stats exam 2 vocab

what is central limit theorem

tells us if the population has a given mean and standard deviation; standard deviation of sampling distribution gets smaller as the same size increases

what is the law of large numbers

as sample size increases, the probability of a sample mean is an accurate representation of population mean as it increases; larger sample sizes are more accurate 

what is a distribution of sample means 

means from many samples of a same size put together 

what is an observed effect 

what is observed in a sample mean vs what we expected based on the population from which that sample was calculated 

what is standard error

the spread of sampling distribution and how likely sample mean is to differ from population, influenced by the sample size and variability of the data

what is probability

likelihood that an event or different types of events will happen

what is frequentism

long term view of probability, used by defining the null hypothesis and calculating the p-value 

what are sample statistics

things you can calculate from your data set, like the mean and SD

what is population mean

the average of all values in a population

what is sampling distribution of the mean 

the distribution of all possible means from a population - the mean of the sample mean is the same as the mean of the population 

what determines the shape of a sampling distribution

the population distribution and the sample size

what is a p-value

the probability of obtaining results at least as extreme as the observed data, assuming the null hypothesis is true

what does .05 determine

the significance level, 5% chance of making a type I error 

what is a critical value

is the threshold at which you can reject the null hypothesis - the specific value from the test statistics distribution that marks the boundary of the rejection region

what is null hypothesis testing

there is no statistical difference or relationship between variables being studied, assumed to be true unless proven otherwise by rejecting an opposite condition

what is an alternate/research hypothesis 

there is a relationship between the variables or difference between groups 

what qualifies for rejecting a null hypothesis

results are statistically significant, p-value is less than .05 which suggests probability of data is extreme and results are within critical regions

what qualifies for failing to reject a null hypothesis

results are not statistically significant and our p-value is greater than .05 which suggests probability of value is not extreme and results are outside critical regions

what is statistical significance 

results have meaning and did not occur due to chance, typically occurs when we reject null hypothesis 

type 1 non-directional alternate hypothesis 

reflects a difference between groups, but direction is not specified - does not specify which group will be higher/lower on a measure 

type 2 directional research hypothesis

direction of difference is specified - participants who take the program will have lower stress levels than participants who don’t take the program

type I error

false positive where you conclude the is a significant effect in results when there is not - ESP exists when it actually does not

type II error 

false negative where you conclude there is no effect or difference in results when there is one - ESP does not exist when it does

what is the power of test 

probability of correctly rejecting the null hypothesis if it is false, small sample sizes lack power 

what are degrees of freedom

used to estimate population parameter, the number of scores in the final calculation of a statistic that are free to vary

what does cohens d tell us

the measure of effect size that quantifies the difference between two groups means expressed in terms of standard deviation

what is a population parameter

numerical value that describes the characteristic of an entire population, like mean of the population

what is a point estimate 

a single value used to approximate an unknown population parameter 

what is a confidence interval

starts with point estimate and creates a range of scores considered plausible based on SD, sample size, and level of confidence we want to use to estimate population parameter

what is margin of error

quantifies uncertainty in a sample statistic providing a range around a result where the true population value is likely to be found

what is a difference score 

subtracting one variable score from another, used to measure change over time or agreement between paired individuals 

what are matched pairs

analyzing data from paired samples where subjects are matched based on shared characteristics, and then one member of each pair is assigned to a treatment group while the other is in the control group

what are related pairs

the analysis of two scores that are related in a systematic way within people or within pairs - before vs after results

what is an unbiased estimator 

average value of a statistic value over many repeated samples is exactly equal to the true population parameters its estimating 

what is a biased estimator

average value is not equal to the true parameter, resulting in a systematic over or under estimation

what is group mean differences

measures the distance between the average values of two or more distinct groups

what are independent samples 

when there is no logical or meaningful way to link individuals across groups or if there is no overlap between groups 

what is pooled variance

the combined estimate of variance using information from each independent sample

what is variance

a measure of how spread a set of data is from the mean

what is homogeneity of variance 

true population variance for each group is the same and any difference in the observed sample variances is due to random chance 

what is a one sample z-test used for 

to test if a sample mean is significantly different from a known population mean, large sample size and SD is known

• a company claims its smartphones have am average battery life of 12 hours 

what is a one sample t-test used for

when comparing one sample to the population, such as the sample mean to the pop. mean, SD unknown

• center thinks the students have anxiety levels that are different from the population of college students

what is an independent samples t-test

used to compare the mean of two independent groups

• examine whether stress levels are higher among parents than non-parents

what is a paired samples (related samples) t-test

compares the mean of the same group at two different points in time, like before and after an event 

• comparing exam scores before vs after drinking caffeine