march 12 Flashcards
Statistical inference
Statistics: are sample values
Parameters are estimated population values
Statistical inference is the estimation of population values by analyzing the sample
Two types of statistics inference: Parameter estimation technique (ex: confidence intervals) and hypothesis testing
Parameter Estimation – Estimating population values using sample data (e.g., confidence intervals).
Hypothesis Testing – Testing relationships or differences between groups (e.g., does advertising increase sales?)
Ex; what is the pop of canada and how do they feel about sustainability—> can take a subset of canadians, see if they care about sustainability and then make inferences about them to see what all canadians think about sustainability
Since it’s usually impractical to survey an entire population, we rely on statistical inference to make educated guesses about the population based on a sample
Statistical inference: Parameter estimation
Parameter estimation: coming up with an interval where the true population parameter lies
Confidence intervals is an interval or range which contains the true population statistic
Ex: 4 in 10 canadians lack confidence in social citations, causing them to avoid meeting new people
Point estimate
Ex of the polls of trump and clinton
If the polls say that two candidates are close , cant really predict bc there is error associated
There is a margin of error associated with polls bc we cant sample the whole population about trump and clinction
Always be some level of error but how much?
The level in this case was +/- 3%–> 40-46% (43+3, 43-3) so we get our range, this is our lower and upper bound, somewhere between his range is the amount of americans that support trump
Theresd variability in how you estimate a candidates likeness to win
Whats key in polling data: margin of error, need to know it
43% was the point estimate –> A point estimate is a single value used to estimate an unknown population parameter. It is the best guess based on sample data
For example, in the context of estimating the average height of all students at a university, if you take a sample of 50 students and find that the average height in your sample is 170 cm, then 170 cm is your point estimate for the true average height of all students at the university.
Confidence level : z% chance of x +- y%
Confidence leve: how sure are you of he results you are reportin
Select the confidence interval so like 95%–> 95 out of 100 times you sample from the same population, your result will be between the intervals determined by your margin of error
What does 95% actually mean→ if you recruit 100 people and you get your estimate and your margin of error, if you repeatedly sample 100 people, but 95 out of 100 times you sample you will get between the margin of errors and your estimate
Hypothesis testing
Creating groups within your sample based on things like gender, need to uniqueness, age, etc
Testing for relationships between variables
Ex: do people who exercise eat healthier (excerise and healthier)
Can also be testing for differences between groups of variables
Ex: do people who are vegan exercise more than people who are not. (dif groups like vegan vs non vegan)
The null hypothesis
Ho: keeping the status quo, nothing to see here . null means nothing
Alternative hypothesis
Ha or h1: somehines up, theres something to see here
Hypothesis criteria
Testable
Ho and ha are mutually exclusive –> The null hypothesis (Ho) and the alternative hypothesis (Ha) must be opposites—only one of them can be true at a time. can tpccur at the same time
Ho and ha are collectively exhaustive –> The two hypotheses must account for all possible scenarios so that one of them must be true. an outcome must happen
Specific
Hypothesis testing
Two possible test results
There is sufficient evidence to reject the null hypothesis in favour of the alternative hypothesis
There is insufficient evidence and we fail to reject the null hypothesis
Types of significance
Statistical significance→ is the difference unlikely to have occurred to due to chance . if a result is statistically significant, it suggests that there is a high probability that the observed difference is real and not just a result of randomness.
Strategic significance→ does the difference have an impact, can it influence managerial decision making . This refers to whether the observed difference or result is important enough to impact decision-making or strategic outcomes.
matetmatical
Can have a statistically difference result but not much of an impact
Statistical significance
P value: likelihood that the result happened by chance
0.05-0.1→ trend
<0.05→ significant
<0.01→ highly significant
<0.001→ highly significant
Its arbitrary, we just chose it as a good cutoff point
Theres a 4% chance that what you got is due to chance
Effect size: strength of the phenomenon
False negative: reated a vaccine thats effective but you are saying its not
False positive: you design a vaccine that is not effective but you are saying its effective
