Testing Hypotheses I Lesson 9

Descriptive vs. Inferential Statistics n Descriptive l quantitative descriptions of characteristics n Inferential Statistics l Drawing conclusions about parameters ~

Hypothesis Testing n Hypothesis l testable assumption about a parameter l should conclusion be accepted? l final result a decision: YES or NO l qualitative not quantitative n General form of test statistic ~

Hypothesis Test: General Form

Evaluating Hypotheses Hypothesis: sample comes from this population

Two Hypotheses n Testable predictions n Alternative Hypothesis: H 1 u also scientific or experimental hypothesis l there is a difference between groups l Or there is an effect l Reflects researcher’s prediction n Null Hypothesis: H 0 l there is no difference between groups l Or there is no effect l This is hypothesis we test ~

Conclusions about Hypotheses n Cannot definitively “prove” or “disprove” n Logic of science built on “disproving” l easier than “proving” n State 2 mutually exclusive & exhaustive hypotheses l if one is true, other cannot be true n Testing H 0 l Assuming H 0 is true, what is probability we would obtain these data? ~

Hypothesis Test: Outcomes n Reject H o l accept H 1 as true u supported by data l statistical significance u difference greater than chance n Fail to reject l “Accepting” H o l data are inconclusive ~

Hypotheses & Directionality n Directionality affects decision criterion l Direction of change of DV n Nondirectional hypothesis l Does reading to young children affect IQ scores? n Directional hypothesis l Does reading to young children increase IQ scores? ~

Nondirectional Hypotheses n 2-tailed test l Similar to confidence interval l Stated in terms of parameter n Hypotheses H 1 :   100 H o :  = 100 n Do not know what effect will be l can reject H 0 if increase or decrease in IQ scores ~

Directional Hypotheses n 1- tailed test l predict that effect will be increase or decrease l Only predict one direction n Prediction of direction reflected in H 1 H 1 :  > 100 H o:  < 100 l Can only reject H 0 if change is in same direction H 1 predicts ~

Errors n “Accept” or reject H o l only probability we made correct decision l also probability made wrong decision Type I error (  ) l incorrectly rejecting H o l e.g., may think a new antidepressant is effective, when it is NOT ~

Errors Type II error (  ) l incorrectly “accepting” H o l e.g., may think a new antidepressant is not effective, when it really is n Do not know if we make error l Don’t know true population parameters n *ALWAYS some probability we are wrong l P(killed by lightning)  1/1,000,000 u p = l P(win powerball jackpot)  1/100,000,000 ~

Actual state of nature H 0 is true H 0 is false Decision Reject H 0 Correct Type I Error Type II Error Errors Accept H 0

Definitions & Symbols  l Level of significance l Probability of Type I error 1 -  l Level of confidence  l Probability of Type II error 1 -  l Power ~

Steps in Hypothesis Test 1.State null & alternative hypotheses 2.Set criterion for rejecting H 0 3.Collect sample; compute sample statistic & test statistic 4.Interpret results is outcome statistically significant? ~

Example: Nondirectional Test n Experimental question: Does reading to young children affect IQ scores?  = 100,  = 15, n = 25 n We will use z test l Same as computing z scores for ~

Step 1: State Hypotheses H 0 :  = 100 l Reading to young children will not affect IQ scores. H 1 :   100 l Reading to young children will affect IQ scores. ~

2. Set Criterion for Rejecting H 0 n Determine critical value of test statistic l defines critical region(s) n Critical region u also called rejection region l area of distribution beyond critical value u in tails n If test statistic falls in critical region Reject H 0 ~

2. Set Criterion for Rejecting H 0 Level of Significance (  ) l Specifies critical region u area in tail(s) n Defines low probability sample means Most common:  =.05 u others:.01,.001 n Critical value of z use z table for  level ~

Critical Regions f  =.05 z CV =

3. Collect data & compute statistics n Compute sample statistic n Observed value of test statistic n Need to calculate ~

3. Collect sample & compute statistics n = 25 :  105.5assume

Critical Regions f  =.05 z CV =

4. Interpret Results n Is z obs in the critical region? l NO l we fail to reject H 0 l These data suggest reading to young children does not affect IQ. n No “significant” difference l does not mean they are equal u data inconclusive ~