STATS FINAL
Nonparamteric Tests
- Are inferential procedures used with either nominal or ordinal data - it is not normal distribution -Allow you to analyze data that violate the parametric assumptions; it uses data such as frequencies reported in categories, such as chi square
Correlation
- Correlation means relationship - Correlation does not mean causation - Range from -1 to +1
Chi square
- One sample chi square, also known as "goodness of fit", looks at only one categorical dimension - Two sample chi-square, also known as "test of independence", includes two variables/dimensions -We usually do independence test between two variables -Null: two variables are independent of each other -Alternative: two variables are not independent of each other -Expected frequency: fe= (cell's row total f0)(cell's column total f0) / N
Linear Regression
- The procedure for predicting unknown Y scores based on known correlated X scores *** X is the predictor variable Y is the criterion variable The symbol for predicted Y score is Y'
Multiple Regression Formula
--- Y1=b1X1+b2+X2+a Y1 = the value of the predicted score X1 = The value of the first independent variable X2 = The value of the second independent variable
For a two tail test for the mean, known:
1. Convert sample statistic to test statistic (z statistic) 2. Determine the critical z values for a specified level of significance α, from a table or computer 3. Decision rule: if the statistic falls in the rejection region, reject H0; otherwise do not reject H0 4. Smaller p-value = stronger evidence
Hypothesis Testing Steps-Using P value
1. Null and alternative hypothesis 2. Test statistic 3. P-value 4. Significance level (chosen) and interpretation
The 7 Steps of Correlation test
1. State clearly the null and alternative hypotheses 2. Choose an alpha α level and decide one or two tailed test 3. Choose the proper test 4. Compute the correlation statistic from the data, r distribution with df=n pairs-1 degrees of freedom 5. Find p value 6. If p < α Reject null hypothesis, rxy≄0 If p > α Retain null hypothesis 7. Make a conclusion
Independent Samples T Test STEPS
1. State clearly the null and alternative hypothesis 2. Choose an α level and decide one or two tailed test 3. Choose the proper t-test 4. Compute the test statistic t from the data t distribution with (nA-1)+(nB-1) degrees of freedom 5. Find p value 6. If p < α (alpha) Reject null hypothesis, mA≄mB If p > α: Retain null hypothesis, mA = mB
Dependent Sample T Test STEPS
1. State clearly the null and alternative hypothesis 2. Choose an α level and decide one or two tailed test 3. Choose the proper t-test 4. Compute the test statistic t from the data t distribution with df= n pairs-1 degrees of freedom 5. Find p value 6. If p < α (alpha) Reject null hypothesis, mA≄mB i.e., μD≄0 If p > α: Retain null hypothesis, mA = mD i.e., μD= 0
Hypothesis Testing With Simple Regression
1. State the regression model (equation) y=BX + a 2. State the pair of hypothesis - Hypothesis are used to describe population parameters. The slope for a population is denoted as B H0 B=0 H1 B≄0 *Will always be a two tailed test
Rejection Rule
1. When a sample's z-score lies beyond the critical value, reject the idea the sample represents the underlying raw score population reflected by the sampling distribution 2. When the z-score does not lie beyond the critical value, retain the idea the sample represents the underlying raw score population (i.e., the sample is similar to the sample)
Review Question: An important application of the chi square distribution is
All of the above alternatives are correct (goodness of fit and testing for independence of two variables )
Hypothesis Testing
Also called significance testing... Tests a claim about a parameter (using data in a sample)
Review Question: he probability of committing a type II error is denoted as
B (beta)
Level of Significance α
Defines the unlikely values of the sample statistic if the null hypothesis is true - Defines rejection region of the sampling distribution - Set at 5% or below - One tailed or two tailed test
Review Question: The chi square tests focus on frequencies. The row totals and column totals from a contingency table can be calculated from
Either the observed frequencies or the expected frequencies. The produce the same row totals
Review Question: In a dependent samples t-test,
Equal variances are assumed automatically
Review Question: A type 1 error is
Falsely claiming an effect when it actually does not exist
Dependent Sample T Test
Includes two samples *Two groups are matched in some way (pairs of twins are divided between two groups) *Typically the same people are in both groups (before and after design) ----- Ex: The North American Bacon Council tests if ------ participants change weight after 6 months of ------- an all bacon diet -----------IV: Diet (normal, all-bacon) -----------DV: Weight
Null Hypothesis
Is a claim of "no difference in the population"
Coefficient of Determination, r2
Is the portion of the total variation in the dependent variable that is explained by variation in the independent variable The coefficient of determination is also called r-squared and is denoted as r2
Review Question: Chi square test for independence assesses which of the following?
It assesses whether there is a significant difference between two categorical variables
P-Value
calculated probability, which is the probability of finding the observed results when the null hypothesis (H0) of a study question is true - Also called observed level of significance
Review Question: What type of data do you need for a chi-square test?
categorical
Review Question: Which of the following statistics is appropriate to test whether a company is biased against female job applicants in its hiring decisions?
chi square
Review Question: Which one of the following procedures is not a parametric statistical procedure?
chi square
Review Question: _______ are defined as samples selected from different populations where values from one population are not related or linked with values from another population
independent samples
Review Question: In the open classroom things are much less structured than in a traditional classroom and she believes that this might affect problem-solving skills. A researcher is interested to see how this has impacted on the kids problem-solving skills. Which type of statistical test should the researcher do?
independent samples t test
critical value
marks the point (inner edge of the region) of rejection - 1.96 is the critical value of z for a criterion of .05 in a two-tailed test
Review Question: A type 2 error
occurs when one accepts a null hypothesis that is actually false
sampling error
occurs when random chance produces a sample statistic not equal to the population
Review Question: in a situation where two samples have similar or equivalent variances it is appropriate to
pool the variances together
hypotheses are used to describe
population paramaters
sample
portion of the population
Review Question: The calculated chi-square values are always
positive
Review Question: When X and Y are moving in the same direction, then its relationship is most likely
positive
criterion
probability defining samples as unlikely to be representing the raw score population - For a criterion of .05, the area in each tail equals .025
region of rejection
range of values that leads the researcher to reject the null hypothesis
Regression
regression model: Y=BX + a *Y= dependent variable X= independent variable B= the slope
representative sample
sample in which the characteristics of the individuals and scores in the sample accurately reflect the characteristics of the individuals and scores in the population
Review Question: The alternative hypothesis...
states the relationship the researchers are interested in
Central Limit Theory
suggests that for a large sample, the sampling distribution is approximately normally distributed, regardless of the distribution of the population.
the degrees of freedom for chi square tests for independence are (r-1)(c-1) where r is number of rows and c is number of columns.
the degrees of freedom for chi square tests for independence are (r- 1)(c-1) where r is number of rows and c is number of columns.
Review Question: In the US legal system the presumption of innocence is analogous to
the null hypothesis
Review Question: The degrees of freedom for the chi-square goodness-of-fit test are
(c-1), where c is the number of columns or categories
Review Question: The degrees of freedom for the chi-square tests for independence test are
(r-1)(c-1), where r is the number of rows and c is the number of columns
Review Question: Consider the following linear regression prediction equation: Y = 12 + 3X. If X=7, what is the predicted value of Y for this observation?
33
Review Question: Two samples have df1=24 and df2=12. Equal variances are assumed. What is the df for the independent samples t-test
36.. ADD THEM TOGETHER
Review Question: Prediction equation: Y = 4 + (-4.2)X. Where the the regression line cross the y-axis?
4
Review Question: r2=40, what percent of the variation in the dependent variable is explained by the independent variable ?
40
Alternative Hypothesis
A claim of "there is a difference" so you can reject the null hypothesis... challenges the status quo... May or may not be proven * Generally the hypothesis that the researcher is trying to prove
Review Question: If the coefficient of determination is equal to 1, then the correlation coefficient
Can be either -1 or +1
Review Question: Independent samples t-tests _____
Contain different individuals in each sample
Review Question: Independent samples t-tests _________
Contain different individuals in each sample
Review Question: A pharmaceutical company wishes to put a drug on the market which they believe increases IQ. The population's IQ = 100. What would the hypothesis statement for H1 be?
Mu > 100
Independent samples t-test
Often interested in whether two groups have the same mean.. - Urban vs rural conditions - Young vs old * Comparison of two diff/separate populations *
Review Question: Regression modeling is a statistical framework for developing a mathematical equation that describes how
One response and one or more explanatory variables are related
linear regression equation
The equation that produces the value of Y' at each X and then defines the straight line that summarizes the relationship *** Yi = a0 + b1Xi ---- a0 is the estimated average value of Y when the value of X is zero -----b1 is the estimated change in the average value of U as a result of a one unit change in X -----a=intercept -----b(beta)=slope If the calculated P value is less than alpha, we reject H0 (null hypothesis) and conclude there is a significant difference
Review Question: x2=, the larger the calculated x2 means that
The greater discrepancies between the observed frequencies and the expected frequencies
Review Question: A small and insignificant x2 for the goodness-of-fit test means that
The observed frequencies are smaller than the expected frequencies
Review Question: Which of the following conditions must be met in order to conduct an independent samples t-test?
The samples must be selected from two non-overlapping populations
Review Question: If two variables, x and y, have a very strong linear relationship, then
There might not any causal relationship between x and y
Review Question: A non directional hypothesis test is also known as a
Two Tailed Test
Review Question: An organizational psychologist implemented new leadership training for store managers. The psychologist wants to test if the leadership training has made a difference in store managers' management style. This is an example of a...
Two tailed test (because of the word difference)
Review Question: A significant x2 for independence test mean that
Two variables are not independent
Z score tells you the probability of that score to occur
Z score tells you the probability of that score to occur
population
all possible values
if the coefficient of determination is .81 the correlation coefeccient could be either .9 or -.9
if the coefficient of determination is .81 the correlation coefeccient could be either .9 or -.9
Sampling Distributions of a Mean (SDM)
describes the distribution of a sampling mean
Review Question: To determine the degrees of freedom of two independent samples when equal variances are assumed we use _____.
df=(n1-1)+(n2-1)
Review Question: When a dependent sample study reports measurements before and after a treatment, the focus of the hypothesis t test is on the ___
differences
Review Question: When a dependent sample study reports measurements before and after treatment, the focus of the hypothesis test is on the...
differences
statistical inference
generalizing from a sample to a population with calculated degree of certainty