Lecture 5-8 Flashcards
What is the central limit theorem? (CLT)
the larger the sample is, the sampling distribution (plotting the mean on histogram ) , the distribution will eventually result a normal distribution. Even if the variable is not normally distributed or skewed, such as Income
What is a Sampling Distribution
Similiar to a frequency distribution.
The sampling distribution charts or graphs the probability of getting an useful value such as the mean.
Relies on repeated samples, and larger sample size
What is the population parameter?
population-level statistics
What does the law of probability? Two types of probability? Examples?
Theoretical probability;
How likely an event is going to happen, theoretically. I.e. Flipping coin- 1/2 or 50% chance of heads or tails
represented from 0-1, or %
Empirical probability: What happens in actual reality. Flipping a coin- if got get 6 heads in 6 flips, your empirical probability is 100%
What is the Law of Large Numbers in Probability?
When the number of tests increases, the empirical will converge with the theoretical probability
How does the Law of Large Numbers apply in Sampling?
The larger the sample size(n) is, the more likely it is to be close to the actual population
What is a Sampling Distribution
Similiar to a frequency distribution
Review- what is inferential statistics?
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What is the standard error of the Mean? (shorthand Std. Error in SPSS)
What are the two factors that determine the Std. Error of the Mean?
Std. Error a measurement of the Error of the Sample mean from the true Population mean.
1) n/ sample size
2) the variation/ std. deviation in the sample size(i.e. income report of a sample)
What does the confidence interval mean?
Based on sample standard error calculation, figuring out a range of values that the True Mean of the population would be
How to calculate the 95% confidence interval of a Mean?
By adding or subtracting 1.96 of the standard deviations from the mean
95%CI= Sample Mean +/- 1.96(Std.Er)
In his Central Limit Theorem simulation, what did the lecturer do?
…
What kind of relationship does the Sample size n have with the Std. Error of the Mean?
Reverse relationship. Bigger the n, smaller the Std. Error of mean
Why does the Std. Error of the Mean Matter?
You can calculate the true mean of the population based on the formula and calculation of Std. Error of mean(confidence intervals)
What does statistical significance actually mean? How is it determined?
The generalizability to the population
By running significance tests
Refresher: What is a research hypothesis? What is the difference between a research and a null hypothesis?
The research hypothesis is a theory or assumption researchers come up with based on prior knowledge and evidence.
A research and a null hypothesis state two opposite statements and seem to contradict one another. But the purpose of both is to work towards proving the research theory
Why do we want to disprove Null-hypothesis? And how?
Based on Karl Popper’s philosophy.
We want to disprove or discredit a null hypothesis because DISproving there is No relationship between two variables is actually One way to establish there IS a relationship.
What does falsification. mean and why is it important?
Falsification means setting of to disprove certain hypothesis. the process of repeated attempts to “disprove” or “discredit” a hypothesis. It’s the only way to “proof” or verify a hypothesis
What does falsification protect us against?
Confirmation bias and one-sided evidence that only “supports” a hypothesis
What are the two types of research theory? what does it affect?
Non-directional.
Directional: theorizes relationship and direction of relationship The type of
What is a significance level and when is it used?
It is used before doing a significance test. The level in social science by convention is the 95% Confidence Interval.
What are the two things we are most concerned about in testing a bivariate relationship?
Magntitude: the strength of relationship
Reliability: generalizability of relationship(statistical significance)
How is statistical signficance related to null hypothesis?
p> =0.05- reject null hypothesis. There is a relationship.
What do Type i & ii errors mean?
Type i: Defining a relationship between two variables as generalizable when it isn’t. Also called False positive. 5% error rate of Type I error.
Type ii: Defining there is no relationship when there is a relationship. False negative.
What do Type i & ii errors mean?
Type i: We are saying there is a relationship in the population when there isn’t. False positive. 5% error rate in social sciences.
Type ii: We are saying there is no relationship when there is. False negative.
What is p value?
It’s called probability value. The measuring value of statistical significance. Certain threshhold value determines if relationships between two variables are generalizable to population, or just random occurences within the sample
What is the p value in social sciences for rejecting null hypothesis? In other disciplines?
In social sciences, a relationship Or a difference is significant at 95 percent. This is written in REVERSE in p values, as p represents the probability of Type I errors occuring. p< .05, or p smaller than 5%.
In biochemical disciplines(chemo treatment) p>= .995
What are the mean controversies and problems of statisitical significance tests?
statisitical significance tests
- does not measure the Strength of a relationship
- has type i error rate
- statisitical significance tests depend on sample size
What is a chi-square test and when are chi-squares used? What is an example?
A significance test. It is used with comparing “no relationship scenario” and determine if there WAS a relationship between “categorical variables” I.e. Guy used an extremely simplified If there Is a relationship between two sexes and employment rate. Chi-square is used to distinguish between “no relationship” and “yes relationship”. If p was less than 0.05
what is the degree of freedom?
analyzed in chi square
how many “unconstraint” or”free” cells there are in a crosstabs