Hypothesis Testing

Experiment Vs. Natural Manipulation study Independent Variable and Dependent Variable Non-manipulated Independent Variable

Inferential Statistics Answers the question “Is the difference between conditions larger than would be expected due to chance?”. Null Hypothesis – no difference between conditions Alternative or Scientific Hypothesis – difference between conditions

Errors Reality Decision Made There is a difference There is no difference Reject Null Correct Type I Error Fail to reject Null Type II Error

Alpha Level: Risk we are will to take of making a Type I error. Analogous to reasonable doubt in a court of law.

Two tailed tests Using Alpha = .05, we allowing a 5% chance of making a Type I error. That error is located in the tails. When we are unsure which direction the difference between conditions might be (i.e., Singles happier or less happy than marrieds) we place half of our alpha in one tail the other half in the other tail.

Distribution of Sample Means If we took repeated samples of size N, the mean of those samples would be the mean of the parameter and the distribution would be a approximate a normal curve (i.e., error is normally distributed).

Standard Error of the Mean ( ) 𝑠 𝑥 Can be estimated for any population from the sample standard deviation. The higher the sample size (n) the lower the 𝑠 𝑥 Used as the denominator of the t-Test. 𝑠 𝑥

T-test Answers the question – How likely is it that two samples are members of the same population? We use an estimate of the sampling distribution for one condition (e.g., married) as our control. We look at the difference in the mean of the second condition (Singles) to determine if it falls far enough out on the tails of the sampling distribution that we would have to conclude that it is unlikely to be a sample taken from the control population.

Measured in Standard Error of the Means The t-Test. Mean of Single condition Mean of Married T- score tells us how many 𝑠 𝑥 the two means differ from each other on the curve representing the distribution of means. We can determine what the probability of obtaining the mean that we did for the single condition, assuming it is just a member of the same population as the Married condition. 6 5 4 3 2 1 0 1 2 3 4 5 6 Measured in Standard Error of the Means

Measured in Standard Error of the Means The t-Test. 𝑡= 𝑥 𝑀 − 𝑥 𝑠 𝑠 𝑥 Mean of Single condition Mean of Married 6.65−5.40 0.27 Observed T = 4.63 Compare this value to the critical t from the t-table. If t observed is > critical t, we reject the null and conclude that there is a statistically significant difference between the two conditions. 6 5 4 3 2 1 0 1 2 3 4 5 6 Measured in Standard Error of the Means

Solution Observed T = 4.63 Degrees of freedom = (20 + 20) – 2 = 48 Critical T = 2.01 Observed t > critical t therefor we reject the null hypothesis and conclude that married persons in Grant county are happier than single persons.