PSY 410 hypothesis testing

empirical research

Empirical research is a way of gaining knowledge by means of direct and indirect observation or experience; usually to test a question or a hypothesis

completely randomized design & randomness

A completely randomized design is probably the simplest experimental design, in terms of data analysis and convenience. With this design, subjects are randomly assigned to treatments.
A completely randomized design relies on randomization to control for t

sample

a subset of a population- Samples are collected and statistics are calculated from the samples so that one can make inferences or extrapolations from the sample to the population.
A complete sample is a set of objects from a parent population that include

statistic

A fact or piece of data from a study of a large quantity of numerical data. (the sample parameter)

hypothesis

precise, testable prediction

parameter

A parameter is a value, usually unknown (and which therefore has to be estimated), used to represent a certain population characteristic. For example, the population mean is a parameter that is often used to indicate the average value of a quantity.
Withi

correlation coefficient

A correlation coefficient is a number between -1 and 1 which measures the degree to which two variables are linearly related. If there is perfect linear relationship with positive slope between the two variables, we have a correlation coefficient of 1; if

type I error

In a hypothesis test, a type I error occurs when the null hypothesis is rejected when it is in fact true; that is, H0 is wrongly rejected.
For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on aver

type II error

in a hypothesis test, a type II error occurs when the null hypothesis H0, is not rejected when it is in fact false. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current d

null hypothesis

The null hypothesis, H0, represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved. For example, in a clinical trial of a new drug, the null hypothe

mean

The sample mean is an estimator available for estimating the population mean . It is a measure of location, commonly called the average, often symbolised
Its value depends equally on all of the data which may include outliers. It may not appear representa

factorial design

A factorial design is used to evaluate two or more factors simultaneously. The treatments are combinations of levels of the factors. The advantages of factorial designs over one-factor-at-a-time experiments is that they are more efficient and they allow i

between-subjects design

each participant appears in only one level of the design (ie. half would respond to light and half would respond to sound; right handed vs. left handed)
*usually any individual characteristic will be between subjects : sex, gender, ethnicity, eye color, e

central limit theorem

The Central Limit Theorem states that whenever a random sample of size n is taken from any distribution with mean � and variance , then the sample mean will be approximately normally distributed with mean � and variance /n. The larger the value of the sam

one-tailed test

A one-sided test is a statistical hypothesis test in which the values for which we can reject the null hypothesis, H0 are located entirely in one tail of the probability distribution.
In other words, the critical region for a one-sided test is the set of

two-tailed test

A two-sided test is a statistical hypothesis test in which the values for which we can reject the null hypothesis, H0 are located in both tails of the probability distribution.
In other words, the critical region for a two-sided test is the set of values

alpha

.

p (probability)

The probability value (p-value) of a statistical hypothesis test is the probability of getting a value of the test statistic as extreme as or more extreme than that observed by chance alone, if the null hypothesis H0, is true.
It is the probability of wro

levels of variables

the IV has a minimum of two levels, the maximum is infinite.
ex. performance vs. anxiety linear relationship is an example of where 3 levels to show U shaped curve instead of a positive or negative slope /

mode

The mode is the most frequently occurring value in a set of discrete data. There can be more than one mode if two or more values are equally common.

normal distribution

Normal distributions model (some) continuous random variables. Strictly, a Normal random variable should be capable of assuming any value on the real line, though this requirement is often waived in practice. For example, height at a given age for a given

population

all of these subjects in who you are interested in (population is infinitely large)
A population is any entire collection of people, animals, plants or things from which we may collect data. It is the entire group we are interested in, which we wish to de

power

The power of a statistical hypothesis test measures the test's ability to reject the null hypothesis when it is actually false - that is, to make a correct decision.
In other words, the power of a hypothesis test is the probability of not committing a typ

significance level

The significance level of a statistical hypothesis test is a fixed probability of wrongly rejecting the null hypothesis H0, if it is in fact true.
It is the probability of a type I error and is set by the investigator in relation to the consequences of su

standard deviation

Standard deviation is a measure of the spread or dispersion of a set of data.
It is calculated by taking the square root of the variance and is symbolised by s.d, or s. In other words
The more widely the values are spread out, the larger the standard devi

independent variables (2 types)

1. qualitative - categorical data ; male/female, where you put the IV on the x axis is arbitrary
2. quantitative - consecutive amounts ; drug dosage, IQ, age - from ascending value on the x axis (position on x axis matters according to ascending values)

dependent variables (2 types)

1. frequency - the number of times an event occurs or does not occur (ie. the number of times horses win from the outside starting position vs. the inside position)
2. score data - can fall anywhere on a continuum (ie. IQ, room temperature, reaction time)

within subjects variable (repeated measures)

independent variable where a subject appears in more than one or more conditions
-when you use a within design you double the data, but you have to counter balance the order of conditions
-ex. if one subject gets the light then sound the counter would be

mixed design

design that has atleast one between variable and one within variable (very common)
-ex. can exercise raise self esteem --> can use between subject (exercise vs. non exercise group) but a better design would be pre and post exercise compared to a control

2 major kinds of research

1. applied research - you care about the outcome (one method is better outcome then another method)
2. theoretical research - what theory explains what is happening (more intellectual)

If we use alpha = 0.05

when there really is not a difference, 5% of the time we will say there is a real difference

Best illustration of a null hypothesis

the means of all these populations are all 100

When alpha = 0.05, the probability for a type I error is?

0.05

if the null hypothesis is true..

the probability of a Type II error is 0

If you decide to use an alpha level of 5% rather than 1%, will you need a smaller or larger difference between your sample means in order to reject the null hypothesis?

smaller

When you conduct a research study, most of the time you will?

make a correct decision, however most common error is type II

If you shift your alpha level from 5% to 1%, you increase the probability of making a

type II error

the null can be rejected with absolute certainty

never, there is no absolute certainty, just probability

the probability of making a type I error when the null is true is

alpha

if the null is true, variation between sample means must be due to

chance and individual differences