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what is a statistic
- any numerical indicator of a set data
- b. the application of procedures to produce numerical descriptions and statistical inferences
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descriptive statistics
- used to summerize the information in a given data set pertaining to a particular sample
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inferential statistics
trying to infer; draw conclusions about the data so that we can make generalizations
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Two key components to Inferential Statistics
- estimation: estimating the characteristics of a population from data gathered on a sample; how representative is my estimation of my population
- significance testing: testing for significant statistical differences between groups and significant relationships between variables; p<.05
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Five Key Types of Descriptive Stats
- Central Tendency: a center point in my data; could be the mean
- Dispersion: how spread out are the participants
- Standard scores: standard deviation and z scores; takes the numbers and standardized
- Frequencies: how many in each group;
- Visual Displays: graphs and charts
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Central Tendency: Mode
- Mode: simplest; what number occurs most often; can have multiple modes
- - Appropriate for nominal data/ not for ordinal
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Central Tendency: Median
- - middle most score in a distribution; cut the distribution in half
- - appropriate for ordinal data
- - it is resistant to extreme scores (outlyer)
- - does not describe "typical"
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Central Tendency: Mean
- - arithmetic average; it is not resistant
- - most appropriate and effective for interval/ration data
- - often fractional (round to two decimal points)
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Dispersion: Range
- - simplest measure
- - reports the distance between our highest and lowest score
- - general sense of the spectrum of scores
- - non resistant: like the mean, an extreme score will affect the range
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Dispersion: Variance
- mathematical index of the average distance of teh scores in a distribution from the mean
- - tells us the amount of error in our study
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Dispersion: Standard Deviation
- - average deviation fromt the mean espressed in the original unit of measure
- - most often used by researchers
- - square root of variance
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Standard Score
- - common unit of measurement that indicates how far any particular score is away from the mean
- - they locate scores within a distribution
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Z score
- several uses beyond "locating":
- - multiple raters
- - same scale but different context
- - different scales
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Frequencies:
- - frequency distribution: used to calculate the mode
- - absolute frequency
- - relative frequency: the proportion of times each data occurs
- - cumulative frequency
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Visual Displays of Frequency
- pie charts
- bar charts
- histograms: like a bar chart, except it is using a ratio or interval variable
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Estimating Population Parameters
guessing at the characteristics of our population, statistically speaking
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estimates
statistics computed
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Normality Assumption
the variable of interest is "normally" distributed in the population
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Random Sample
rarely have a true random sample
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Normal Distribution
- - theoretical distribution representing the location of deviations about the mean and the probablity of these deviations happening
- - interval or ratio data
- - deviations about the mean are expressed in units: SD's
- - the normal distribution tells researchers the probability of a score falling in any given area of the curve
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68-95-99.7 Rule
- 99.7 of scores fall 3 SD above of 3 SD below the mean
- 95% of scores fall between 2 and -2 SD
- 69% of scores fall between 1 and -1 SD
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Abnormal Distributions
- it is not perfectly symmetrical
- can be abnormal in two ways
- - kurtosis: how pointed is my normal distribution
- - skewness: direction of asymmetry
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Mesokurtic (0)
Perfectly normal distribution
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Leptokurtic (>0)
pointy kurtosis
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Platykurtic (<0)
flat kurtosis; most people are widely distributed
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Skewed Distribution
all about the direction of the tail; mode, median, then mean (not all perfectly aligned)
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Central Limit Theorem
- - larger sample size: the distribution of the means is normal
- - larger samples give more accurate results than do smaller samples
- - if you cant do random, do large
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Making Inferences
- -standard error of the mean: how much does my sample mean differ from my population mean; look at sampling distribution
- - confidence level: how confident am I that my mean in my sample, represents the populatin mean
- - confidence interval: range of my mean score associated with the confidence level
- - size of CL influenced by: variability: factors you cant necessarily control that could affect your findings confidence level: sample size
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Statistical significance
patterns or relationships between variables are likely to exist in the real world
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Do we really test research hypotheses?
We dont actually test the hypotheses proposed in the study. We test the null hypothesis
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Null Hypothesis
- - a statement that statistical differences or relationships have occurred for no reason other than chance
- - we use statistics to determine whether or not to accept or reject the null, not to prove or disprove H's
- - we focus on estimating the probability that H's are true/not true. Hence, our language regarding findings is qualified and tentative
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Null Decision
- - accept or reject the null
- - based upon statistical significance
- - in making this decision, we risk making one of two errors
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