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Research skills and methodologies Quiz 3
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Terms in this set (63)
Define correlation
Denotes the association between 2 quantitative variables with the assumption that the association is linear, and is completely symmetrical i.e. the correlation between A and B is the same as the correlation between B and A
Define bivariate correlation
Appropriate for exploring the association between two variables, where neither is categorical.
Define (Pearson's) correlation coefficient
Refers to the measure (degree) of the correlation (association) being observed
What do correlation coefficients range from?
-1 through 0 to 1
What is the complete absence of a correlation is represented by?
0
What do correlations not require us to specify?
IV and DV
Advantage of non-parametric tests
Greater efficiency - they don't need as many participants to either accept or reject the hypothesis
What assumption do all inferential tests make?
They assume that the same is randomly sampled from the population
What are the 7 assumptions of Pearson's correlation coefficient (parametric)?
Both variable must be ratio/interval, linear association, association shows homoscedasticity, sample size greater than 100, no bivariate outliers, show bivariate normality (normal distribution), degrees of freedom should be N (sample size) 2
In a Pearson's correlation coefficient why should the sample size be greater than 100?
Because with smaller samples there is a risk that one or two extreme data points 'drive' the association
Define heteroscedasticity
When the variability of a variable is unequal across the range of value of a second variable that predicts (where the data points are NOT evenly distributed along the regression line)
Define homoscedasticity
Where the data points are evenly distributed along the regression line
Define degrees of freedom
The number of value which are free to vary
Define the correlation of determination
r squared (Pearson's correlation squared) - tells you how much of the variability of the dependent variable is explained by the independent variable(s)
Is a non-directional hypothesis one-tailed or two-tailed?
Two tailed
What type of hypothesis is one-tailed?
Directional hypothesis
What should you do to the p-value if the t-test is one-tailed?
Half the p-value
What do you do if you have a legitimate reason for believing that the association can only go in one direction?
You can specify a directional hypothesis in the study inception, apply a one-tailed test and halve the p value
What is the non-parametric equivalent to the Pearson's correlation coefficient?
Spearman's rho
When is Spearman's Rho used instead of Pearson's correlation coefficient?
Where one or both variables are ordinal or where both variables are ratio/interval, but the parametric assumptions have been violated/breached
What does Spearman's rho calculate?
It calculates the ranked scores for each variable and considers the association between the ranks
What what sample size is Spearman's rho appropriate?
When n (sample size) is at least 20 or more
What test can be used when data doesn't meet the parametric assumptions and the sample is less than 20 (n<20)
Kendall's tau
How do you evaluate how well a set of data fits a simple linear regression model?
Perform a statistical test regarding the slope of the theoretical regression line
What is a null hypothesis for simple linear regression?
The slope is zero; there is no relationship between the variables
What is an alternative hypothesis for simple linear regression?
The slope is not zero; there is a linear relationship between the variables.
What are the 3 general conditions for linear regression?
Both variables must be ratio/interval, the association between the variables must be linear, there should be no bivariate outliers
What are the 6 parametric assumptions for linear regression?
No discernible pattern, no outliers, normally distributed, mean of 0 at all values of x, errors should be independent of each other, errors should have constant variance
How are the parametric assumptions of linear regression checked?
By viewing the residuals (graph of residuals)
What is meant by residuals?
The difference between the predicted value of y and the actual value of y (for all cases) - an observable estimate of the unobservable statistical error
What is the regression equation?
y = a + b (x)
What is y in the regression equation?
y is the predicted value of y (dependent variable)
What is b in the regression equation?
b is the coefficient or slope of the line associated with x (independent variable)
What is a in the regression equation?
a is the value of y when x=0 (the y-intercept)
What is simple linear regression?
It gives more information about the relationship between the two variables and how we can use this for analysis and prediction
What is the coefficient of determination in simple linear regression?
The extent to which x is explained by y
SPPS gives the r squared and adjusted r squared value. Which should be interpreted in an exam?
Adjusted r squared
What is the standardised coefficient (beta) in simple linear regression?
Specifies the predicted effect on y if x increases by 1 SD
When is standardised coefficient (beta) useful?
In multiple regression (multiple IVs)
What are the similarities between regression and correlation?
Both investigate linear associations between ratio/interval variables, minimum sample of 100, random sample
What does ANOVA stand for?
Analysis of variance
What is ANOVA?
A parametric test used to test for differences (variance between and within conditions)
When is ANOVA used?
When we have more than two groups and/or more than one independent variables
What is an advantage of ANOVA?
It allows you to investigate the effect of multiple factors on your dependent variable at the same time
Why shouldn't you use several t-tests rather than an ANOVA?
Experiment wise error rate - by running multiple t-tests you increase the chance of making a type 1 error but ANOVA controls for these so the Type 1 error remains at 5%
What are the 4 assumptions for ANOVA?
DV must be interval/ratio data, normally distributed, homogeneity of variance, independent groups design
Define homogeneity of variance
The samples being drawn are drawn for populations with the same variance
Define between-groups variance
The variation (difference) between mean values in each condition
What 3 sources do between-group variance arise from?
Treatment effect, individual differences and random errors
What are treatment effects?
The effect of the independent variable
What are individual differences?
The natural variances in individuals (e.g. ability)
What are random errors?
Errors with no pattern, out of the blue, a fluke (e.g. participant's focus, motivation, weather, differences in time of day when testing)
Define within-group variance
The variation between people within the same group
What causes within-group variance?
Individual differences and random errors
According to the logic of ANOVA....
Subjects in different groups should have different times because they have been given different experimental conditions but subjects within the same group should have the same or similar times
What is meant by partitioning the variance?
The comparison of variance due to nuisance factors (error variance, individual differences) compared to variance due to our experimental manipulation
What is the F ratio in the ANOVA?
The ratio of variance due to our manipulation of the IV (between groups variance) and the error variance (within-groups variance)
How do you calculate the F-ratio?
between-groups variance / within-groups variance
What will the F-ratio be if the error variance is small compared to the variance due to manipulation?
Great than 1
What does a F-ratio of less than 1 indicate?
The effect of the IV isn't significant (the greater the F-ratio the better)
What is the P value in an ANOVA?
The probability of getting this F ratio by chance alone
What 3 things do you need to specify when describing an ANOVA?
How many factors involved in the design, how many levels in each factor, whether the factor(s) are within or between subjects
What are the 2 types of ANOVA?
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