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# PSCI2702

### Quantitative Research Methods

TermDefinition
Dependent Variable Effect/Result An individual’s level of health depends on his/ her social class (H1)
Independent Variable Cause An individual’s level of health depends on his/ her social class (H1)
Nominal Variables & their level of measurement Cannot quantify or even rank order the categories: Nominal data has no order. Cat. of varb. have to be: mutually exclusive, exhaustive or homogeneous Ex: Gender, Area code, province of residence, religion, party affiliation (No averages) --- Mode
Ordinal Variables Rank order categories! Example: Lower class, working class, middle class, upper class Limitations: Cannot calculate absolute difference or averages Mode and Median
Interval Ratio Variables Rank order! Calculate absolute differences Example: Age, number of children, income Mode, Median, Mean!
Measures of Central Tendency Mode, Median, Mean
What is the Mode? The value that occurs most frequently and is used for nominal variables.
What is the Median? Represents that exact center of a distribution of scores. Half and half (meet int he middle)! 1) Distinguish between even or odd cases! 2) Rank order 3) With odd you have one middle, with even take the two middle numbers and cal mean No nom.
What is the Mean? Add the score together and divide them by the number of cases!
How do you calculate the Standard Deviation? See notes!
Why do we need to convert original scores into Z scores? To find the percentage of the TOTAL AREA (or number of cases) above, below or between scores *Standardizing the normal curve
Finding total area below a positive score: What is the total number of students who scored less than 117? X= 117 X(bar)=100 S=15 Z=(117-100)/15=1.13 PAGE 505 Appendix A 1.13(z)0.3708 (column B)> 37.08% Total area= 50%+37.08%=87.08% Interpret! 87.08% OF THE 1000 STUDENTS WHO TOOK THE IQ TEST HAVE AN IQ THAT IS LOWER THAN 117
When finding the total area for Z scores, when to you use +50%? 1) Finding the area below a positive Z score 2) Finding the area above a negative z score
How do you calculate the Z score? Z=x-x(bar) divided by S X=your value X(bar)=your average S=Standard Deviation
What is estimation? *specify sample average and population estimate with 95% Estimate population values from statistics computed from samples Look at number of observations (N) and sample mean (second chart) Perdition for population average is between upper and lower bound
What does representative mean? It has to reproduce important characteristics of the population
EPSEM Equal Probability of Selection Method *We select a sample so that every element/case in the population has an equal probability of being selected Simple random sample Systematic sampling Stratified sample Cluster sampling
What does Hypothesis Testing 1 measure? Does the difference between the sample mean and population mean refectory real difference? Is this difference statistically significant or caused by random chance?
Example of Research(H1) and Null Hypothesis(H0) for Hypothesis Testing 1 Research Hypothesis: The mean sample of income if respondents who live an exciting life is significantly different than the average income of the overall American population. Null Hypothesis: is no different than the average income of overall A.pop
For Hypothesis Testing 1, what do you need to do, to run the test? 1)Select sample of respondents with IF CONDITION in SELECT CASES 2)Run One-sample T Test *Test value comes from estimation. Test variable is interval or ordinal variable
What is "Normal Distribution"? When the graph has a bell-shaped curve and half the cases are above the median and the other half are below the median.
Where do the frequencies cluster in a normal distribution curve? They cluster around the median (average).
In "Normal Distribution", what is the relationship between the mean, median and mode? Mean = Median = Mode
What is "Positively Skewed Distribution"? When the graph has a curve that declines rapidly towards the right. The curve is skewed because there are extreme cases on the right side of the spectrum. (i.e. wealth)
In "Positively Skewed Distribution", what is the relationship between the mean, median and mode? Mode < Median < Mean (correct measure of central tendency would be the median)
How can you normalize a positively skewed distribution to make it a normal distribution? Eliminate outliers/extreme cases from the data set.
What is "Negatively Skewed Distribution"? When the graph has a curve that declines rapidly towards the left. The curve is skewed because there are extreme cases on the left side of the graph (i.e. age)
In "Negatively Skewed Distribution", what is the relationship between the mean, median and mode? Mean < Median < Mode (correct measure of central tendency would be the median)
Why is the Mean not always the best measure of central tendency? The mean is not always the best measure of central tendency because it can become artificially inflated by outlier/extreme cases. The mean always moves towards the most extreme cases.
What is Standard Deviation? A measure of dispersion. It lets the researcher know how representative the sample actually is. It measures whether or not values cluster around the average.
Distributions with LOW standard Deviation... A. Cluster around the average B. Have scores that encompass the whole range of scores. A. Cluster around the average.
Distributions with HIGH standard Deviation... A. Cluster around the average B. Have scores that encompass the whole range of scores. B. Have scores that encompass the whole range of scores.
When does Standard Deviation increase? The Standard Deviation increases in value as the distribution becomes more valuable and decreases in value as the distribution becomes more similar.
Please identify the meaning of these symbols in the Standard Deviation Equation 1. S = ______________ 2. Xi = ______________ 3. ̅X = ______________ 4. N = ______________ 1. S = Standard Deviation 2. Xi = Scores 3. ̅X = Average 4. N = Number of Cases
In the Standard Deviation equation, what does (Xi - ̅X) measure? (Xi - ̅X) measures the scores distance from the mean.
What is the Z score equation Z = (Xi - ̅X)/ 2
What is the use of a Z score? To compare standardize different scores in order to compare them.
When using Appendix A to find the percentage for the Z score, when do you use Column B? When the score is POSITIVE, and BELOW the mean (Below+) OR When the score is NEGATIVE and ABOVE the mean (Above-) If it touches the mean line, use this column.
When using Appendix A to find the percentage for the Z score, when do you use Column c? When the score is POSITIVE and ABOVE the mean (Above+) OR When the score is NEGATIVE and BELOW the mean (Below-) If it does not touch the mean line, use this column.
Which test do you use in Hypothesis Testing One? One-sample test
What does the One-Sample Test deal with? It test significance levels and inferential statistics.
Define Significance Testing (Hypothesis Testing) Reveals the probability that a relationship between two variables reflects observed trends in the population
Does the One-Sample T test demand nominal variables? NO. It demands Interval and Ordinal.
Accept the null hypothesis when... the significance is HIGHER then 0.05
Reject the null hypothesis when... the significance is LOWER then 0.05
Why might a researcher recode variables? Recoding is used to collapse certain groups in order to create categories that have higher and more similar frequencies.
What is Hypothesis Testing II? Independent Sample T Test (Two sample case)
What does the Independent Sample T Test measure Significance of the difference between two separate populations.
What outputs are included in the Independent Sample T Test? Levene's Test for Equal Variance and T-Test for Equality of Means
What is the Levene's Test? This test helps the researcher to determine the correct T-Obtained score (to figure out which Sig-2 tailed to use).
How does a researcher determine which Sig 2-tailed to use in the Levene's Test? There are two outputs, one for variances assumed, one for variances not assumed. If the sig value is less then 0.05, use variances NOT assumed. If the sig value is more then 0.05, use variances assumed.
What is Hypothesis Testing III? ANOVA
What is ANOVA testing ANOVA (Analysis of variance) Testing can be used in situations where the researcher is interested in the difference in sample means across three or more categories.
What kind of variables should be used in ANOVA testing? Independent variables with more than two categories should be used in ANOVA testing.
How to input variables into SPSS for ANOVA testing Factor Box contains nominal or ordinal variable that distinguishes between populations. The Dependent List box contains the interval-ratio or ordinal variable for which the sample means are calculated.
What is SSW and SSB? SSW = sum of squares within (reflects the variance within the samples) SSB = sum of squares between (reflects the variance between the samples)
What is Hypothesis Testing IV? Chi-sqaured and Measures of Association
What is the Chi Square test? Chi Square Testing encompasses three kinds of MOA (Measures of Association) including Phi and Cramer's V in addition to the Lambda test.
What kind of variables should be used in Chi Square tests? Variables measured at the nominal level
What is measure of association it looks at the strength of the relationship between two variables.
What is Phi and Cramers V? These values represent how strong or weak a relationship is between variables.
In terms of Phi and Cramers V, what do the values represent? 0.0 - 0.10 = weak 0.11 - 0.30 = moderate 0.30 - 1.00 = strong
What is the Lambda test? The value represents the percentage of predicting errors. I.e. the researcher will make 7.9% fewer errors in predicting respondents opinions on allowing racists to teach (DV) on the basis of their race (IV) rather then w/out the latter.
Is the Lambda test symmetric or asymmetric? Asymmetric
What is Regression Analysis? Regression analysis allows a researcher to determine if there is a relationship between two variables, how strong it is and in which direction it goes.
What kind of graph is used in Regression Analysis? Scattergrams
What goes on the X and Y axis of the Regression Analysis graph? X axis = IV Y axis = DV
What is the regression line? It is a straight line generally in the centre of the cases on the scatter gram
What does the regression line represent? The regression line represents the general direction or trend of the data.
What can regression lines be used to predict? Regression lines can help predict the relationship between two variables.
What are "Coefficients of Determination"? Pearsons R and R sqaured.
What is Pearson's R? It is a correlation coefficient which captures the association between variables measured at the interval level.
What do the Pearson's R's values mean? (-0.3) to 0 or 0 to 0.30 = weak (-0.6) to (-.31) or 0.31 - 0.6 = moderate (-1) to (-6) or 0.6 - 1 = strong
What is R squared? it is a coefficient of determine which works with PRE to predict the dependent variables value. Basically tell you how much one's IV accounts for you DV happening.
What does PRE stand for? Proportional Reduction in Error
What is the equation for single regression? y = a + bx
What do the values in the regression equation stand for? A = Y intercept (starting point where RG crosses y axis and x is 0) B = Slope X = IV
What is multiple regression This is when there is more then one IV being tested. Basically, the equation represents a PARTIAL slope which means it accounts for a change in y for a unit while controlling the effects of the other IV's. Holding them constant.
What is a way to remedy the fact that IV's in multiple regression represent different units of measure? Use the Z scores (refereed to as beta weights)to standardize.
Created by: paigekirk