understanding data distributions, correlations, z-scores-psych

-a frequency table shows how often each value of the variable occurs

*how many people belong to a certain group

-visual representation of info contained in a frequency table

• -the way score frequencies are distributed with respect to the values of the variable
• *it can take on different forms

-mode of distribution refers to the most frequently occuring score

-in this distirbution, one score occurs much more frequently than others

-more than one mode exists (or approx. so)

-2 modes exist

• -is balanced
• *if we cut it in half both sides will be equal

-normal distribution resembles a bell

• - is unbalanced, has more values on one end than the rest
• 

-it is heaveir on the larger quantity side, ending in the lighter side

it is heavier on the lighter side and ending on the larger side

most typical or common score

• -mode
• -median
• -mean

most frequently occuring score

the value at which 1/2 of the ordered scores falls above and 1/2 of the scores fall below

balancing point of a set of scores; average score

• normal distribution
• *bell-shaped in the center

-scores are positively skewed

- mean is dragged in direction of skew

negatively skewed.

degree to which there are variation in the scores

• an index that is used as common way of quantifying 
• dispersion

• -SD is an average that can be interpreted as the average amount of dispersion around the mean
• *larger SD= more dispersion

exp) peoples scores are usually less or more than 2.6 units away from mean on average .

-using a common way called correlation coefficient (r)

- they range between -1 to 1

-value of the correlation conveys information about the form of the relationship between 2 variables

- (r) can be interpreted as the slope of the line that maps relationship between 2 standarized variables

- r>0= relationship is positive

- r<0= relationship between 2 variables is negative

- r=0= there is no relationship between 2 variables

• -correlation between variables rarely get larger than .30
• * variables are influences by many things

• -standarized scores provide a way to express how far a person is from the mean, relative to the variation of the scores
• 

1. mean is always zero for a set of zscores

• 2. the SD of a set of standardized scores is alwasy 1
• *-2-1-0-1-2

• 3. distribution of a set of standardized scores has same shape as the unstandardized scores
• *beware of the normalizaton misinterpretation

4. standard scores may be used to compute centile scores

5. z-scores provide way to standardize different metrics*different varaibales expressed as zscores can be used under same metric(zscore)

• population 
• *this is what we aim in our research

sample

• -difference we observe as a result of studying a sample of a larger population
• *we are only working with subsets of a large population

• it tells us how far on average we would expect our sample mean to vary from our expected population mean
• *quantifies amount of smapling error

-we can expect the participants to score about 5% from the mean

is by using larger sample sizes

null hypothesis significance tests

• -scientists agree that something is unlikely to be due to chance if it is likely to occur less than 5% of the time
• *does not mean it could not be due to chance, just unlikely

• reject null hypothesis
• *results support research hypothesis

• retain null
• *results are likely due to sampling error

we fail to reject the null hypothesis

-it will indicate it occurs less than 5 %. 

- if it falls on the middle than the null hypothesis will be supported

• -reject the null hypothesis when it is actually true
• *accept as "real" an effect that is due to chance only
• *error determined by choice of critical value (.5,.1.001)
• *worst error

• -accept null hypothesis when it is actually false
• *assume that a real effect is only due to chance
• *error influenced by alpha
• *way to prevent it, is to collect sufficient sample size

• -t-tests
• -analysis of varience (ANOVA)
• -z-tests
• -chi-squares