Exam 3 Flashcards
What are the Assumptions for Parametric Tests
- Interval or Ratio Data
- Population follows Normal Distribution Curve
- Homogeneity of variance in the population
- Numerical score for each individual
When to use Parametric Test?
= Normal Distribution
- Interval/Ratio scale data
- Sample size 30 or more
What are the Assumptions for Non-Parametric Tests
- Nominal or Ordinal Data
- Not normally distributed
What does the P Value mean
- Probability that the result would occur if H0(null hypothesis)were true
- Probability of a Type 1 Error.
What are the P Value cut offs (Alphas)?
.005, .01. .05, .10, .25
.05 and .01 most common
What is a Parametric Test?
Ordinary hypothesis testing procedure that requires assumptions about the shape or other population parameters.
What are Degrees of Freedom?
(df) the number of scores in a sample that are free to vary
- an honesty factor when comparing samples to population
(generalizing a sample to population we lose some power due to sample size.)
How do we calculate Degrees of Freedom (df)?
- df for Pearson’s correlation (n-2)
- df for Goodness of Fit Test: k(number of categories) - 1
- df for Test of Independence: df = (k-1)(k-1) one k for row, one k for column
What is the Correlation Method?
The technique where two or more variables are measured and naturally occurring relationship between them is accessed.
What are the Characteristics of a correlational Relationship?
Direction: negative or positive, indicated by the + or - sign of the correlation coefficient
Shape/Form: linear is most common
Magnitude/Strength: between two variables varies from 0 to +/- 1
Correlation is not a ___________
proportion
Squared Correlation (r2) is defined as what?
Coefficient of Determination
What are the Assumption of Correlation Method
- Causality: the assumption that a correlation indicates a causal relationship between the two variables.
- Directionality: inference based on direction of a causal relationship between two variables.
- Correlation ‘describes’ a relationship but does NOT demonstrate causation.
What is the Experimental Method?
A research technique that establishes the causal relationship between an IV (x) and a DV (y) by randomly assigning participants to experimental groups characterized by differing levels of x, and measuring the average behavior y that results in each group.
The experimental method is the only method that allows a research to establish a ________ ___ _______ relationship.
cause and effect
- the researcher has full control of the experimental environment.
What is the strength of the experimental method?
it isolates the relationship between the independent and dependent variable.
What are concerns with Correlational Method?
there might be other influences on the variables (third variable) that make it hard to measure how strong the relationship between the two is.
What conclusions can be made from the Correlational Method?
Predictions about the likelihood of two variables occurring together.
What conclusions can be made from the Experimental Method?
- Experiments are generally the most precise studies
- have the most conclusive power.
- effective in supporting hypothesis about cause and effect
What are the components (numerator, both pieces of the denominator) of the Pearson’s r equation?
numerator: co-variability of X and y
denominator: variability of X and Y seperately
What information do we gain from r?
r(for a sample), is an estimate of a population coefficient of correlation.
How do we interpret the r?
a measure of the strength and direction of the linear relationship between two variables that is defined as the ‘sample’ co-variance of the variables divide by the product of their (sample) standard deviations.
Can we conclude there is a cause and effect relationship based on a correlation?
NO
What is the r2 and why do we use it?
- Coefficient of Determination
- Measures the proportion of variability in the data explained by the relationship between X and Y.
Example: r2 = 0.64 (or 64%) of the variability in the Y scores can be predicted from the relationship with X.
What are the different types of correlations and when are they used?
- Pearson’s r: interval or ratio variables
- Spearman’s rho (r): at least 1 ordinal variable
- Point-biserial: 1 dichotomous, 1 interval/ratio
- Phi (f) coefficient: dichotomous variables.
What is the Third Variable Problem?
A correlation between two variables being dependent on another third variable.
What are the Correlation Concepts
- Relationship between two variables
- Ratio of change in one variable with respect to another
- Can be positive, negative, none or curvilinear
What are indicators ofSignificance of Correlations
- Obtained correlation must exceed the magnitude/strength of the critical value
- Computing r alone, only provides a measure of strength
- Significance takes into account strength AND number of participants in study.
What are the three Correlation Magnitudes/strengths and Directions/powers
Strong: ±.70 – 1.00
Moderate: ±.30 –.69
Weak: ±.00 –.29
What do the components of the chi-square equation indicate?
- χ2 is the lower-case Greek letter Chi
- O is the Observed Frequency
- E is the Expected Frequency
Describe the components of the Chi-Square Formula
The sum of the squared difference between observed and expected frequencies, divided by the expected frequency.
= (O - E)2 / E
Why and how do we calculate Effect Size with Phi Coefficient?
For a 2x2 matrix, the phi coefficient (Φ) measures the strength .(effect size) of the relationship
square root of x2/N
What are the two ‘ways’ to calculate Effect Size?
- Phi Coefficient
- Cramer’s V
Why and how do we calculate Effect Size with Cramer’s V
- For a Larger Matrix, the Cramer’s V measures the strength (effect size) of the relationship
Note: with Cramer’s V, the df* is the smaller of the rows or columns (k - 1)
square root of x2/(N)(df smaller)
What are the three Phi Coefficient Effect Size Interpretations for x2. “Magnitude and Power}
.10 – .29 Small effect
.30 – .49 Medium effect
.50 or greater Large effect
How do we report Chi-Square Statistic in APA format?
x2 (df, N = sample_size) = obt_value, significance.
Why do we use Goodness of Fit (one nominal variable):
- Uses sample data to test hypotheses about the same or proportions of a population distribution
- Tests the fit of the proportions in the obtained sample with the hypothesized proportions of the population
What are the Goodness of Fit Assumptions
- Individual are classified in each category (grades, exercise frequency)
- Observed frequency is tabulated for each measurement category(classification)
- Each individual is counted in only one category) no overlap.
When do we use a Chi-Square Goodness of Fit Test?
- Used to see how well an Observed Frequency distribution fits an expected (or predicted) frequency distribution.
- Non-parametric data
- Data distribution does not follow the normal curve
- Subjects do not have two scores within the same study (repeated measures)
- Data must be a categorical/nominal variable (or transformed into nominal data)
Why use a Test of Independence?
- Tests for evidence of a relationship between two variables
- two nominal variables/each with several categories)
- Each individual jointly classified on each variable(male - tall)
- Counts are presented in the cells of a matrix
- Design may be experimental or non- experimental
- Frequency data is used to test for relationship between the two variables using a two-dimensional frequency matrix.
What does a Test of Independence Null hypothesis mean?
the two variables are independent (no relationship)
What are the two versions of the Test of Independence?
- Single Population: no relationship between two variables in this population
- Two Separate Populations: no ‘difference’ between the distribution of variables in the two populations.
Reasons you would use a Test of Independence?
- Non-parametric data
Data is not interval or ratio-scaled - Data distribution does not follow the normal curve
- People cannot have two scores within the same study (repeated measures)
- There are two nominal variables, each with several categories
= Too see whether paired observations on two variables are independent of (different population), or have a relationship to (same population), each other.
What is the meaning of Expected Frequency
- Expected frequencies are based on the null hypothesis (H0) prediction of the same ‘proportions’ in each category(population)
- Expected frequency of any cell is jointly determined by its column proportions and it’s row proportion.
- Computing Expected Frequencies
E = (Column total)(Row total) \ N total
What is the meaning of Observed Frequency
Frequencies in the sample are ‘observed’ frequencies for the test
When do we use a Cramer’s V or Phi?
- Cramer’s V: Larger than a 2x2 Matrix
- Phi: 2x2 Matrix
If the calculated chi-square value is greater than or equal to the critical chi-square value (from table), what do we do?
Reject the null hypothesis.
If I increase the categories what happens to the critical value?
Critical value goes up
What are the components of the line of best fit?
- Regression is a method of finding an equation describing the best-fitting line for a set of data
- Both variables are measured at the interval level (interval data)
- Data must be from a random sample
- Normal data distribution (or have a large sample)
- How to define a “best fitting” straight line when there are many possible straight lines?
- The answer: A line that is the best fit for the actual data that minimizes prediction errors
Why do we use regression?
• The goal for regression is to find the best-fitting straight line for a set of data. For every X value
in the data, the linear equation determines Y values on the line.
What information do we know and what information are we trying to predict with a Regression Line?
- If we know the equation of the regression line, we can predict values of criterion variable Y, so long as we know X: Ŷ = bX+a
- The regression procedure produces a line that minimizes total squared error of prediction
- This method is called the least-squared-error solution
- The purpose of regression equation makes a prediction of a value Y from value X
- Precision of the estimate is measured by the standard error of estimate (SEoE)
- In regression, predicting Y from X also involves error for the same reason as we found in our z-test
- Residual: The amount of error we make in predicting Y from X
How is Standard Error of Estimate related to correlation?
The relationship between correlation and SEoE:
As the correlation becomes stronger (as r goes from 0 to ±1) SEoE decreases to 0 because there is less error variability in the data
What is basic APA FONT/Margin formatting?
Times Roman font
12 point size
1 inch margins all around
What are aspects of an APA Reference page?
Begins on new page after end of Main Body
- References centered at top of page
- Double-spaced, using hanging indent, alphabetically
- Only references cited within text should be listed
What goes in an APA formatted Abstract page?
Identify your purpose Explain the study Explain your methods Describe your results Conclusion Keywords
When do we use a Wilcoxon Rank-Order Test?
- Non-parametric (define) data
- Data is not interval or ratio-scaled
- Data distribution does not follow the normal curve
- You want to know if two groups (such as an experimental group and a control group) differ from each other
What are Assumption of the Wilcoxon Rank-Order Test?
- Data must be converted to ranked (ordinal data) before conducting the test
- Data distribution does not follow the normal curve
- Observations are independent
- Compares medians (Md) rather than means
- Null hypothesis is that the two populations have the same median
What are the steps to transform the data for a Wilcoxon Rank-Order Test?
- Transform the scores to ranks (lowest score is rank is 1…)
- When two scores are tied, both ‘ranks’ become the average of the two scores
(2+3)/2 = 2.5 use 2.5 for the rank for both scores. - Add up total ranks in the group that you expect or hypothesize that have a lower score, then compare that total to Critical Values for W table(?).
- How to check that you ranked the scores correctly:
- (n1+n2) = Total both groups
- N(N+1)/2 = Sum of ranks
- Both should match
What are we looking for with a Wilcoxon Rank-Order Test?
You want to know if two groups (such as an experimental group and a control group) differ from each other, but have nonparametric data.
Using the Wilcoxon Rank-Order Test, do you want it to be greater than or less than the critical value?
You want less than critical value
Why do you use Power when planning a study?
To help you decide how many participants you need
Important to understand power when you read a researcher article and want to make sense of how practical are the results.
What is beta and what type of error is it?
Beta = probability of a Type II error
Beta (β)
How is Power related to beta?
• Power: the probability correctly rejecting the null hypothesis (when the null hypothesis isn’t
true)
- Type II error (b): the probability of failing to rejecting the null hypothesis (when the null hypothesis is not true)
- B; beta (B), since power is 1-b
What happens to Power as you increase effect size, sample size or power itself?
- As effect size increases, power increases
- As sample size increases, power increases
- As power increases, beta decreases
- One-tailed tests have a less stringent critical value than two-tailed tests, using a one-tailed test increases power
What are 2 problems with Power?
If your n is too small, you will increase your chances of making a type 1 error
If your n is too big, you may find statistically significant results, but they may not be practically important
How do we Decrease Power?
Reducing alpha level(making the test more stringent) reduces power
- Using two-tailed (non-directional) reduces power
When to calculate Power?
A priori = before you run the analysis
Post hoc = after you run the analysis
When to use a z-Test?
- Parametric Data
- Normal Distribution
- Interval Data
- When there is large enough sample size (at least 30)
- Standard deviation is known
- Random sampling
Variance:
If there is large shift in data, there is a ___ of variance.
A little shift, _____ variance.
No shift, ____ variance.
Every change in X has a corresponding change in __..
lot
small
no
Y
What does Restricted Range mean?
A variable that is truncated and has limited variability, looks like a distorted variable. Can give false impressions
What are 3 Chi-Square Concepts?
- Can have fractions or percentages (multiply by totals)
- Each observed frequency is generated by a different individual
- Should not be performed with an ‘n’ less than 5
What is the table called that is used with Test of Independence?
Contingency table (or Matrix) - a table in which the distribution of two nominal variables are set up so that you have combined observed frequencies and expected frequencies as well as the row and column totals.
Regression:
X is to Y as _______ is to __________
Predictor, Criterion
What is the regression formula?
Ŷ = bX+a
What is Inter-rater Reliability?
The degree of agreement among raters. It gives a score of how much homogeneity, or consensus, there is in the ratings given by judges.
How is Inter-rater Reliability calculated?
Number of agreements(yes or no) / total number of samples
What is Restricted Range?
Whenever a sample has a restricted range of scores, the correlation will be reduced.
Researchers found a negative correlation between hours spent playing fantasy football and number of dates.
What does that mean?
The more you play fantasy football the less dates you go on
What is the APA stat for a pearson’s r?
r (N – 2) = .value, p = .significance, r2 = .value
When would you use a point biserial correlation?
1 dichotomous and 1 Interval / Ratio
When do you use Spearman Rho’s?
When there is at least one ordinal value
When do you use Phi Coefficient?
When there are Two dichotomous variables
What is a Strong Correlation?
> .7
What are small and medium correlations(magnitude and number)?
Small = .00 - .29 Medium = .30 - .69
What is a strong correlation in psychology?
.50
What is the difference between Parametric and NonParametric tests?
With parametric you are making assumptions about the population parameters with nonparametric you are not assuming the population has any sort of distribution
What are Expected Frequencies?
The frequency value that is predicted from the proportions in the null hypothesis and the sample size (n).
The expected frequencies define an ideal, hypothetical sample distribution that would be obtained if the sample proportions were in perfect agreement with the proportions specified in the null hypothesis”
What are Observed Frequencies?
The number of individuals from the sample who are classified in a particular category.
Each individual is counted in one and only one category.
What does the Null Hypothesis state?
No Preference/Equal proportions or No Difference from a known population
What is the shape of Chi-Square distribution?
Positively skewed, what effects the distribution?
Chi-Square: Degree of f\Freedom, how do you calculate it?
K - 1
Do you determine effect size for goodness of fit?
NO
Whats the APA stat?
X2 (df, n = ) = #, p < .05
How is Regression related to Correlation?
You get Regression from Correlation
How is Regression and Correlation different?
Regression allows you to ‘predict’ a value
What are the ‘components’ of the Line of Best Fit?
Y = bX + a
a(y intercept)
b(slope)
Assume the equation for the line of best fit equals y=.3X+.5. If this line is for the positive relationship of ice cream sales (x) to temperature (y), what is the expected temperature if ice cream sales were 100?
30.5
.3 * 100 + .5 = 30.5
What are the assumptions for Regression?
Both variables are measured at the interval level (interval data)
■ Data must be from a random sample
■ Normal data distribution (or have a large sample)
What is the relationship between Correlation and Standard Error of the Estimate?
As the correlation gets closer to +/-1 the SEoE goes down.
The value you are predicting is more accurate
What is the difference between Goodness of Fit and Test for Independence?
Test for Independence involves 2 Variables, Goodness of Fit involves just 1.
When do you use Cramer’s V?
When it is larger than 2X2, how do you find the df for the formula?
■ You use the smaller of the two df
When do you use the phi coefficient?
For 2x2 matrix
How do you determine the degrees of freedom for Test of Independence?
Df=(k-1)(k-1)
Why do you need to be concerned with power when planning a study?
Allows you to determine how many participants you will need.
When do you use a Wilcoxon rank-order test?
When you want to compare two groups but they are nonparametric data
What is the only test where you want your obtained value to be less than the critical value?
Wilcoxon rank-order test.
How is the Wilcoxon rant-order test similar to the z-test?
Raw scores are converted into ranked scores (aka interval/ratio data is transformed into ordinal data) and the medians (not means!) are compared
What happens to power as the effect size increases?
Power increases
What happens if you decrease sample size?
Power decreases
How does one vs. two tail test effect power?
Reducing alpha (making the test MORE stringent) decreases power, thus one-tail has more power
How is power related to type two error?
P= 1-β, “The power of a test is the probability that the test will correctly reject a false null hypothesis” therefor decreasing the risk of type 2 error increase the power
What is the Null Hypothesis?
■ the two variables are independent (no relationship exists)
