CR2030: DATA ANALYSIS FOR PSYCHOLOGISTS
Inferential statistics
Populations: a complete set of elements that possess some common characteristic defined by the
sampling criteria established by the researcher.
Samples: the selected elements chosen for participation in a study; ppl are referred to as ppts.
Data is described by distributions. Describes variations in the shape of the distribution of a set of
scores.
Variance/SD: variability of the scores around the mean.
Standard Normal Distribution: can be standardised so that it has a mean of 0 and SD= 1.
Inference: drawing logical conclusions from known data.
Null Hypothesis Significance Testing: when testing a statement of inference, it is split into two. Null
hypothesis (H0) and alternative hypothesis (H1). Null hypothesis is when the difference between
means = 0.
Sampling distribution: variability of a statistic over repeated sampling from specified population.
= Has a mean (0) and SD. Standard error is the SD of the sampling distribution.
P value = probability value.
The sampling distribution tells us that it is unlikely we get a difference of 6, if the means come from
samples from identical populations. 6/10000, probability = 0.0006. The null hypothesis is rejected and
alternative is accepted because it is below 0.05.
Usual level of significance is 0.05 (5%). This means that 5% is left for results to be left to chance.
The null hypothesis is rejected and alternative is accepted because it is 0.0006 is lower than 0.05
significance. It is rare to accept the alternative. We work under the idea of null because it is easier.
Central limit theorem: used to estimate the mean and standard error of the sampling distribution when
we are interested in testing hypotheses about the means.
A small p value only indicates that data are unusual under the assumption that the null hypothesis is
true (p<0.5). A Significant p-value only indicates that the effect (relationship, difference between
means) may not be zero in real life.
Effect size: size of the difference, or strength of an association.
Type one error: When null hypothesis is rejected when actually null is true. (There is no significance).
Only accept 5%
Type two error: When null hypothesis is accepted but actually it not null. (There is a significance).
Only accept 20%
Introduction to correlational techniques
Types of correlational studies: Survey research, Archival research.
Correlational research tests for relationships between variables. See if the observed relationship is
statistically significant.
, How to get correlation:
Variance: measures dispersion of the data. Average distance of the points from the mean.
Covariance: the degree to which two variables vary together. If x is positive and y is negative then
covariance is negative. Size of covariance is dependent on the scale (kg, cm, etc.) it uses, so it is
difficult to interpret which is why correlation is used to standardise it. Does it for two variants.
Correlation: covariance divided by the units of measurements for both variables gives a standardised
measure of the degree of relationship = correlation. Correlation will only be from -1 – 1. Closer to 1 =
stronger positive correlation.
Correlation provides information of the linear relationship between two variables.
The correlation coefficient is just a descriptive statistic. We need to test if it is statistically significant.
To test the significance of correlation, we first assume that X and Y are unrelated in the
population (the null hypothesis), and then look at how likely it is to observe the correlation we
have just observed if we WERE sampling from that population where correlation = 0.
We randomly sample from population with the correlation zero, we compute and record the
correlation coefficient for each sample. Using a t-test, we test the distribution. If the null hypothesis
(H0) is true then the mean of the distribution is around 0.
The t-test will provide the probability for rXY (correlation coefficient) to emerge from a population
with correlation zero.
• If this probability is too small, say p <.05, we have to reject the Null hypothesis
• We then conclude that the correlation is significantly different from 0.
Effect size: the correlation coefficient might be significant, but it may not be important. The effect
size for correlation:
- Small: +/- .1
- Medium: +/- .3
- Large: +/- .5
Reporting correlation: (APA style)
• “Weight was significantly and positively related to height, r(505)= .72; p < 0.001.”
(For correlation: -2 for degrees of freedom).
Regression and Multiple Regression
Regression: if variables are related to each other, it should be possible to predicted one of them from
the other. Regression is r. Shows the relationship between a dependent variable and an IV.
Simple regression: one predictor variable and one outcome variable
Multiple regression: more that one predictor variable and one outcome variable.
Line of best fit minimises discrepancies between observed values Y and predicted Y. A line should
that makes the distance between all points as small as possible. We need to know where the line starts
and how it gets steeper when becomes larger.
Observed Y is red dot and predicted y is the point on the regression line.
Ypred = B0 + B1X
B0= intercept and is the value which tells us where the line starts. It represents the mean of Y when
x=0.
Inferential statistics
Populations: a complete set of elements that possess some common characteristic defined by the
sampling criteria established by the researcher.
Samples: the selected elements chosen for participation in a study; ppl are referred to as ppts.
Data is described by distributions. Describes variations in the shape of the distribution of a set of
scores.
Variance/SD: variability of the scores around the mean.
Standard Normal Distribution: can be standardised so that it has a mean of 0 and SD= 1.
Inference: drawing logical conclusions from known data.
Null Hypothesis Significance Testing: when testing a statement of inference, it is split into two. Null
hypothesis (H0) and alternative hypothesis (H1). Null hypothesis is when the difference between
means = 0.
Sampling distribution: variability of a statistic over repeated sampling from specified population.
= Has a mean (0) and SD. Standard error is the SD of the sampling distribution.
P value = probability value.
The sampling distribution tells us that it is unlikely we get a difference of 6, if the means come from
samples from identical populations. 6/10000, probability = 0.0006. The null hypothesis is rejected and
alternative is accepted because it is below 0.05.
Usual level of significance is 0.05 (5%). This means that 5% is left for results to be left to chance.
The null hypothesis is rejected and alternative is accepted because it is 0.0006 is lower than 0.05
significance. It is rare to accept the alternative. We work under the idea of null because it is easier.
Central limit theorem: used to estimate the mean and standard error of the sampling distribution when
we are interested in testing hypotheses about the means.
A small p value only indicates that data are unusual under the assumption that the null hypothesis is
true (p<0.5). A Significant p-value only indicates that the effect (relationship, difference between
means) may not be zero in real life.
Effect size: size of the difference, or strength of an association.
Type one error: When null hypothesis is rejected when actually null is true. (There is no significance).
Only accept 5%
Type two error: When null hypothesis is accepted but actually it not null. (There is a significance).
Only accept 20%
Introduction to correlational techniques
Types of correlational studies: Survey research, Archival research.
Correlational research tests for relationships between variables. See if the observed relationship is
statistically significant.
, How to get correlation:
Variance: measures dispersion of the data. Average distance of the points from the mean.
Covariance: the degree to which two variables vary together. If x is positive and y is negative then
covariance is negative. Size of covariance is dependent on the scale (kg, cm, etc.) it uses, so it is
difficult to interpret which is why correlation is used to standardise it. Does it for two variants.
Correlation: covariance divided by the units of measurements for both variables gives a standardised
measure of the degree of relationship = correlation. Correlation will only be from -1 – 1. Closer to 1 =
stronger positive correlation.
Correlation provides information of the linear relationship between two variables.
The correlation coefficient is just a descriptive statistic. We need to test if it is statistically significant.
To test the significance of correlation, we first assume that X and Y are unrelated in the
population (the null hypothesis), and then look at how likely it is to observe the correlation we
have just observed if we WERE sampling from that population where correlation = 0.
We randomly sample from population with the correlation zero, we compute and record the
correlation coefficient for each sample. Using a t-test, we test the distribution. If the null hypothesis
(H0) is true then the mean of the distribution is around 0.
The t-test will provide the probability for rXY (correlation coefficient) to emerge from a population
with correlation zero.
• If this probability is too small, say p <.05, we have to reject the Null hypothesis
• We then conclude that the correlation is significantly different from 0.
Effect size: the correlation coefficient might be significant, but it may not be important. The effect
size for correlation:
- Small: +/- .1
- Medium: +/- .3
- Large: +/- .5
Reporting correlation: (APA style)
• “Weight was significantly and positively related to height, r(505)= .72; p < 0.001.”
(For correlation: -2 for degrees of freedom).
Regression and Multiple Regression
Regression: if variables are related to each other, it should be possible to predicted one of them from
the other. Regression is r. Shows the relationship between a dependent variable and an IV.
Simple regression: one predictor variable and one outcome variable
Multiple regression: more that one predictor variable and one outcome variable.
Line of best fit minimises discrepancies between observed values Y and predicted Y. A line should
that makes the distance between all points as small as possible. We need to know where the line starts
and how it gets steeper when becomes larger.
Observed Y is red dot and predicted y is the point on the regression line.
Ypred = B0 + B1X
B0= intercept and is the value which tells us where the line starts. It represents the mean of Y when
x=0.
