it is large enough to allow us to reject the null
hypothesis.

5 steps of chi square hypo testing

1) Assumptions 2) State the research and null hypothesis 3) Selecting the sampling distribution and specifying the test statistic 4) Computing the test statistic (chi-square test);
5) And making a decision and interpreting the results

assumptions of chi square

It assumes random sampling requirement satisfied. However, Chi-square requires no assumptions about the shape of the population distribution from which a sample is drawn. It can be applied to nominally or ordinally measured variables.

Research hypothesis statement for chi square test

H1: The two variables are related in the population. Gender and fear of walking alone at night are statistically dependent.

null hypo statement for chi square test

H0: There is no association between the two variables. Gender and fear of walking alone at night are statistically independent.

Analysis of Variance

An inferential statistics technique designed to test for significant relationship between two variables in two or more samples. similar to t test but extended for groups.

One Way Anova

When ANOVA procedure are applied to data with one dependent variable and one independent variable, it is called one way ANOVA. This is an analysis of variance procedure using one dependent and one independent variable. Is difference between sample means s

5 steps of ANOVA testing

1) Making Assumption 2) Stating the Research and Null hpo and Selecting Alpha 3) Selecting the Sampling Distribution and Specifying the Test Statistic 4) Computing the Test Statistic 5) Making a Decision and Interpreting the Results

Assumptions of ANOVA testing

1. Independent random samples are used.
2. The dependent variable is measured at the interval-ratio level. Some researchers, however, do apply ANOVA to ordinal level measurements. (True w caution)
3. The population is normally distributed.
4. The populati

Research hypo statement for ANOVA test

H1: At least one mean is different from the others.

Null hypo statement for ANOVA tst

H0: ?1 = ?2 = ?3 = ?4

the between group sum of squares

the sum of squared deviations between each sample mean to the overall mean score.

within group sum of squares

sum of squared deviations within each group, calculated between each individual score and the sample mean.

total sum of squares

The total variation in scores, calculated by sum of between-group and within group (SSB+SSW)

mean square between

Sum of squares between divided by its corresponding degrees of freedom.

mean square within

Sum of squares within divided by its corresponding degrees of freedom.

F statistic

Used in an analysis of variance, the F statistic represents the ratio of between-group variance to within-group variance.

F obtained

The test statistic computed by the ratio for between-group to within-group variance.

F critical

The F score associated with a particular alpha level and degrees of freedom. This F score marks the beginning of the region of rejection for our null hypothesis.