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42 Cards in this Set
- Front
- Back
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Five questions to ask about your data |
1. What were the questions/variables? 2. What were the response options/possible values? 3. Who did the data come from? 4. When was the data collected? 5. What was the context in which the data war collected? |
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Descriptive Statistics |
- Summarize a set of data including shape and nature of data
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Examples of descriptive statistics |
- E.g. frequencies, measures of central tendency, measures of variability |
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Population vs Sample |
Population : parameter :: sample : statistic |
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Nominal scale |
Numbers are used only to distinguish among objects; for classification purposes only
E.g. 0=Female, 1=Male |
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Ordinal scale |
Numbers place objects in order along a continuum. No information about distance between objects. |
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Interval scale |
Equal intervals between objects represent equal differences. E.g. degrees Celcius
No zero point |
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Ratio scale |
Scale with a true zero point - e.g. weight |
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Measures of central tendency |
Numerical values that refer to the center of the distribution.
MEAN MEDIAN MODE |
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Pros and cons of median/median/mode |
- Does the value actual occur in distribution? - Does it represent all of your numbers - Is it affected by extreme scores? |
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Variability |
The degree to which individual data points are spread out (distributed) around the mean. |
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Measures of variability |
RANGE
VARIANCE
STANDARD DEVIATION |
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What does the SD tell us? |
- How closely scores fall to the mean in standardized units |
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Possible generalizations about the SD in a SYMMETRICAL distribution |
-68% of scores will fall within 1 SD of mean
- 95% within 2 SDs
- 99.7 within 3 SDs |
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When to use Z scores |
- When interested in describing an INDIVIDUAL score in a distribution (where an individ score falls in relation to other scores)
- Allows for comparison of two scores when on different scales
- Convert raw scores into std dev units to tell how far below or above the mean it is
- With normal diet, can be used to determine percentile scores |
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Central Limit Theorem |
As sample size INCREASES, sampling distribution of the mean becomes more and more normal regardless of the shape of the distribution of the sample. |
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Levene's Tests |
- Tests if variances in different groups are the same
+ Significant = variances are NOT equal + Non-significant = variances ARE equal |
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What are inferential statistics? |
Generalizations about a large group of people or objects based on data collected from a small subset of this group.
Based on hypotheses and probability
Purpose is to make conclusions about a population |
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Steps to inferential statistics |
- Form a research question - Form null hypothesis - Obtain data - Evaluate data with 5 questions - Descriptive statistics - Apply statistical test - Get results - Compute probability of statistical tst -Make decision about the null - Determine effect size - Make 'real world' interpretation |
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Falsification principle of science |
We can only prove hypotheses false, not true. |
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Explain the null hypothesis |
To answer statistical questions, we test the hypothesis that is directly counter to what we want to find. We assume the null hypothesis is true, and if we find a difference, we can reject the null. |
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Significance level |
The probability with which we are willing to reject the null.
The probability of type 1 error is alpha
alpha - usually set at .05
If alpha < .05, we reject the null; |
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Type 1 Error |
The error of rejecting the null when it is true.
The probability of type 1 error is alpha
The probability of a correct decision is 1 - alpha |
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Type 2 Error |
The error of not rejecting the null, when it's false
The probability of a type 2 error is beta
The probability of correctly rejecting null is 1-beta |
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Standard error |
The standard deviation of the sampling distribution of a statistic.
The average difference between the expected value (pop mean) and a specific sample mean. |
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T distribution vs z distribution |
When the SD of the population is not known, or the sample size is small, use the T DISTRIBUTION.
Because it adjusts for sample size. |
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Effect size |
The degree/magnitude of the effect. Is the statistical significant finding PRACTICALLY significant? |
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Independent Sample t-test |
A statistical analysis for examining differences in the mean between two independent groups. |
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Degrees of freedom |
The number of independent pieces of information remaining after estimating one or more of the parameters |
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Correlation |
The relationship or association between variables.
Tells the direction and magnitude of the relationship.
Standardized using SD - so they range from -1 to 1 |
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Correlations in scatter plot
(What are X and Y variables?) |
X is predictor variable
Y is criterion variable |
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When to use Pearson correlation coefficient |
Both variables must be CONTINUOUS |
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t-table vs r-critical table for probability of correlation |
-t table, when you've created a t value from the correlation coefficient and want to see if it's significant
-r critical table, when you want to take the correlation coefficient and df directly to a table, to see if it's significant |
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Issues with correlation |
- Restriction of range
- Nonlinearity
- Not all correlations are meaningful
- Heterogeneous sub samples |
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Range restrictions |
Cases where the range over which x and y varies is artificially limited.
May cause r to increase or reduce; normally it reduces r |
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Nonlinearity |
Sometimes, a straight line doesn't best fit the data.
E.g. pay and performance |
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Not all correlations are meaningful |
correlation doesn't equal causation |
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Heterogeneous sub-samples |
If data from the sample could be subdivided into 2 distinct sets on the basis of some other variable. E.g. height/weight and gender
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Types of correlation coefficient |
Pearson Spearman's Rho Point biserial Phi |
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When to use Spearman's Rho coefficient |
To correlate ranked data |
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When to use point biserial correlation |
If one variable is dichotomous and the other is continuous |
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When to use Phi coefficient |
If both variables are measured as dichotomous |
