# Statistical Hypothesis Testing and Linear Regression

**Topics:**Statistical hypothesis testing, Regression analysis, Type I and type II errors

**Pages:**7 (1823 words)

**Published:**April 29, 2013

* samples and populations

* population – everyone in a specified target group rather than a specific region * sample – a selection of individuals from the population * sampling

* simple random sampling – identify all the people in the target population and then randomly select the number that you need for your research * extremely difficult, time-consuming, expensive * cluster sampling – identify clustering units in the population * opportunity sampling – selecting participants who just happen to be available at the time and the place that you are conducting your research * snowball sampling – referrals from participants * volunteer sampling – where you might advertise your study and wait for people who have read your ad to come forward to take part * how generalizable are data?

* Q: are the means for our sample approximately equal to the mean from the population? * randomly selected sample because of this random factor, sample may not be exactly representative * sampling error

* the difference between the sample mean and the population mean * ensure that you have enough participants so that you get an accurate reflection of the population that you are interested in * population mean (parameter), sample mean (statistic) * the larger the samples, the closer to the population parameter the statistics will be * probabilities

* the number possible outcomes that you are interested in divided by the total number of possible outcomes associated with an event * null hypothesis significance testing (NHST)

* the null hypothesis states that there is no effect in the population of interest * if the probability of obtaining the data is high, the null hypothesis is true * no effect in the population

* distribution

* normal distribution

* skewness

* the peak of the distribution is shifted away from the middle of the graph to either left or the right * bimodal distribution – two identifiable peaks

* often the participants drawn from two populations; you would try to identify the two different populations and analyze the data from each group separately * parametric tests

* making assumptions about the parameters of the underlying population * you need to ensure that your samples do not include any outliers or extreme scores * the standard normal distribution (SND)

* probability distribution

* subtract the mean from the score and divide by the std deviation * standardizing – converting a set of scores into z-scores * represented in std deviation units

* z-score of 0 is equal to the mean of the sample * the area beneath the curve between two points gives the probability of randomly selecting a score between those two points * calculating the p-value

* probability of obtaining our pattern of data if there were no difference between our groups * helps us to decide whether to accept or reject the null hypothesis * the probability is presented as a p-value

* tells us how likely it would be to obtain our pattern of data if the null hypothesis was true * one- and two- tailed hypothesis

* one tailed – the direction to the difference between the two groups is specified * one tailed is more sensitive and more likely to confirm an effect * type I and type II errors

* type I: when you reject the null hypothesis when it is in fact true * type II: where you fail to reject the null hypothesis when it is in fact false * statistical significance

* probability of obtaining the pattern of results

* p-value less than 0.05 > statistically significant result...

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