Mind Map Gallery Beguinners Research Statistics with SPSS
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Beguinners Research Statistics with SPSS
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Edited at 2022-11-28 11:39:48
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- Outline
Statistical Samples
Popoulations
Collect samples from the population to generally understand phenomena
Researchers overcome
Generalisability
Are effects they discover real?
Unsystemic variations
Strive to create an experiential environment to maximise systemic variation and limit standard error
Randomization
Counterbalancing
Limit or minimise biased outcomes
Increase the sample size
The more representations of the population
Where statistics are extrapolated from
Research question & experimental hypothesis
It makes a clear prediction prior to testing
Phrases the hypothesis based on the research questions
Types of tailed hypothesis questions
One-tailed or two-tailed
Two Tailed
The results can go either way
‘Participants who perceive a relationship between a victim and perpetrator will be less willing to intervene than participants who believe the couple to be strangers.
One Tailed
Directional hypothesis
Null Hypothesis (H0: Devil)
Zero
No change
Drinking coffee does not affect exam performance
Directional Alternative Hypothesis
One tailed
Drinking coffee increases exam performance
Drinking coffee decreases exam performance
Alternative Hypothesis (H1: Angel)
Agrees with the question attributed to change
Two-tailed
Does drinking coffee affect exam scores?
Types of research questions for a hypotheses Does drinking coffee affect exam performance?
Research Methods
Flow of the research process
Environment
Laboratory
Natural
Field
Correlational
Natural review over time of an IV
Measures variables change over time
Do they increase or decrease
High ecological validity
Increases confounding variable
Experimental
Laboratory testing
Controlled conditions
IV conditions manipulates DV
Low ecological validity
Minimises confounding variable
Cause/Effect
Cause
Mamnipulated
Independent Variable (IV)
Effect
Measured
Dependent Variable (DV)
Calculating Results on SPSS
t-test
Paired Sample or Repeated Measure
Within
Independent
Between
Conditions
Each condition will create its mean dataset, where distribution values from causes of the IV's 'real' systematic variations and environmental error from unsystematic variances that affect the DV
Variable
IV
Control
Experiemental
Dependent Variable
Between Participants
Establishes whether the means of two groups containing different people are statistically different from each other
t-test measures the mean score and the measure of dispersion to assess if difference between the two conditions. Are the differences due to?...
Effects of manipulating the IV?
Sampling error?
A t-test judges the difference between their means relative to the variability in the scores.
In a between-participants design this random variation is the result of random fluctuations in performance between the participants in the different experimental groups
Random Allocation to condition A or B
Two groups of people assigned to different experimental condition
Main Topic
The t-statistic allows you to make inferences about the likelihood that your samples are from the same overall population.
Independent t-test
Compares two means
How does the t-test work
Condition 2
2 strangers fighting
Calculate Mean
Willingness to intervene
Calculate the SD of the mean
How spread out the score is from the average
Calculate the Standard Deviation (SD) of the mean
How spread out the score is from the average
Calculate Mean
Willingness to intervene
Condition 1
A couple fighting
As unsystematic variability in the data can mask the effects of the manipulation, the t-test has to take into account this ‘noise’ to show whether or not the mean scores are truly different.
Writing up an Independent t-test
Step One
You can describe the pattern of your data using the means and standard deviations from the first output table. In this case, you could say something like:
"Results showed participants who saw a relationship between the couple had lower willingness scores (M=1.60, SD=.75) than those who did not (M=2.35, SD=1.22)."
Step Two
Use both words and numbers to formally report whether or not this difference is significant:
An independent t-test found this pattern to be significant, t(31.58) = -2.33, p < 0.05.
Step Three
Finally, you need to put this information together to interpret and summarise what you have found in terms of your hypothesis. This should be written in plain English, for example:
Together this suggests the perceived relationship between the victim and perpetrator affects participants’ willingness to intervene, supporting our hypothesis.
Interactive Cohen's d
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1990346§ion=3.5.1#cohens_d
Within Participant
Classic pre-post design
Measure participant's scores on a DV before and after (pre-post design) treatment or intervention.
Looking for changes in performance due to IV
Instead of comparing scores between two conditions
A t-test judges the difference between their means relative to the variability in the scores.
In a within-participants design, this is due to performance fluctuations from one testing session to another.
Prevent disadvantages affecting systematic variance
Counterbalancing
Controls the order effects
Administers conditions different sequences
1/2 of the group does A then B
Other half does B then A
Randomise the tests
Not possible for a pre-pos designt
Disadvantages
Performance levels may vary from test 1 to test 2
Participants might get bored or tired
Test 2 might differ because of practice in Test 1
Advantages compared with Between Participants
Reduces standard error
Higher validity from Systematic Variation
The same participants are used to minimises differences from using different people
The repeated measures test is more powerful than the between participants
Main Topic
Randomised
Counterbalanced
to prevent systematic practice
Comparing the performance of the same group taking part in two conditions
Known as the paired samples or related t-test
Repeated Measures t-test/Paired Samples t-test
As unsystematic variability in the data can mask the effects of the manipulation, the t-test has to take into account this ‘noise’ to show whether or not the mean scores are truly different.
Writing up an Repeated Measures t-test
Step One
Describe the pattern of your data using the means and standard deviations from the first output table. In this case you could say something like:
Results showed participants made a larger amount of ‘shoot errors’ for black suspects (mean= 3.95, SD = 2.69) than for white suspects (mean = 2.80, SD = 2.54).
Step Two
Report whether or not this difference is significant:
A repeated-measures t-test found this difference to be significant, t(43) = 4.85, p < 0.001.
Step Three
Finally, you need to put this information together to interpret and summarise what you have found in terms of your hypothesis. This should be written in plain English, for example:
Together this suggests that race may affect erroneous shoot decisions made for unarmed suspects, supporting our hypothesis.
Interactive Cohen's d
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1990346§ion=3.5.1#cohens_d
Table 3
Table 1
Independent t-tests is in a family of parametric tests
Assumption of independence
Data collected from one condition should not influence the data collected from another condition.
Assumption that the data is interval data
For psychologists using the Likert scale, ordinal data can be used as interval data as long as the response scale is symmetrical and equal. I.e. 5 point Likhert
On SPSS this ordinal data needs configuring to interval data
Ordinal
Interval
Assumption of homogeneity of variance
Scores of variance between both conditions are roughly equal
SPSS
Assumption of normality
Sampling distribution must be normally distributed = Not skewed
Repeated measures t-test's family of parametric tests
Assumption of normality
Sampling distribution must be normally distributed = Not skewed
Independence within groups
Each score relates to only one individual from the condition
The scores do not affect anyone else's scores
Assumption that the data is interval data
For psychologists using the Likert scale, ordinal data can be used as interval data as long as the response scale is symmetrical and equal. I.e. 5 point Likhert
On SPSS this ordinal data needs configuring to interval data
Ordinal
Interval
Collecting data from variables
Variables
Catagorical
Nominal
Two of more categories
Gender
Binary
Only two categories
Dead or alive
Ordinal
Categories of a logical order
Likert scale
Continuous
Interval
Ratio
Two methods of variable collection
Independent design
A between-groups/subjects
Repeated measures
A within-subject
Validity & Reliability
Are we measuring correclty?
Is the measuring consistant?
Two types of variation
Systematic Variation
Experimenter manipulating one condition but not the other
Unsystematic Variation
Random factors affect differences in each condition naturally.
Statistical models are made up of variables and parameters
SPINE
Standard Error
Standard deviation
the dispersion (or variation) of sampled data in relation to the mean
Sampling distributon
Mean is always on 0
z-scores (standardised scores) = positive or negative score above or below the mean
Standard Normal Distribution (SND)
The SND is known as a probability distribution
Sampling error
Indicates the dispersion of multiple samples means in multiple sampling distribution
https://www.youtube.com/watch?v=A82brFpdr9g
Parameters
No measured
Truth of variables in the model
E.G. Mean, median: central tendency
Interval Estimates
Null Hypothesis
Estimation
Statistical models are made up of variables and parameters
Standard Error
Standard deviation
the dispersion (or variation) of sampled data in relation to the mean
Sampling distributon
Mean is always on 0
z-scores (standardised scores) = positive or negative score above or below the mean
Standard Normal Distribution (SND)
The SND is known as a probability distribution
Sampling error
Indicates the dispersion of multiple samples means in a sampling distribution
Unsystematic variation
Between participants
Naturally occurring differences of the participants
Tends to be higher in the amount of differences
Within participants
Difference in participants characteristics
Tend to be lower in the amount of differences
Small variation
Not much variation between conditions
Small mean differece score
Occurs by manipulation
Large variation
Large natural differences between conditions
Large mean difference score
Occurs by chance
Standard error is estimated by dividing the standard deviation of the sample by the square root of the sample size [SE = SD/√n]
Standard error is a measure of how much natural (unsystematic) variation is to be expected in the population of scores
https://www.youtube.com/watch?v=A82brFpdr9g
Parameters
Main Topic
Main Topic
Main Topic
Interval Estimates
Main Topic
Main Topic
Main Topic
Null Hypothese
Hypothesis testing starts with the assumption that the null hypothesis is true
Inferential statistics gather evidence to try to reject this assumption
Mean difference score between conditions = Approximately Zero
The null hypotheses predicts there would be no difference between the mean scores
Main Idea
Main Topic
Main Topic
Main Topic
Statistical Significance
p-value
p-value runs from 0 - 1 i.e.0% - 100%
0 - 0.05
(<) smaller than = p<.05
5% chance and below that results are not due to standard error alone
assume validity in the the experimental manipulation
results are statistically significant
reject the null hypothesis and accept the alternative hypothesis
0.051 - 1
(>) bigger than = p >.05
up to 95% chance that the results are due to sampling error
experimental manipulation results not validated
accept the null hypotheses
Sig.
SPSS term
https://www.youtube.com/watch?v=Rsc5znwR5FA&list=PLblh5JKOoLUK0FLuzwntyYI10UQFUhsY9&index=13
Are the results due to...
Sampling Error
or
Experiment Manipulation
The p-values tell us whether the differences between the IV and DV conditions are statistically significant or not
Effect Size
How much of an effect is the sig. score of the IV over the DV
0.8 or more can be considered to be large effects 0.5 or more are medium effect sizes 0.2 or more are considered small.
Cohen d
Take the difference between the group means
Divide it by the Standard Deviation of the groups
SPSS
https://learn2.open.ac.uk/mod/oucontent/view.php?id=1990346§ion=3.5.1
Sometimes a statistically significant result is quite small
Statistics: Analysing Data Parameters
Frequency distributions or Histogram
Normal distribution or bell curve
Deviate from normal distribution
Positive or negative scew
Positive or negative kurtosis
Central Tendency Parameters
Mode
Most frequent score
Median
Subtopic
Middle score
Mean
Sum of all scores divided by the number of scores
Range
Dispersion of distribution
Subtract the smallest score from the largest score = range
Standard Deviation
Deviance of Error
Distance of each score from the mean
Sum of squared errors
Amount of errors in the mean
The variance
Distance of scores from the meam
The standard deviation
The square root of varience
Range
Distance between the highest and lowest score
The interquartile range
The middle 50% of the scores
Distribution of scores = probability of a score occuring
Probability density function (PDF)
Statistical models are made up of variables and parameters
Variability of t-test results
T-test controls the noise from unsystematic variations and makes the ability to read inferential statistics to understand the details of the mean to find any true value in systematic variances
Variability in data masks differences between each mean
Sometimes there is a difference in the means = t-statistic
Large t-value = large difference between the two means and SD is small
Small t-value = small difference between the two means and SD is large
p-value will offer any significance in the statistic
The more overlap of the two means from each condition = higher variability of standard deviation
Similar means but not significantly different
Higher in Unsytematic Variation
Standard Deviation is high = Standard Error
p-value > 0.05 = no statistical significance
IV has not had a significant effect
Accept the null hypothesis
The less overlap of the two means from each condition = lower variability, i.e. difference in standard deviation is lower dispersion
Similar means and are significantly different
Higher in Systematic Variation
Low standard deviation and standard error = no sampling error
p-value < 0.05 = statistical significance
IV has had a significant effect = genuine difference: the effects are "real"
Reject the null hypothesis and accept the alternative hypotheses
SPSS Terminology
Variables
Interval
Ordinal
Catagorical
Descriptive Statistics
N
Number of participants
Range
Highest - lowest variable value
Minimum
Lowest variable
Maximum
Highest variable
Mean
Average of variables
Std. Deviation
Spread of scores around the mean
Grouping variable
IV
Define Groups
Display Variable Names
2nd box to inspect = Inferential Statistics
Levene’s Test of Equality of Variances
F-value
Determines the significance of the homogeneity of variance
Sig. F-value < 0.05
Significant: the variances are not equal
Homogeneity has not been met
Read the second row
Sig. F-value > 0.05
Not significant: the variances are equal
Read the top row
Homogeneity has been met
t-test for Equality of Means
t
t - Obtained Value of t
t -test calculated by SPSS
The larger the value of t, the smaller the probability that the results occurred by chance i.e. The more systematic variation there is compared to the unsystematic variation the more a significant result.
df
Value that represents the size of the sample
The number of participants minus the conditions
N - 2 = 38
sig (2-tailed)
p-value
If directional 1 tailed; divide the p-value by 2
1st box to inspect = Descriptive Statistics
N
Number of participants
Mean
Mean of both conditions
Std. Deviation
Spread of scores in wider: (SD=1.23) (SD=0.75)
Report these descriptive statistics when reporting your results
Std. Error Mean
To assess if these scores are statistically significant the inferential statistics box needs inspecting
The independent t-test SPSS
2. Inferential Statistics
Output from the independent t-test
F-value (is it significanrt?) = 1st row for homogeneity or equality of variance
Sig = p-value (if under .05 the F-value is significant = 2nd row for homogeneity or equality of variance
If these are similar the following stats are significant
t - Obtained Value of t = Equality of Mean (SPSS will calculate this)
df - Degrees of Freedom (round up decimal points) = Equity of Mean (SPSS will calculate this)
Sig (2-tailed) p-value or if 1-tailed due to a directional hypothesis: divide 2-tailed result by 2
writing up the results of your t-test t (df) = t value, p = p value
t(31.58) = -2.33, p = 0.026
1. Descriptive Statistics
Group Statistics
Mean
Std. Deviation
Statistical Decision Tree