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Null hypotheses
The rather convoluted thinking of null hypotheses is necessary if we are going to set (he scene For testing hypotheses using statistical tools. As noted in Chapter 1, theories survive and gain support as a result of not being disproved, rather than being proven conclusively. For sound theories, this docs not imply a licking bomb waiting to explode in the form of some researcher in the future proving it wrong. What it does suggest is that researchers are usually trying out components of a theory in different situations or with different groups; they are looking for the limits of applicability or refinements in detail. Hypotheses, as described nhove, express anticipated outcomes as predicted by a given theory or (he expected consequence of un application of principles to a situation, stated in more specific terms Minn those of a general research question.
When it comes to testing hypotheses, all that statistics can tell us is whether the outcomes we ultimately sec could have happened due to some causal relationship or simply by chance alone. In other words, the effect has to be big enough, whether it is the difference in average scores on some performance task for two groups, or the size of a correlation coefficient. The null hypothesis simply states that 'no significant difference' is expected between what wc obtain and what would happen by chance alone. If the difference observed is greater than some minimum, then it is considered significant and whatever has happened (probably) did not occur by chance alone. U is still up to the researcher to prove through sound design and data collection that nothing could have caused ihc observed effect other than what is described in the hypothesis.
So the next stage in refining our statement of hypotheses would be to try (O express them as null hypotheses related to the data that will be collected. As a consequence of a given study, several types of null hypothesis could be generated - for example, describing differences in scores or frequencies of events between the sample and the population (normative), or between two groups or among three or more groups - i.e., they actually belong to the same population, not to separate populations (experimental, quasi-experimental or ex post facto). The statements simply anticipate that any diffcrcncc(s) will be too small to be attributable to anything but chance.
Alternatively, if one were carrying out a correlational study, the null hypothesis of 'no significant correlation' anticipates correlations that will he so small that they could have happened by chance alone. To illustrate this, the hypotheses of Table 2.2 above are provided in Table 2.3 with corresponding possible null hypotheses.
The process of specifying a null hypothesis is one that focuses the attention on what will happen next, stating the implications of the proposed relationship among variables in IcrmH Ihut am be resolved by Statistical instruments (see Figure 2.14). At this stage, it is sometimes possible to identify potential difficulties in carrying out the research. For example, where arc we going to find the
CHAPTER 2   BEGINNING Tf IP DESIGN PROCESS
55
I l',|'i-lll.'..
.Null liypollicws
A random »ample of assembly-line workers in factories in Birmingham will be found to suffer a greater frequency of sleep interruptions, and a longer amount of time awake after going lo bed, tlum Ihe population as a whole.
One of ihice counselling approaches. A, B or C, will produce a greater reduction in frequency of return to drinking among Alcoholics.
It is expected that there will be a negative correlation between social class and drug use, and a negative correlation between educational achievement and drug use for a representative selection of 18—24-year-olds.
For a sample of identical twin boys who arc Ihc sons of alcoholic fathers anil fostered or adopted from infancy separately from each oilier, one to a family wilh ai least one alcoholic parent, one group will show a greater tendency towards alcoholism than the other.
In a given hospital, patients on 24-hour prescriptions will be expected to fee) more rested if they are awakened for medicines at times that follow RUM rather than just at equal lime intervals.
(Doth of tiro hypotheses assume that population dala exist.) The i e will be no significant difference between the mean number of limes per night lhal .isscmbly-linc workers in Birmingham awaken and the mean for the population of employed adults as a whole, or between the mean number of minutes that these workers are awake per night and that for the population of employed adults.
There will be no significant difference frequencies of'dry' and return drinkers across three equivalent scls of alcoholics participating in the three counselling approaches, A, H. C.
There will be no si^inlkaiil correlation twtween BOdal class and frequency of drug use. or between educational achievement and frequency of drug use for a random selection of 18-24-year-olds (i.e., any correlation will not differ from that which could be expected by chance alone).
There will be no significant difference in frequency of alcoholism between groups of separated iwiiu, all sons of alcoholics, when one twin goes lo a family with at Icasi one alcoholic parent und the other goes to a family with no alcoholic
parents.
There will 1« no significant dillcrciiec in the perception of feeling rested, as measured by the Bloggs Resledoess Scale completed by patients, between two groups: those whose medication was administered at regular lime intervals and (hose whose medication w;li administered at times close to times prescribed but following a period of REM.
sample of twins implied by Ihe fourth proposal in Table 2,3V Some of the more interesting questions generate very difficult scenarios for resolving them, compelling researchers to rethink the hypotheses resulting from a question. Obviously, it is better to consider such issues curly in the research process before too much is invested in an impossible task.
resting the null hypothesis
ľ'fľ normally (lisifibuinl Irails, tlio.se lliat produce sample means out in cilher of the (nils of » distribution or sampling mams «re liifhly unlikely. Social .science researchers commonly accept Mini evciHS which occur less frequently iliiin 5% ľl i lie lime tire unlikely lo have occurred by chance alone and eonsc-i|iiciilly mc considered slalislicnlly significant. To npply litis lo a normal distribution would mean that the 5% must be divided between llic lop ami Itic hollom (nils of llic (li.strilmljon, wild 2.5% For each ((here arc occasions when all 5% would occur in one tail, liul lhal is Ihe exception, lo be discussed later). Consulting Tabic B.I in Appendix B. lite lop 2.5% is Írom 47.5% onward, ot (interpolating) 1.96 standard deviations (SliMs) or mote from Ihe mean. The two ranges of sample means that would be considered statistically significant, and result in the rejection of Ihe null hypothesis since they probably did nol occur as par! of the natural chance variation in the means, arc shown shaded in Figure 13.8.
360
lUltNINi; »ATA INTO INľOKMATtON Mf.lN<''. SI'AIISIUľS
t'lCURE 13.8 Normal distribution of sample means with 5% significance
«lev ľ., where >> u the
population menu
H-ji«! n,
r)«nt„
Xniii|tlr Mr am
Thus for llic situation above involving ihe mean IQ of the sample of ll-ycar-olds. ihe null hypothesis »nd ihe siaicmcni of expected outcomes need an addition:
. . . mid. is Ihe probability thai the difference between the sample mean and the population mean would occur naturally more or less tlum 5% (Ihe chosen level of significance (hat will be used as the lest criteria)?
The CUl-ofF point of 1.96 standard deviations (SHM.s) would correspond to 1.96 x 2.5 = 4.9 points above or below the mean. Thus a sample mean IQ of less lhan 95.1 or greater than 104.9 would be considered significant and the sample nut representative 0f Ihe population. Therefore, in the example, Ihe group with a mean IQ of 106 would be considered siaiislically significant and the group nol typical, and it is unlikely thai they are a representative sample of ihe whole population, for IQ.
Some researchers present results that arc supported by an even lower level of probability, usually designated by (he Greek letter ri. lo support Ihcir argument, such as 1% (o = 0.01), 0.5% (a m 0.005), or even 0.1% (ft = 0.001). Two problems arise with such h practice. First, for llic lest to be legitimate, one school of thought says (he level of significance should he set before ihe lest (or even the study) is conducted. Remember thai the hypothesis is a statement of expectation, one that should include what will l>eexpccicd in terms of statistical outcome. H is not fair lo wrile Ihe rules after the game has begun. Second, there is a feeling that a lower significance level (hau 5% (/> < 0.05), such as 1% [p < 0.01), provides greater support for Ihe tesulU. In oilier words, if the probability of Ihe relationship existing is only I in 100. (hat must be a stronger Statement than if il were only I in 20. 'Ulis supposition will be challenged in Chapter 14 when the concept of the power »fa statistical test is introduced.