all quantitative

what is a correlational design

Testing associations of X and Y using a single group of participants (based on observations of what is going on - this naturally occurs)

• regression allows for predicitions to be made

how do we prove causation instead of just correlation

you need to manipulate variables to test for causation

what is covariance

how much the variables vary in relation to one another

what is variance

the average amount the data varies around the mean

what is the third variable problem

in correlation you can’t assume causality as there is likely a third variable effecting the outcome that isnt being measured

what is spurious correlations

there is no obvious link between variables but yet a strong correlation is present

e.g. naming your child olivia and how many potatoes grew in that year

What is pearsons r

• standard correlation coefficient

• continous and parametric

• in correlation DOF is N-2

what is R vs R squared

R = correlation coefficient = -1 to 1

R2 = how much the variance in one variable is explained by the variance in the other variable

• ranges from 0-1 (0 = there is no explanatory power, 1 is a perfect fit)

what are the non parametric tests

Spearmans Rho and Kendalls tau for correlation

• we don’t assume the data is normally distriubuted

how do correlational tests work for non parametric testing

• principle of ranking the data - e.g.the lowest score = 1

• a similar number of highs and lows between groups suggests dependent variable doesnt differ between groups

What is Spearmans Rho

• pearsons correlation test on ranked ordinal data (does not use raw data)

• stronger relationship than Kendals

• less sensitive to outliers than Pearsons

E.g. does a high score on X correlate with a high score on Y

What is Kendal’s tau

• better than Spearmans for small sample

• tied ranks e.g. is there agrrements between observation

E.g. does one judges scores for contestants correlate with the other judges scores

when in PHI used

• categorical → correlation between two categorical variables based on chi squared

• the chi squared tells us if there is a relationship then look for PHI for the correlation coefficient

• ranges from -1 to 1

• when both variables are binary (yes/no)

when is point biserial correlational

one categorical (binary) and one continious

looks the same as pearsons but sign doesnt tell us the direction

What is partial correlation

Measures the relationship but adjusting for the effect of the third variable (on both variables)

• on SPSS the bottom R value gives you the score when controlling for a third variable (e.g. time spent revising)

What is semi-partial correlation

Only applies to regression, remove the additional variance in one of our predictor variables

what is the difference between correlational research and experimental research

correlational = we observe naturally what is going on

experimental = we manipulate variables to test something

What is regression

• we make a model to predict the DV using the IV

What is the linear model of regression

Y = b1X + B0

• slope (gradient) = B1 → direction of the relationship

• Intercept = B0

how do you draw a line of best fit through regression slope

• each point will not sit perfectly on the line - this is the residual error

• some points are above some are below - these would cancel

• so we sqaure them then add → known as SSR (residual sum of squares)

We want a model with this value as low as possible

What is SST, SSR and SSM

SST (total sum of squares) = all the variation in your data, how much it is spread throughout the mean

SSR(residual/error) = variation your model fails to explain

SSM (model) = variation your model does explain → we want this number to be high

SST = SSM + SSR

What is R squared

SSM/SST → how good your model is overall at explaining the variation

what is the F statistic

is the model actually better than just guessing the mean

• large F which is sig. model explains more than no model

• ratio of how much mean variance can be explained by how much mean error

What are the assumptions of regression

• independence

• continous dependent variable / continous or categorical independent variable

• sample size

  • Liberal - 15 participants per predictor (stevens)

  • Conservative = N = 50 + 8m (ivs) (green)

• Linearity

• Outliers

• Multicollinearity

What is a univariate outlier

only present in one variable - one participant varies from the rest → can be seen in box plot/ stem and leaf diagram

what is a multivariant outlier

• result from the combinaion of two or more variables

  • e.g. they are in the same range as the others but their pattern varies

how to find out a multivariant outlier

• standerdised residuals, if it is +3 or -3 in the ANOVA spreadsheet on SPSS

• Cooks distance - how each individual influences the overall fit of the model → if it is greater than 1 we don’t want that

what is multicollinearity (VIF)

-exists if predictors are highly correleated

VIF - indicates a strong linear relationship → 0.8 and above but we want this less than 10

what is multiple regression

two or more predictor variables and one outcome variable (DV)

what are the two hypothesis driven ways to enter data into SPSS

Forced Entry (enter) - all the variables are entered at the same time → researcher does not decide the order

Hierarchical - predictors are entered based on previous research are entered first then we add the others

• good for testing a theory → bad becuase it relies on pre competence of research and researcher

What are the two data driven methods of entry in SPSS

stepwise

• we want to avoid this in psychology → only used in exploration research as SPSS will intepret any size difference as importanr

Forward

Backward

what does standerdised beta allow for

comparisions because they are both standard deviations

What is a population?

A population is the collection of units to which we want to generalise a set of findings or a statistical model.

What is a sample?

A sample is a smaller but hopefully more representative collection of units from a population used to determine truths about that population.

What is central tendency?

Central tendency is an indication of the typical scores in a sample and is an estimate of the middle point in the scores; examples include the mean, mode, and median.

What is sampling error and why does it occur?

Sampling error occurs because we are not testing all members of the target population, meaning we are likely to overestimate or underestimate the mean.

How does sample size affect sampling error?

The larger the sample, the more likely we are to measure the extremes of the values, which makes the sample mean more likely to be a good estimate of the population mean.

What is sample error?

Sample error is the difference between the population statistics and the sample statistics.

What is dispersion?

how much variation in a dataset which indicates how much variation there is in the sample.

• range, sum of squared error, variance and standard deviations

What is the sum of squared errors?

adding the total squared deviations from the mean to eliminate the issue of positive and negative deviations cancelling each other out.

How is variance calculated from the sum of squared errors?

Variance is calculated by dividing the sum of squared errors by the number of scores to account for the actual size of the sample.

What is the standard deviation?

The standard deviation is the square root of the variance, returning the measure to the original units.

• how much the data varies around the mean.

What is the standard error of the mean?

The standard error of the mean indicates how representative the sample is of the population.

What is a sampling distribution?

A sampling distribution is a hypothetical distribution created by selecting an infinite number of samples from a population, calculating a statistic for each sample, and plotting them as a histogram.

Why is a sampling distribution considered hypothetical?

A sampling distribution is hypothetical because we do not have access to the entire population and therefore cannot observe all possible samples.

How does sample size affect a sampling distribution?

Larger samples produce a smaller sampling error within the sampling distribution.

What is standard error?

Standard error refers to the standard deviation of a sampling distribution, specifically the standard deviation of all sample means.

What does standard error tell us about the sample mean?

Standard error tells us how good the sample mean is as a representation of the population mean.