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chapter 10-quantitatve analysis.docx

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David Naussbaum

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Quantitative Analysis Chapter 10: Nestor & Schutt Research Methods in Psychology Types of Statistics  Descriptive = describe variables in a study  Inferential = estimate characteristics of a population from a random sample  Is the effect we observed due to chance alone?  Used to test hypotheses about the relationship between variables  Must consider level of measurement Frequency Table  Shows the number of cases and/or the percentage of cases who receive each possible score on a variable  Often precedes the formal statistical analysis  May group the values if:  There are more than 15-20/ category  It would clarify the distribution  Resulting categories:  Should be logical  Should be mutually exclusive and exhaustive  Mutually exclusive- if ppl in one category cant be in other eg male and female  Exhaustive- everyone fits into one of these categories.. There is nothing else  Bar charts  Bars separated by spaces  Good for nominal data  Histograms  Displays a frequency distribution of a quantitative variable  -quantitative analysis- have continual lines –ordinal-no gaps  Qualitative data: Categories-discontinuous, can have bars for each group bit cant draw line graph-gaps –order doesn’t matter b/c data is nominal not ordinal  Frequency –how often a score of for eg occur  Begin the graph of a quantitative variable at 0 on both axes  Always use bars of equal width  The two axes should be of approximately equal length  Avoid “chart junk”  -can make a non statistically difference look like it is twice as much for eg, if cut off too high therefore need to start at 0 for both axes  -can skew how chart looks if you have for eg, a very high y axis and small x axis  -should avoid puttting too much data in the chart= chart junk- takes away from main idea..  Three key features of a distribution’s shape:  Central tendency  Variability  Skewness  Skewed: distribution is not normal, therefore can’t use t-tests, f-tests ( normal parametric statistics)  Mode (probability average)  Most frequent score  May be more than one  May fall far from the main clustering of cases in a distribution  Median (position average)  Point that divides the distribution in half  Cannot be used at the nominal level  Normal dist: mean, mode, median have same values  Range  High score – low score  Drastically influenced by one high or low score  Variance  Average squared deviation of each case from the mean  Standard Deviation  Square root of the variance  Mean (arithmetic average)  Sum numbers and divide by N  Cannot be used at the nominal level (and sometimes not at the ordinal level)  Mean vs. Median  Should consider the purpose of the statistic  Median often makes more sense if the scale is at the Ordinal level  Median is better for skewed distributions  - No median at nominal level variables  Confidence that the mean of a random sample from a population is within a certain range of the population mean  Calculating confidence limits:-don’t need to know how to calculate  Calculate the standard error  Decide on a degree of confidence  Multiply the standard error by 1.96  Add and subtract the value in step 3 from the sample mean  >0.5 – could happen by chance.  Confidence interval- how confident you want to be that what you’ve measured is representative of the population –if want to be more confident: need a wider range. But the broader it is you loose precision and its not v. likely.  Can be used to estimate a population parameter from a sample statistic  Can also be used to test a hypothesis  Two of the most common hypothesis tests:  t-test  F-test T-test:  Used for comparing two group means  t = difference in group means / variance of the entire sample  Generates a statistical value  Value is compared to a critical value found in Student’s t-table  If the calculated value exceeds the critical value, the null hypothesis is rejected.  Degrees of freedom (df)  Based on the sample size  Helps determine critical value  Larger values associated with greater statistical power  One-tailed vs. two-tailed tests  One-tailed tests specify direction  Two-tailed tests are the convention  d.f=number of observations- 1  -based on sample size.  -helps determine
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