1) State Your Hypothesis

2) Set the Criteria for a Decision

3) Collect Data and Computer Sample Statistic

4) Make a Decision

The most important of the two hypothesis; states that the treatment has no effect.

H₀

Simply states the opposite of the null hypothesis; states that the treatment DOES have an effect

H₁

A specific probability value that represents the low-probability samples. Common ones are .05, .01 and .001. The values that fall within these alpha levels are considered in the CRITICAL REGION

Data located in this region reject the null hypothesis

α

Using the alpha level and a unit normal table you can determine where the critical regions are

x table, t table, f table

2 tail is divided by 2 (+/-) and 1 tail is not (+ or -)

Type I Error occurs when you reject the null hypothesis when in fact there isn't any treatment effect

Most dangerous type of error because you would move forward with a treatment that is ineffective

α level determines the probability of obtaining a Type I Error

Less serious than a Type I, occurs when a researcher fails to reject the null hypothesis when the treatment really does have an effect

Type II Errors do not have a specific measurable statistics but the probability of obtaining a Type II error is represented by β

Reject Null Hypothesis: z=(?), p<.05

Fail to Reject: z=(?, p>.05

1) The Size of the difference between the sample mean and the original population (the numerator of the z-score)

2) The variability of the scores, which is measured either by the standard deviation or the variance. Variability influence the standard error in the denominator

3) The number of scores in the sample. This value also influence the size of the standard error

1) Random Sampling: The sample must be representative of the population so it must be chosen at random

2) Independent Observation: The sample values must be independent of each other

3) The value of the standard deviation doesn't change

4) Normal Sampling Distribution: The unit normal table we use to find the critical regions can only be used with normal distributions

Notation includes a greater than/less than sign and the null hypothesis includes a greater than/less than and equal to symbol such as

H₁>μ

H₀≤μ

The alpha level is only found in a single tail

Also called a directional test because the researcher specifies which direction they expect the effect to occur

1) Hypothesized Population Parameter (null hypothesis)

2) Sample Statistic (M or μ)

3) Estimate of Error

4) The Alpha Level

1) Hypothesis testing is focused on data rather than on the hypothesis

2) Statistical significance does not provide any real information about the absolute size of a treatment effect

1) Systematic: there is a treatment effect and the sample mean probably comes from a distribution with a different population mean

2)Random: Sampling error - the sample mean is just different because its based on a sample and not the population

σ_{M= σ/√n or}

s^2/√n

Z score Hypothesis Notation

Two Tailed: H₁^: μ = X bar, H₂: μ ≠ X bar

n-1

The greater the value of df, the better the sample variance matches the population variance

This means that df of the sample variance describes how well t represents z

A t distribution will be flatter than a z distribution. why?

When calculating a z score, the denominator of the equation will be the same for every sample because we are using the population variance

With t scores the denominator varies because we have to use the sample variance which is different for every sample

As df increase, the t distribution begins to look more like a normal distribution or z distribution

1) The values in the sample must consist of independent observation

2)The population sample must be normal

x bar is expected to approximate µ

The standard error σ sub x bar measures how well a single sample mean approximates the population mean

We quantify our inferences by using a z score

the z score formula requires more info than is usually available

specifically

a z score requires that we know the VALUE OF THE POPULATION STANDARD DEVIATION σ or variance σ²

Use when two sets of data come from two completely separate samples

This type of statistic uses special notation using subscripts to identify each sample

H₀:  μ₁-μ₂=0

(Xbar₁-Xbar₂)-(μ₁-μ₂)/s_xbar1-xbar2

Where μ₁-μ_{2 always equals 0}

Actual difference between M1 and M2/Standard differene between M1 and M2 is H0 is true

which means that a big t score proves existance of a treatment effect

When the two samples are unequal (n1 does not equal n2)

Pooled variance is an UNBIASED statistic because it averages the two variances together, giving the correct amount of influence over the total

This is due to the fact that the larger sample has a large df value (this goes in the denominator of the equation) thus making the variance smaller and the calculation more accurate

estimated mean difference/standard deviation or

Xbar1-Xbar2/the square root of the pooled variance

The observations must be independent

the two populations the samples came from must have normal distributions

the two populations must have normal variances

Also known as homogeneity of variance

Measures if the Independent Measures T sample variances meet the homogeneity of variance assumption

F Max = s²largest/s²smallest

If the F Max is large than the variances are different, if it is close to one than the variances are similar and the assumption is reasonable

Find the critical value in teh table by using k and df and alpha in the F-max table

Uses two sets of data obtained from one sample of individuals ex: patients scores before therapy and after therapy

Good type of study design because it removes sigma or variance

Uses differences between scores rather than raw scores (Xbars)

There is only one sample of n individuals, they are simply measured twice

The sign of each D score tells you the direction of the change

μ_D is what we use to define the population

so H₀: μ_D= 0

1) Samples WITHIN each treatment must be independent

2)The population distribution of scores (D Values) must be normal

Advantage: Very Precise

Disadvantage: Little confidence that it is correct

1) When you reject the null hypothesis..rejecting the null hypothesis says you have an effect, estimation tells you how much effect

2) You already know something has an effect but want to see how much

3) You simply want to find out more information about an unknown population

1)% of confidence: the more confidence, the wider the interval

the less confidence the smaller the interval

2) A larger sample size (n) allows you to make a more precise estimate (narrower interval)

This is because n controls standard error so as n increases standard error decreases and the interval gets smaller

3)

Used to test hypothesis mean differences in situations with 2 or more treatments or populations

The main advantage of ANOVA over t tests is its ability to look at 2 OR MORE

ANOVA can be used with both independent and repeated sample designs

1) Systematic: The treatment does have an effect and thats why they're different

2) Unsystematic, random: Individual differences account for the difference

When we compute between treatment we are testing for systematic differences, when we test within we are checking for unsystematic

n is the number of scores in each treatment

N is the total number of scores

Source   SS  Df  MS    F

Between

Within

Xbar     Xbar-GM   Xbar-GM²

GM

Use the z formula when you have population paramaters

Use t when all you have is sample data

The power of a hypothesis test is =1-Beta (the probability of failing to reject H₀

This means the probability that the test will CORRECTLY reject the null hypothesis or the probability that it will result in a type II error

Power is usually calculted before a study is conducted to see if its worth while

Look at the expected treatmet effect and at that to mu to get what your sample mean should be. Calculate both distributions standard error

To know the exact power we have to determine what portion of the distribution is shaded and makes up the critical region

To find this simply multiply z(standard error)=some number

Add some number to the original mean then find where the new mean is located using the z score formula

Look up the z score and then find the correspond alpha level there is your power

As treatment effect goes down the power goes down as well,

As effect size increases, the probability of rejected null hypothesis also increases

1) Sample Size: Increasing sample size increases power

2)Alpha Level: Reducing the alpha level will reduce power

3)One tailed vs Two Tailed: changing from one tailed to two tailed test increases power