Research-hypothesis testing

Choosing to use z or t depends on

-Hypothesis -Distribution of the target population -Sample size -Other sample characteristics. If the researcher hypothesizes a difference between sample means and size is < 30 then use the t statistic

steps of hypothesis

1.State hypothesis 2.Set level of risk 3.Choose sample size 4.Determine critical value 5.Compute test statistic 6.Reject or accept the hypothesis

step 4: determining the critical value

Hypothesis testing requires a cutoff point that can be used to separate sample results that should lead to rejecting the null, from results that should lead to accepting the alternative hypothesis

power

Power is defined as the probability of rejecting the null when it is false (a correct decision). Sample size is a factor that influences the power of the statistical test.

type 2 error

The probability of a Type II error is designated by the Greek letter β (beta).

hypothesis testing

a binary decision-making process •Hypothesis either • (1) accepted or •(2) rejected based on statistical tests

hypothesis

statement that describes the proposed relationship between two or more variables.

Null (H0) hypothesis

states opposite of what is expected. In other words, an accused is presumed innocent until proven guilty, this is the null!

Alternative (H1 or Ha) hypothesis

states the expected result of the research

step 1:state your hypothesis

your educated guess on what you believe the outcome will be.

step 6: decision

•After calculating test statistic, compare it to the critical value. •If test statistic exceeds the critical value reject the null •If test statistic does not exceed the critical value accept the null

process of the hypothesis

•Begins with a statement of hypothesis and ends with the decision to accept or reject the hypothesis

two major classes of stats:

•Descriptive stats - describe data without inferring anything about the population •Inferential stats - make conclusions about populations from sample data

step 2: Set an acceptable level of risk:

•Four possible outcomes when testing a research hypothesis: •Accept H0 when it is true (correct decision) •Reject H0 when it is false (correct decision) •Reject Ho when it is true (Type I error) •Accept Ho when it is false (Type II error)

To make reliable decisions about research , two opposing views must be considered:

•Null hypothesis •Alternative hypothesis

step 3: choose sample size

•Sample size (n) determines: • probability distribution to be used •Power of the test For example, z statistic (standard normal distribution) requires relatively large sample (n>30). However, the t statistic is appropriate for relatively smaller samples (n <30) •A larger sample usually results in a more powerful test of the Ho. •Conclusions drawn from studies with small samples such as n <10 are at high risk for accepting the Ho when it is false (Type II error)

step 5: computing test statistics

•This is a standard score of z or t statistic •These indicate the number of standard errors or standard deviations from the hypothesized mean

type 1 error

•Type I error considered more serious of two possible errors. •In medical research Type I error can have serious consequences for human life •Consequently alpha (α) is conventionally set at the conservative level of .05 or less. Alpha equal to .05 this means the researcher is willing to risk a Type I error 5/100 or 5% times. If alpha is .01 what is he/she willing to risk?

two types of alternative

•one-tailed (directional) for example researcher might hypothesize that treatment A is better than treatment B •Two-tailed (nondirectional). This does not predict direction for example a researcher might hypothesize that A is different from B