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Statistics
- an objective way of interpreting a collection of observations.
- Types of statistics – Descriptive techniques – Correlational techniques – Differences among groups
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Inference
generalization of results to some larger extent/group
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Sample
- a group of participants, treatments, or situations selected from a larger group
- a selection of people or items from the population
- easier/quicker to use
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Population
- refers to all people or items with a particular characteristic of interest
- the larger group from which a sample is taken
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Systematic sampling
- i.e picking every 100th name in phone book
- select a sample for telephone interviewing by selecting every 20th name in the student directory
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Stratified random sampling
- Method of stratifying a population on some characteristic before random selection of the sample
- i.e picking 20 males from 1000 random 20 females from 1000 random
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Random assignment
i.e assign id numbers to clients pick clients at random
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Post Hoc
Justification that the sample repressents some groups at large
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Central tendancy
- a single score that best represents all the scores
- Indication of the typical score in a data set
- – Mean – Median – Mode
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Variability
- the degree of difference between each individual score and the central tendency score
- measures of how scores vary
- – Range – Interquartile range – Standard deviation
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Standard Deviation
- an estimate of the variability of the scores of a group around the mean (Rmpa)
- measure of how much the score varies around the mean
- *spread of scores about the mean
- gives us the average amount by which the scores deviate from the mean
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Variance
the square of the standard deviation
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Mean
- Most frequently used measure of central tendency
- add all numbers divide by sum of participants
- influenced by extremes
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Median
middle of all scores in order
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Mode
most frequent score occuring
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Range
- Highest- lowest
- variability score
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Confidence Interval
- Present an interval estimate of the population mean
- Indicates the interval within which we are confident the population mean will fall
- Centered around the sample mean
- Provies an expected upper and lower limit for a statistic at a specified probability level
- Can be represented in error bar charts
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Normal Curve
- Distribution of data in which the mean, median and mode are at the same point.
- and in which is from the mean includes
- Skewness – Kurtosis
- 68% of the scores 1+ from the means
- 95% 2+ from score and 99% is 1+
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Parametric statistics
- Normal distribution Equal variances – Independent observations
- Test based on data assumptions of normal distribution equal variances and independent observations
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Non- Parametric Statistics
- Distribution is not normal
- any of a number of statistical techniques used when the data do not meet the assumptions required to perform parametric
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Statistical power
- the probability of rejecting a false null hypothesis
- The probability of making a correct decision!
- Directly related to the probability of making a type II error
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Skewness
- description of the dirction of the hump of the curve of the data distribution and the nature of the tails of the curve
- *term that describes the position of the hump in the curve of a distribution is
- side to side
- Left positive skewness
- Right negative skewness
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Kurtosis
- Description of the vertical characteristics of the curve
- Whether the curve is more peaked or or flatter
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Statistical Significance
- A criterion for significance is set
- This is usually a probability set at .05
- if our calculated p-value is less than the criterion for significance
- This is classed as ‘statistically significant’
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Meaningfulness
The importance or practical significnat of an effect or relationship
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Probability
Odds that a certain event will occer
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P-value
- The probability that your results are due to chance or sampling error
- chance your results are due to chance or sampling error
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Null hypothesis
- a statement of no difference or no relationship.
- statistical hypothesis that assumes that there is no difference among the effects of treatments
- i.e There is no difference between the vocabulary scores of average- and high-ability students.
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alpha a/ level of significance
level of probability set by the experimenter before the study
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type 1 error
- rejecting the null hypothesis when its true
- probability of making a Type I error is denoted by the alpha (α)
- researcher claims that there is a difference between treatments (i.e., rejects the null hypothesis) when there really is no difference
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Type 2 error
- accepting the null hypothesis when its true
- a Type II error is denoted by the beta (β) level
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Beta
Magnitude of a type 2 error
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Sample size
the number of participants in the study being evaluated or planned
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Effect size/ delta
- the outcome of a study typically expressed in standard deviation units
- standardized value that is the difference between the means divided by the standard deviation
- Meaningfulness The size of the difference (Cohen’s d)
- the strength of the relationship (r2)
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standard error
variability of the sampling distribution
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Descriptive statistics
statistical techniques which helps us describe data
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Inferential statistics
statistical techniques devised to allow us to generate from our data to populations
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Quartiles
values which divides data set into exactly 4 equal parts
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variance
the average of the squared deviates from the mean
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cluster sampling
sampling where the population is divided into smaller identifiable clusters and one or more of these cluster are then randomly selected. Participation are then randomly selected from smaller cluster to take part in a study
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Opportunity sampling
sampling from those people who are available at a particular time and place
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snowball sampling
a sampling technique where individuals who have taken a part in a study provide detail of people they know who might also be willing to participate
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Volunteer sampling
sampling which relies on participants coming forward to volunteer to take part in a study usually in response to an advertising
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sampling error
bias in the estimation of population paremeters that arise from using samples
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parameters
statistical descriptions of populations
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statistics
description applied to samples
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chance
same as probality odds of something happening
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normal distribtution
a distribution of a scores which is symmetrical peaked in the middle, is bell shaped and equal on both sides of the peak
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Bi-directional/ two-tailed hypothesis
- Suggests a difference or relationship but not the specific direction of these
- *researcher predicts that there will be a difference between 2 groups but is unable to predict which group will score higher than the other
- There will be a difference between hearing aid and control groups in social anxiety scores
- a hypothesis where we have not specified the direction of the predicted difference or relations
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Directional, uni/one-tailed hypothesis
- States the direction of the difference or relationship
- ie. the hearing aid group will have lower social anxiety than the control group
- specified direction of the hypothesis.
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a priori
Information needed in planning research • Alpha • Effect size • Power • Sample size
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