# Statistics

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• Created by: Shannon
• Created on: 28-12-15 18:23
What is a Hypothesis?
A statement expressing the expected or predicted relationship between two or more variables
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What is a variable?
Anything that varies and can be measured
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What are Independent Variables?
A proposed cause. A predictor variable. A manipulated variable
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What is a dependent variable?
The proposed effect. An outcome variable. Measured not manipulated
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What is a level of measurement?
The relationship between what is being measured and the label/numbers that represent it
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What does the level of measurement tell you?
What test to use and how to present the data
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What is Nominal?
Category/Qualitative - Yes/No
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Give examples of Nominal data
Gender, Colours
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What is the test for Nominal data?
Chi-square
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What are the graphs for Nominal data?
Bar charts and Pie charts
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What are binary variables?
Only two categories. e.g. Yes/No
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What is Scale?
Score/Numerical/Quatitative
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Give examples of scale data?
IQ Score, Height, Weight
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What is the test for Scale data?
Pearson's correlation
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What are the graphs for Scale data?
Histograms/boxplots
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What is ordinal data?
Ordered/ranked
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What is the difference between Interval and Ratio data?
Ratio has an absolute zero whereas Interval doesn't
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Example of interval data
Temperature
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Example of ratio data
Height, Weight, Age
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What are descriptive stats?
Describes a data set by summarising and simplifying it
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What do do descriptive stats show?
Trends and patterns in data
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What are frequency distributions?
Tells us how many times a score or category occurs within our sample
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How many central tendencies are there?
6
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What is the mode?
Score that occurs more frequently
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What is bimodal distribution?
Two modes
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What is multimodal distribution
More than two modes
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How is the mode shown in a histogram?
Tallest bar
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What is the median?
The middle score when you put the scores in orer
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How do you calculate the median when there is an even number of scores?
Calculate the mean of the two middle scores
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What is the mean?
The total of all scores then divides by the number of scores
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Formula
See paper
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What is the range?
A measure of variability
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What does the range tell us?
The dispersion of the scores - how much spread there is
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How do you work out the range?
Take away the smallest score from the largest score
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What does the interquartile range tell you?
About the middle 50% of scores
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What is the 2nd quartile?
The median - splits the data set in two
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What is the lower quartile (Q1)?
The median of the lower half of the data set
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What is the upper quartile (Q3)?
Median of the upper half of the data set
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How do you work out the IQR?
Q3-Q1
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What are outliers?
Description of the data can be affected by extreme scores
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How do you work out outliers?
LQ-(IQR X 1.5) OR UQ + (IQR X 1.5)
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What should a normal distribution look like?
Symmetrical and the mean, median and mode should be located in the 50th percentile and are the same
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What is skew?
Whether scores tend to be higher or lower than the median
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What do skewed distributions look like?
Lack of symmetry, lopsided distribution, clustered at one end of the scale
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What does a negatively skewed distribution look like?
Left skewed/higher on the right/ tail on the left / mean and median to the left of the mode/ extreme scores of the lower end of the data
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What does a positively skewed distribution look like?
Right skewed/Higher on the left/ tail on the right/ mean and median on the right of the mode/ extreme scores on the higher end of the data
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What is a kurtosis?
The extent to which the scores are clustered around the mean or not
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What is leptokurtic distribution?
Positive kurtosis/ steep curve/ lots of scores in the tails/ pointy
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What us platykurtic distribution?
Negative kurtosis/shallow curve/ flatter than normal/ thin in the tails
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What is Variance?
Measure of the variability of scores
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The formula for variance
See paper
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What does variance show?
The difference between each score and the mean shows how much that score deviates from the average
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How to work out the variance?
1. Work out the mean 2. Take away the mean from each score then square it 3. Add up all the score-mean squared totals 4. Divide by how many scores there are in total
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How do you work out the standard deviation?
Square root the variance
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What is standard deviation?
The average amount by which scores differ from the mean or average score
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What is the formula for standard deviation?
See paper
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What does a small SD show?
The scores are close to the mean and so the mean is a good representation of the data
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How are large SD presented in a graph?
Flatter distribution
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How are small SD presented in a graph?
Pointy distribution
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What are Z-scores?
Represents the number of SD a score is from the mean
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How does you work out the Z-score?
Score - mean score / SD
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What does a large Z-score show?
The less typical a score is from the typical score within the sample
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What is the difference between SD and Estimated SD?
SD = looks at the SD in the actual data we collected / ESD = Generealises beyond the sample
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What is the formula for ESD?
Look on paper
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What is population?
Every member of the group
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What is a sample?
A collection of people who could represent the population
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What is Standard error?
Tells us how accurately a sample represents the population by
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What does a large SD show?
Lots of variation between samples therefore is NOT representative of population
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What is the formula for SE?
See paper
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What is sample mean?
The mean for each sample
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What is sampling variation?
Sample scores vary due to different members of the population
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What is sampling distribution?
Tells us the frequency distributions of sample means from the sample population
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What is a hypothesis?
A statement expressing the expected or predicted relationship between two or more variables
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What is a null hypothesis?
There is no difference or relationship
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What is an alternative hypothesis?
There is a relationship or difference
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What is a directional hypothesis?
States the direction of an effect/relationship
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What is a non-directional hypothesis?
Doesn't state the direction of an effect/relationship
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What are inferential stats?
infers something about the population based on what we have found within a sample
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What is probability
How likely it is that a score will occur?
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Formula for probability
See paper
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What is the p-value?
The probability of this event occurring if the null hypothesis is true
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When do you reject the null hypothesis?
at 0.05 or 5%
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When are the results not statistically significant?
when above 0.05 - accept null
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When are results statistically significant?
When below 0.05 - reject null
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What is Chi-square the test of?
Association
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What level of measurement data does Chi-square use?
Nominal
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What is c-s explore?
The relationship between two nominal variables
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Does C-S use scores or frequency counts?
Frequency counts
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What kind of design is c-s?
Between groups design
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What does c-s do?
Compare the frequency counts of two nominal variables
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What kind of table do you use for c-s?
Contingency/cross table
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What is residual?
The difference between observed and expected
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What is the formula for chi-square?
See paper
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The bigger the difference between the observed and expected frequencies...
The bigger the chi-square
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How is chi square presented?
See paper
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What is the degree of freedom?
The number of scores that are free to vary
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What are type 1 errors?
Thinking there is a genuine relationship when there isn't one / rejecting null when should reject alternative
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Whare type 2 errors?
Thinking there is no genuine relationship when there actually is / accepting null when should accept alternative
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What are effect sizes?
An objective and standardized measure of the size of an observed effect
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What does the effect sizes show us?
The magnitude of the difference between conditions of the strength of a relationship
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What statistical test can be used to calculate effect size?
Pearson's correlation coefficient
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What is statistical power?
The ability of a test to find a significant effect is one exists in the population // the probability of NOT making a type 2 error
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What does a bigger sample size // significance level // effect size show?
Greater power
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What does greater variability show?
Lower power
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Which graphs are used for nominal data?
Pie charts and bar charts
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Which graphs are used for scale data?
Histograms and boxplots
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Which graph to use for two score variables?
Scatterplot
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Which graphs to use for Nominal and Score data?
Table of means and SD // Bar chart showing means // multiple boxplots
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What are boxplots?
Show the range of scores and whether the data is symmetrical or skewed
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What do boxplots show?
Median // IQR // UQ and LQ // Most and least extreme scores // Outliers --> Look at diagram on paper
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What does the correlation coefficient lie between?
-1 and +1
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What is correlation coefficient (r)?
A ratio between covariance and a measure of each of the separate variances
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What is covariance?
Variance shared between 2 variables
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What does (r) indicate?
The strength and direction of a relationship between 2 variables
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What does the number between 0.00 and 1.00 show?
How much variation there is around best fit line
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What does r= 1 show?
Explains all variance // as one increases the other changes to proportionate amount
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What does r = 0 show?
Explains none of the variance // the increase of one variable does not lead to proportionate change
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What does the pearson correlation coefficent assume?
There is a straight line relationship between the variables
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How do you present the Pearson correlation?
r (df = n-2) = - .**, P = .**
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What is spearman's rho?
When data is not normally distributed or with ordinal data
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How to work out percentage variance?
r (squared) x 100
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What is regression?
Used to predict a score on a variable based on the score for another - 2 score variables
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What is the DV in regression?
The value to be predicted // criterion variable // Y
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What is the IV in regression?
Used to make the prediction // predictor variable // X
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What does regression tell us?
How much Y will change is X changes
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What is the formula for regression?
Predicted Slope (Y) = constant (a) + slope of regression line (B) x The score on the X axis from which we will predict the score on the Y axis (x)
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What does the constant tell us?
What point the regression line cuts the vertical line
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What does the slope of regression line tell us?
The change in the outcome associated with a unit change in the predictor
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What is the confidence interval?
Statistically derived interval estimate of a population parameter
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What is the point-estimate approach?
An alternative approach to inferential statistics
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What is point estimate?
Single figure estimate
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What is interval estimate?
A range within which we think that single figure will fall
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## Other cards in this set

### Card 2

#### Front

What is a variable?

#### Back

Anything that varies and can be measured

### Card 3

#### Front

What are Independent Variables?

### Card 4

#### Front

What is a dependent variable?

### Card 5

#### Front

What is a level of measurement?