PY2501.1 ~ {Recap of PY1502(Key Skills 2)}
what is the point of analysis
to investigate whether your research hypothesis is supported by the data that you collect
what are descriptive statistics designed to present
an initial impression of your data and ideally reveal a trend that is worth investigating further
relational designs
if you hypothesise a correlation between continuous variables
use a scatterplot to show positive relationship
models information and data into a set of tables with rows and columns
something we can anticipate in the nearest future
quasi-experimental design
if you hypothesise differences between groups [when IV is nominsl, DV is continuous
we use bar graph
aims to establish a cause-and-effect relationship between an independent and dependent variable
descriptive statistics
summary statistics
summarize + present features of a population sample using qualitative methods
key components of descriptive statistics
measures of central tendecy [ mean + median + mode ]
measures of variability [ variance ]
graphs and charts
frequency distribution
relational designs [google]
when you hypothesise a correlation between continuous variables
study that investigates the connection between 2 or more variables
[use a scatterplot to show relationship]
inferential statistics
to test; using your sample data if the trend is meaningful and if it is likely to be present in the broader population or if the pattern of results has arisen by chance
involves parameter estimation and hypothesis testing
when doing inferential statistics what do we need to get
the test statistic + p value
what dictates what analysis to use
research design
you either test for relationship between continuous variables or difference between nominal groups
testing for relationship between continuous variables
continuous DV + continuous IV + 1 IV + correlation or simple regression
testing for differences between nomial groups
continuous DV + nominal IV + 1 IV + 2 levels + t-test + independent groups / repeated measures
independent groups
independent samples t-test
Mann Whitney U test [ if data arent normal ]
repeated measures
paired samples t-test
Wilcoxon test [ if data aremt normal ]
independent samples test
typically you perform this test to determine whether 2 population means are different
it is an inferential statistical hypothesis test so it uses samples to draw conclusions about populations
Mann Whitney U test
used to test whether 2 samples are likely to derive from the same population
comparing medians between 2 populations
nonparametric hypothesis test that compares 2 independent groups
paired samples t test
used to determine whether the mean difference between 2 sets of data from the same / matched participants is zero
has 2 competing hypotheses: the null hypothesis and the alternative hypothesis
wilcoxon test
used for non-parametric tests of differences between 2 independent groups of scores
used to compare 2 samples of continuous data
Central Tendency
gives indication of typical score in each group
statistical measure that identifies a single value as representative of an entire distribution
it aims to give an accurate description of the entire data
when reporting central tendency
mean - if data is normally distributed [if Shapiro-wilk p>.05]
median - if data aren't normally distributed [if Shapiro-Wilk p<.05]
measure of dispersion
can be thought of as a 'margin of error'
when you report mean: report standard deviation or standard error
when you report median: report the iterquartile range
for inference of hypothesis predicting the data
we need to calculate signal vs noise ratio
[how good vs how bad is your hypothesis]
noise/error
unsystematic or within condition variance
how much of DV is not explained by changes in IV (research hypothesis) [how inaccurate are the group means]
[things we can't control]
signal
how much more variance is DV is explained by our research hypothesis (means of each IV group) than by null hypothesis (overall mean)
research hypothesis
the DV will differ for each type of treatment group so its represented by difference between group means
null hypothesis
no difference (0) between group meand. This is represented by the flat dahsed line that shows overall mean.
signal vs noise
used to describe the underlying pattern or relationship [signal] and the random irrelevant fluctuations [noise] that occur in dat a
signal [gpt]
the true, meaningful patterns or relationships in the data that reflect real effects or phenomena. A consistent finding across different studies. It is what researchers are trying to detect. Part of data that we belive is consistent, reproducible and meaningful
signal examples [gpt]
positive correlation between 2 variables [stress + anxiety] or a reliable treatment effect in an experiment
what researchers are trying to detect, interpret or generalize from their data
noise [gpt]
the random variability, measurement errors or irrelevant factors that obscure the signal. This can make it difficult to detect the signal, leading to misleadng conclusions or a failure to find meaningful relationships [type II errors]
noise examples [gpt]
individual differences in participants + inconsistencies in how data is measured/extraneous varkables that aren't being controlled for in an experiment [ mood influctuations, environmental factors, rando error in a test ]
type II error
false negative / error of the second kind
occurs when a statistical test fails to reject a null hypothesis that is actually false [when a test incorrectly concludes that there is no statistically significant difference between groups or that a relationship doesn't exist when it actually does]
how do we determine ratio size
signal is large and noise is small - large ratio
signal is small and noise large - small ratio
how is ratio calculated
between condition variance [signal]
test statistic = ________________________________
within condition variance [noise]
how is t-statistic calculated [signal vs noise]
(mean1 - mean2) - null
t= __________________________________
standard error of (mean1 - mean2)
[dividing by standard error converts signal to a t-statistic]
how does t-statistic tell us whether hypothesis is supported
finding evidence against our null hypothesis [that there'll be no effect]
t-statistic are typically close to zero if null hypothesis is true, a larger one is unlikely, so offers evidence againstyour null hypothesis, and in turn, supports your research hypothesis
the t-statistic and hypothesis testing
when you compare means or assessing whether a sample comes from a population with a specific mean. It helps determine whether the observed data supports the null or alternative hypothesis
alternative hypothesis
there is an efect, a difference, or a relationship. [e.g. stating that the population mean is not equal to a certain value]
t-statistic
tells you how many standard errors the sample mean is away from the hypothesized population mean
sample mean - hypothesized pop mean [ from NH]
t = _____________________________________________
sample SD / square root of sample size
small and large t-statistic and what it means
closer to zero if NH is true
large t-statistic is unlikely so offers evidence against our NH, and in turn, supports your RH
ronald fisher
probability [p] of your t-statistic indicates weight of evidence against your null hypothesis
if p < .05, then we conclude our test statistic was unlikely yo occur were the null hypothesis true
probability [p] significance
if p<.05 then the difference between groups is significant [ NH is unlikely to be true, RH is supported]
if p>.05 then the difference between groups is not significant [ NH likely to be true, RH is supported]
identify IV and DV in this scenrio
suppose you wanted to know whether a team of 100 shot putters could throw dogs or cats further.
IV - animal [cats , dogs]
DV - distance thrown [m]
effect size
standardized waay that quantifies the magnitude of a relationship or difference between variables in a study, measures the strength or practical significance of that effect
different types of effect sizes + when to use
cohen's d - t-statistic [comparing 2 groups] to measure size of difference between 2 means
Pearson's r - measures strength and direction of the relationship between 2 continuous variables . [ranges from -1 to 1, 0=no correlation 1/-1 perfect linear relationship]
Eta-squared - ANOVA to measure the proportion of variance in the DV explained by IV
importance of effect size
even is result is statistically sognificant, might not have a meaningful impact in real world settings
helps assess the practical importance of the findingd
allows researchers to compare magnitude of effects across different studies or pops
helps with power analysis
95% Confidence Intervals
give a range of values within which 95% of population values would fall [ visually demonstrated as error bars]
can be used to judge whether 2 groups differ from each other
what 95% Confidence Intervals show
when the 2 samples overlap, we can be reasonably confident samples are from the same population, when they don't overlap we are confident they aren't from the same population
how does the 95% CI work
provides a range between a lower and upper bound [calculated based on sample data]
percentage reflects the likelihood that the true value of the parameter lies within the interval
[this applies if the same sampling process were repeated many times]
95% CI width
reflects the precision of estimate
narrower = more precision
wider = more uncertainty